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GENERAL CHEMISTRY
For first years of Faculties of Science,
Medicine and Pharmacy
Part 1
Prepared by:
٢
Prof. Dr. Talaat I. El-Emary
Prof. of Organic Chemistry
Chemistry Deaprtment
Faculty of Science
Assiut University
Assiut, Egypt
٣
CREDIT TEXT BOOKS
1. GENERAL CHEMISTRY, Principle& Structure
Fifth Edition, by JAMES E. BRADY
2. GENERAL CHEMISTRY, by Whitten and Gailey
3. GENERAL COLLEGE CHEMISTRY,
Further Reading List:
(1) GENERAL CHEMISTRY, by Ebbing DD
(2) GENERAL CHEMISTRY, by Hill J. et al
٤
CHAPTER 1
MATTER AND ENERGY
Matter is anything has mass and occupies space. Mass is a measure of the
quantity of matter in a sample of any material.
Energy: is most commonly defined to be the capacity to do work. We are
all familiar with many forms of energy is every energy life, including mechanical
energy, electrical energy, heat energy, and light energy. Energy can be classified
into two principal types. Potential energy and kinetic energy.
Potential energy: is the energy that an object or sample of material
possesses because of its position or composition.
kinetic energy: is the capacity of doing work directly, and is easily
transferred between objects.
Chemical reactions are either exothermic reactions or endothermic ones.
Exothermic reaction: is that type of reaction in which energy is released
to the surrounding, usually as heat
Endothermic reaction: is that type of reaction in which energy is
absorbed from the surrounding.
The Law of Conservation of Matter: There is no observable change in
the quantity of matter during ordinary chemical reaction.
The Law of Conservation of Energy: Energy cannot be created or
destroyed, it may only be converted from one form to another.
The Law of Conservation of Matter and Energy
٥
The relationship between matter and energy is given by Albert Einstein's
equation:
E = mc2
Were, m is the mass of matter, and c is the velocity of light.
States of matter
Matter is conveniently classified into three states, solid state, liquid state and
gaseous state.
In the solid state, the substances are rigid and have definite shapes, and the
volumes do not vary much with changes in temperature and pressures.
In the liquid state: the substances are not rigid and have no definite shapes, it
takes the shape of the container in which it is placed in, and the volumes vary
with changes in temperature and slightly compressed with pressures.
In the gaseous state : the substances are not rigid and have no definite shapes
and volume, it fills and takes the shape of the container in which it is placed in,
and the volumes vary much with changes in temperature and compressed with
pressures.
Chemical and physical properties:
Chemical properties: are properties that matter exhibits as it undergoes
changes in chemical composition.
Physical properties: are properties that can be observed in the absence of
any chemical reaction. Color, density, hardness, melting point, boiling point, and
electrical and thermal conductivities are physical properties.
Chemical and physical changes
Both chemical and physical changes are always accompanied by either the
absorption or liberation of energy. Energy is required to melt ice, and energy is
required to boil water. Conversely, the condensation of steam to form liquid water
always liberates energy, as does the freezing of liquid water to form ice.
٦
MEASURMENTS IN CHEMISTRY
The International System of Units (SI) is based on the seven fundamental units
listed in table 1-1 & 1-2 & 1-3 and all other units of measurements are derived
from these.
Table 1-1
THE SEVEN BASIC UNITS OF MEASURMENT
Physical property Name of Unit Abbrevation
Length Meter m
Mass kilogram Kg
Time Second s
Electric current Ampere A
Temperature Kelvin K
Luminous
intensity
Candela Cd
Quantity of
substance
Mole mol
M
.
P
. =
0
O
C
B
.
P
=
10
0
O
C
٧
The distances and masses in metric system illustrate the use of some common
prefixes and the relationships among them are listed in table 1-2 &1-3.
Table 1-2. The sixteen SI prefixes
Prefix Symbol Factor Prefix Symbol Factor
exa E 10
18
deci d 10
-
1
peta P 10
15
centi c 10
-
2
tetra T 10
12
milli m 10
-
3
giga G 10
9
micro µ 10
-
6
mega M 10
6
nano n 10
-
9
kilo k 10
3
pico p 10
-
12
hecta h 10
2
femto f 10
-
15
deca da 10
1
atto a 10
-
18
Table 1-3
COMMON PREFIXES USED IN THE METRIC
SYSTEM
Prefix Abbreviation
Measuring Example
mega M 10
6
1 megameter(Mm) =
1 x 106 m
kilo k 10
3
1 kilometer (km) = 1
x 103 m
dec- d 10
-
1
1 decimeter (dm)=
0.1 m
centi- c 10
-
2
1 centimeter (cm) =
0.01 m
micro- µ 10
-
6
1 microgram (µg)= 1
x 10-6g
nano- n 10
-
9
1 nanogram (ng) = 1
x 10-9g
pico- p 10
-
12
1 picogram (pg) = 1
x 10-12g
Mass and Weight
The basic unit of mass in the SI system is kilogram is shown in
table 1-4. one kilogram weight 2.205 pounds, and a one-pound object has a
mass of 0.4536 kilogram.
٨
Table 1-4
SI UNITS OF MASS
Kilogram Base unit
Gram, g 1000 g = 1 kg
Milligram, mg 1000 mg = 1 g
Microgram, µg 1 million µg = 1 g
Table 1-5 illustrate conversion factors relating length, volume and mass units
Table 1-5
CONVERSION FACTORS RELATING LENGTH, VOLUME
AND MASS UNITS
Metric English Metric-English
Equivlents
Length
1 km = 10
3
m
1 cm = 10
-
2
m
1 mm = 10
-
3
m
1 nm = 10
-
9
m
1 A
0
= 10
-
8
cm
1 ft = 12 in
1 yd = 3 ft
1 mile = 5280 ft
1 in
= 2.54 cm
1 m
= 39.37 in
1 mile
= 1.609 km
Volume
1 mL
= 1 cm
-
3
=
10-3liter
1 m
3
= 10
6
cm
= 103 liter
1 gal = 4 qt = 8 pt
1 qt = 57.75 in
3
1 liter = 1.057 qt
1 ft
3
= 28.32 liter
Mass
1 kg = 10
3
g
1 mg = 10
-
3
g
1 metric tone = 10
3
kg
1b = 16 oz
1 short
ton
= 2000 1b
1b = 453.6 g
1 g = 0.03527 oz
1
metric
tone
= 1.102 short
ton
ft: foot, 1 yd, pt: pint, qt: quart
Dimensional analysis
Unit factor method
Unit factor may be constructed from any two terms that describe the same amount
of whatever we my consider. For example, 1 foot is equal to exactly 12 inches, by
definition, and we may write an equation to describe this equality:
٩
1 ft = 12 in
Dividing of both sides of the equation by 1 ft gives
ft1
in12
ft1
ft1
or
ft
1
12
1
We can write numerous unit factors, such as
ton1
1b 2000
,
gal 1
qt4
,
ft 5280
mile1
,
in36
yd1
,
ft3
yd1
Conversion from decimal to exponential
In scientific (exponential) notation, we place one nonzero digit to the left of the
decimal as in the following examples
4,3 0 0 ,000. = 4.3 x 10 6
6 is places to the left, therefore, exponent of 10 is 6
0.00 0 3 4 8 = 3 .4 8 x 1 0 -4
4 is places to the right, therefore, exponent of 10 is -4
CONVERSIONS AMONG` SI` UNITS
Example 1.1: A desk is found be 1437 mm wide. What is this
width expressed in meters?
Solution:
14 3 7 mm = 14 3 7 x 1 0 -3 m
١٠
14 3 7 mm = 1 4 3 7 x 1 0 -3 m
x 10 - 3
Example 1.2: A certain person is 172 cm tall. Express this
height in decimeter.
Solution: As a beginning let's relate the problem in the form of an
equation.
172 cm = ? dm
We can write the following relationships
1 cm = 10-2 m
1dm = 10-1 m
We can construct the following two conversion factors:
cm
1
m 01
and
m
10
cm 1 -2
2-
If we multiply our given 172 cm by the second factor, the units cm will cancel
and we will have converted centimeters to meters.
m 1.72
cm 1
m 10
x cm 172
-2
Similarly, we use the second equation to convert meters to
decimeters.
dm 17.2
m 0 1
dm 1
x m 72.1 1-
We can also " string together" conversion factors and obtain the same net
result.
١١
dm 17.2
m 0 1
dm 1
x
cm 1
m 10
x cm 172 1-
-2
t o m e te r
to d ec im e ter
Example 1.3: Calculate the number of cubic centimeter in 0.225
dm3.
Solution:
0.225 dm3 = ? cm3
1 dm = 10-1 m
1 cm = 10-2 m
(1 dm)3 = (10-1 m)3
1 dm3 = 10-3 m3
(1 cm)3 = (10-2 m)3
1 cm3 = 10-6 m3
3
3 6-
3
3
3-3
3cm 255
m 0 1
cm 1
x
dm 1
m 10
x dm 225.0
Example 1.4: How many millimeter are in 1.39 x 104 meters?
Solution:
mm 10 x 1.39
m
1
mm0001
xm 10 x 1.39mm ? 74
Example 1.5: A sample of gold weigh 0.234 mg. what is its weight
in g? in cg?
١٢
Solution:
g 10 x 2.34
mg 0001
g1
xmg 0.234g ? 4
cg 10 x 2.34or cg 0.0234
mg 01
cg1
xmg 0.234cg ? 2-
Example 1.6: How many square decimeters are there in 215
square centimeters?
Solution:
2222 dm 2.15 )
cm
0
1
dm1
x(cm 215dm ?
Example 1.7: How many cubic centimeters are there in 8.34 x 105
cubic decimeters?
Solution:
28222 cm 10 x 8.34 )
dm
1
cm01
( x dm 105 x 8.34cm 1 ?
Example 1.8: A common unit of energy is the erg. Convert 3.74 x
10-2 erg to the SI units of energy, joules and kilojoules. One erg is
exactly 1 x 10-7 joule.
Solution:
kj 10 x 3.74
J
kj 10 x 1
x J 10 x 3.74
J 10 x 3.74
erg 1
J10 1
x erg 10 x 3.74
12-
-3
-9
-9
-7
2-
x
Example 1.9: Express 1.0 mL in gallons.
Solution: 1 quart (qt) = 0.9463 liter, 1 liter = 1.056 quarts (qt)
١٣
gal 10 x 2.7
qt 4
gal 1
x
L 1
qt .061
x
mL 1000
L 1
x mL 1.0gal ? 4-
Density and specific gravity
The density of a substance is defined as the mass per unit volume.
V
M
Dor
volume
mass
density
Densities may be used to distinguish between two substances or to assist in
identifying a particular substance. They are usually expressed as g/cm3 or g/mL
for liquids and solids, and as g / L for gases. These units can also be expressed as
g cm-3, g mL-1, respectively.
Density is constant for a given substance at a given temperature. It is also
an intensive property, that is, a property that does not depend on the amount of
material examined. Both mass and volume are extensive properties, in that they
depend on the amount of material in the sample. Obviously, the volume occupied
by two kilogram of lead is twice that of one kilogram of lead, but both samples
have the same density. Table 1- 5 illustrate the densities of some common
substances.
Substance Density, g/mL
Hydrogen (gas) 0.000089
Carbon dioxide (gas) 0.0019
Cork 0.21
Oak wood 0.71
Ethyl alcohol 0.79
Water 1.00
Magnesium 1.74
Table salt 2.16
Sand 2.32
Aluminum 2.70
Iron 7.86
Copper 8.92
Lead 11.34
Mercury 13.59
Gold 19.3
١٤
Example 1-7: A 47.3 mL sample of liquid weighs 53.74 g. What is
its density?
Solution:
g/mL 1.14
mL
47.3
g 53.74
V
M
D
Example 1-8: If 100 g of the liquid described in example 1-7 is
needed for a chemical reaction, what volume of liquid would you
use?
Solution:
mL 87.7
g/mL 1.14
g 100
D
M
V so ,
V
M
D
The specific gravity of a substance is the ratio of its density to the density of
water.
D
D
Gr. Sp.
Water
Substance
The density of water is 1.000 g/ml at 3.980C, the temperature at which the density
of water is greatest. However, variation in the density of water with changes in
temperature are small enough that we may use 1.00 g/mL up to 250C without
introducing significant errors into our calculations.
Specific gravities are dimensionless numbers, as the following example
demonstrates.
Example 1-9: The density of table salt is 2.16 g/mL at 200C. What
is its specific gravity?
2.16
mLg/ 1.00
mLg/ 2.16
D
D
Gr. Sp.
Water
Salt
١٥
Example 1-10: Battery acid is 40.0% sulfuric acid H2SO4, and
60% water by weight. Its specific gravity is 1.31. Calculate the
weight of pure sulfuric acid, H2SO4, in 100 ml of battery acid.
Solution:
We may write
Density = 1.31 g /mL
The solution is 40.0% H2SO4 and 60% H2O by weight. From this information we
may construct the desired unit factor.
soln. g 100
SOH g 40.0
42
We can now solve the problem:
SOH g 52.4
soln 100g
SOH g 40.0
X
soln mL 1
soln g 1.31
Xsoln mL 100 SOH ? 42
42
42
We first used the density as a unit factor to convert the given volume of solution
to mass of solution, and then used the percentage by weight to convert the mass of
solution to mass of acid.
Heat and temperature
Heat is one form of energy. Temperature measures the intensity of heat,
the "hotness" or "coldness" of a body. Heat always flows from a hotter to a colder
body-never in the reverse direction.
Temperatures are commonly measured with mercury-in-glass
thermometers. As mercury expands in the reservoir, its movement up into the thin
column is clearly visible.
Anders Celsius, a Swedish astronomer, developed the Celsius
temperature scale formally called the centigrade temperature scale.
Temperature are frequently measured in the united state on the
temperature scale devised by Gabriel Fahrenheit, a German instrument
maker. On this scale the freezing and boiling points of water are defined as 32 0F
and 212 0F, respectively.
In scientific work, temperature are expressed on the Kelvin (absolute)
temperature scale.
Relationships among the three scales illustrated in the following figure.
Every Kelvin temperature is 273.150 above the corresponding Celsius
temperature. Thus the relationship between the two scales is simply
١٦
K 1.0
C1.0
K) 273.15 -(xK C OR
C1.0
K 1.0
C)273.15 C x( K
0
0
0
00
W at e r
f r e ez e s
W a te r b o lis
(a t n o rm a l
a tm o sp h e r i c
p r es s u re )
1000
3 2 0F00C2 73 .1 5 0K
2120F 10 0 0C3730K
F a h r e n h e it C e l s iu s
(c en t ig r a d e )
K el v i n
1000
1800
We can construct the unit factors
F
1.8
C1.0
and
C
1.0
F 1.8
0
0
0
0
F32 )
C
1.0
F 1.8
X C x( F ? 0
0
0
00
) F32- F x(
F
1.8
C 1.0
C ? 00
0
0
0
Example : When the temperature reaches "100 0F) in the shade," it's hot. What is
this temperature on the Celsius scale?
١٧
) F32- F 100 (
F1.8
C 1.0
C ? 00
0
0
0
C38 ) F32- F 100 (
F1.8
C 1.0
C ? 000
0
0
0
Example : When the absolute temperature is " 400 K). What is Fahrenheit?
C127
K
1.0
C1.0
K) 273-K (400 C ? 0
0
0
F261F32
C1.0
F1.8
X C127 C ? 00
0
0
00
Another expressions for the relationships among the three scales
of temperature.
32] [t
9
5
t F)(C)( o0
273.15 t t C)(
(k) o
(1.8) C)( 32 F 00
SIGNIFICANT FIGURES, EXACT, PRECISE AND
ACCURATE
Significant figures are digits believed to be correct by the person who makes a
measurements. We assume that the person is competent to use the measuring
device. Suppose one measures a distance with a meter stick and reports the
distance as 343.5 mm. what does this number mean?. In this person's judgment,
the distance is greater than 343.3 mm but less than 343.7 mm, and the best
estimate is 343.5 mm. The 343.5 mm contains four significant figures-the last
digit, 5, represents a best estimate and therefore doubtful, but it is considered to
be a significant figure. In reporting numbers obtained from measurements, we
report one estimated digit, and no more. Since the person making the
measurement is not certain that the 5 is correct, clearly it would be silly,
meaningless, and wrong to report the distance as 343.53 mm.
١٨
Strictly speaking, the distance should be reported as 343.5 ± 0.2 mm
because it is difficult to estimate distances less than 0.2 mm on an ordinary meter
stick.
The term exact is used for quantities that have an infinite number of significant
figures. For example, by definition there are exactly 1,000 cubic centimeters in 1
liter. We could write that there are 1,000.00000000….. cubic centimeters in
1.00000000…. liter, with no limit to the number of zeros. For example, the inch is
defined as exactly 254 x 10-2 meter, or 254 centimeters. Exact quantities either are
defined arbitrarily or result from counting objects one by one; no measured
quantities, other than by simple counting, are exact.
Exact = طﻮﺒﻀﻣﻖﯿﻗد ،
The term precise refers to how reproducible measurements of the same
quantity are. Suppose that two calibrated 250 cm3 beakers are each tested three
times to determine their volumes. Beaker A is found to have volumes of 248, 249,
and 247 cm3. The set of values for beaker A is more precise, varying only ± 1
from the average value of 248 cm3.
ﻖﻗﺪﻣ ،ﺢﯿﺤﺻ
The term accurate ( ﺢﯿﺤﺻ) refers to how closely a measured value is a
true or accepted value. In the case of the two beakers, beaker B, with an average
volume of 249 cm3, is closer to the calibrated value of 250 cm3. For most
experimental measurements a true value is not known, so the accuracy cannot be
determent. The accuracy is commonly expressed in terms of the error or the
percent error. Error is defined as the difference between a measured value and
true (or most probable)value. In the case of beaker A, the error between the
average of the three measurements and the calibrated value is
250 cm3 – 248 cm3 = 2 cm3
The error is a positive quantity whether the measured value is higher or lower
than the true (or most probable) value. The percent error is
100 x
valueprobable)most (or true
error
error %
% 0.8 100 x
cm
250
cm 2
error % 3
3
Scientific notation and significant figures
For instance, a measured length of 23.6 cm obviously contains three significant
figures, and a measured length of 1.203 cm has four. But how about the numbers
0.00215 m and 12.30 m?. Do the zeros in these measured value count as
significant figures?
The general rule is that a zero does not count as significant figures if its
function is merely to locate the position of the decimal point. For example,
consider the measured value 0.00215 m. Without the zero to the left of the 2, we
wouldn't know where the decimal point belongs and we wouldn't know how large
١٩
the measurement is. Now, notice what happens to these zeros when we rewrite the
number in scientific notation.
0.00215 m = 2.15 x 10-3 m
We see that the zeros disappear; their function was just to locate the decimal point
and they are really not measured digits. A rule that we can apply, therefore, is that
zeros that lie to the left of the first nonzero digit are not counted as significant
figures.
How about the zero in the measured value 12.30 m? This zero is counted
as a significant figures because it would not have been written unless the digit had
been estimated to be a zero. Also note that this zero does not disappear when the
number is written in scientific notation.
12.30 m = 1.230 x 101 m
This leads to another general statement: in a measured quantity, a zero that lies to
the right of the decimal point and also to the right of the first nonzero digit always
counts as a significant figures. If we put all this together, in the measurement
below only the nonzero digit plus the zeros above the line is count as significant
figures
0.0054070 m
And the measurement therefore contain five significant figures. Below we see
three different ways of expressing a length of 1200 m, each expressing a different
number of significant figures.
1.200 x 103 m (four significant figures)
1.20 x 103 m (three significant figures)
1.2 x 103 m (two significant figures)
Significant figures and calculations
In almost all cases, the numbers that we obtain from measurement are used to
calculate other quantities, and we must exercise care to report the calculated result
in a way that neither overstates nor understates the amount of confidence we have
in it. This mean that we must be careful to report the computed value with the
proper number of significant figures.
To see problems can arise, suppose we wished to calculate the area of a
rectangular carpet whose sides have been measured using two different rulers, to
be 6.2 m and 7.00 m long. We know the area is the product of this two numbers.
area = 6.2 m x 7.00 m = 43.7 m2
٢٠
The question is " How many significant figures are justified in the answer?
The length 6.2 m has two significant figures, which implies an uncertainty
of about ± 0.1 m. suppose an error of 0.1 m had, in fact, been made and that the
scale of the ruler should have read 6.3 m. How much of an error would this have
caused in the area? Let's see by recalculating the area using 6.3 m instead of 6.2
m.
area = 6.3 m x 7.00 m = 44.1 m2
notice that this error in the measured length would cause a change in the second
digit of the answer (it changes from a 3 to a 4). An uncertainty in the second digit
of the length causes an uncertainty in the second digit in the answer.
The length of the other dimension, 7.00 m, has an implied uncertainty of
about ± 0.01 m. if the 7.00 m were in error by this amount, instead of the other
measurement, how much would this influence the answer? As before, let's
recalculate the area, this time using 7.01 m.
area = 6.2 m x 7.01 m = 43.5 m2
An error in the third digit of 7.00 m causes a change in the third digit of the
answer, so if only the 7.00 m were in error, the answer would have its uncertainty
in the third digit.
For multiplication or division, the product or quotient should not have more
significant figures than are present in the least precise factor in the calculation.
As an illustration, consider the calculation below, in which we will assume that all
the numbers are measured values. A calculator gives the answer shown.
51.34745242
4.5
x
3.62
21.95
The least precise factor (i.e., the one with the fewest number of significant
figures) is the value 4.5, which contain two significant figures. The answer,
therefore, should contain no more than two significant figures and should be
rounded* to 1.3.
For addition and subtraction, the procedure used to determine the number
of significant figures in an answer is different. Here, the number we write as the
result of a calculation is determined by the figures with the largest amount of
uncertainty. For example, consider the following sum:
4.371 m
+ 302.5 m
306.871 m (before rounding)
٢١
The first quantity, 4.371 m, has an uncertainty of ± 0.001 m; the second an
uncertainty of ± 0.1 m. When we add these quantity, we expect the answer to be
uncertainty by at least ± 0.1 m, so we must round the answer in this case to the
nearest tenth; it should be reported as 306.9 m. The rule for addition and
subtraction, therefore, can be stated as follows.
The amount of uncertainty in a sum or difference will be at least as large as the
largest uncertainty in any of the terms involved in the calculation.
when wish to round off a number at a certain point, we simply drop the
digit that follows if the first of them is less than 5. Thus, 6.2317 rounds to
6.23, if we wish only two decimal places. If the first digit after the point of
round off is larger than 5, or if it is a 5 followed by other nonzero digits,
then we add 1 to the preceding digit. Thus, 6.236 and 6.2351 both round to
6.24. Finally , when the digit after the point of round off is a 5 and no
other digits follow the 5, then we drop the 5 if the preceding digit is even
and we add 1 if it is odd. Thus, 8.165 rounds to 8.16, but 8.175 rounds to
8.18.
A little practice will enable you to determine with confidence the number
of significant figures in different quantities. The following examples illustrate
some typical cases:
Quantity
No. of figures
1.062 4
751 3
0.006110 centimeters 4
1.2 x 10
8
stars 2
$ 683,462.02 8
7,685,000 4
7.6850 x 10
6
people 5
SUBSTANCES, MIXTURES, ELEMENTS, AND
COMPOUNDS
A pure substance is defined as any kind of matter for which all samples
have identical composition and identical properties.
Mixtures are combinations of two or more substances in which each
substances retains its own identity and properties. Mixtures can be separated by
٢٢
physical means. For example, the mixture of salt and water can be separated by
evaporating the water and leaving the solid salt behind. A mixture of sand and salt
can be separated by dissolving the salt in water, filtering out the sand, and then
evaporating the water to obtain the solid salt. Very fine iron powder can be mixed
with powdered sulfur to give a mixture. The iron may be removed by magnet, or
the sulfur may be dissolved in carbon disulfide, which does not dissolve iron.
M A T T E R
P u r e su b s t a n ce s
(c o n s i st a n t co m p o s iti o n )
M i x t u r e s
(v a r i a b le c o m p o s i ti o n ) P y s ic a l ch a n g e s
E l e m e n ts
C o m p o u n d s ch e m ic a l ch a n g e s
H e t re r o g e n e o u s
m i x t u r es
H o m o g e n e o u s
m i x t u r es
O il
W ate r
O i l a n d w a t e r f o r m
a h e te o g e n e o u s
m i x t u r e
Elements are pure substances that cannot be decomposed into simpler
substances by chemical changes. Oxygen, nitrogen, silver, aluminum, copper,
gold, and sulfur are all elemental substances. A list of the currently known
elements is included inside the periodic table.
٢٣
The periodic table of the elements
Compounds are pure substances consisting of two or more different
elements in a fixed ratio. All compounds can be decomposed or resolved into their
constituent element by chemical changes. The physical and chemical properties of
a compound are different from the properties of its constituent elemental. A
chemical reaction between iron and sulfur gives iron sulfide.
Water can be decomposed into hydrogen and oxygen by electrical energy
A chemical reaction
Heating a heterogeneous mixture of
iron (powder) and sulfur
Iron sulfide, a black solid compound that is
nonmagnetic and insoluble carbon disulfide
Heating
٢٤
Electrolysis of water
Platinum
electrode
Anode
(oxidation)
Battery Battery
Dil. H2SO4
Hydrogen
gas
Valve
Oxygen
gas
٢٥
CHAPTER 2
ATOMS, MOLECULES AND MOLES
An atom is the smallest particle of an element or compound that can have a
stable independent existence. A molecule that consist of one atom is called a
monatomic molecule, like helium, neon, and argon. A molecule that consist of
two atoms is called a diatomic molecule, like oxygen, nitrogen, fluorine, chlorine,
bromine and iodine. Other elements exist as more complex molecules.
Phosphrous exist as molecule consisting of four atoms, while sulfur exist as eight-
atom molecule.
Most molecules are composed of more than one type of atom. A water
molecule, for example, consists of two atoms of hydrogen and one atom of
oxygen. A molecule of methane consists of one carbon atom and four hydrogen
atoms.
HHO O FFII
H2
H y d ro ge n
m o l e cu l e
O2
O x y ge n
m o l ec u l e
F2
F l ou r i n e
m o lecu le
I
I o d i ne
m o l ec u l e
٢٦
P h o sp h r o us
m o l e cu le
P
P
P
P
S
S
Su lf u r
m o le c u le
S
S
SS
SS
SS
O
H
H
H2O
( W a t er )
CO
O
C O 2
( C a r b o n d i o x id e )
C H 4
(M et h an e )
c
H
H
H
H
H
H
H
HH
O
C
C
H
C2H6O H
(E th y l a lc o h o l)
SYMBOLS, FORMULA, AND EQUATIONS
٢٧
Each of the elements has been assigned a chemical symbol that we can think
of as a shorthand way of representing the element. The symbol consist of one or
two letters that usually bear a resemblance to the English name of the element.
For instance, carbon = C, Chromium = Cr, Chlorine = Cl, Calcium = Ca, and Zinc
= Zinc. Notice that the first letter is capitalized, but if there is a second letter, it is
not. Some of the elements have symbols have Latin names. Some examples are
Potassium (L Kaluim) = K, Sodium ( Natrium) = Na, Silver (Argentium) = Ag,
mercury (hydrargyrum) = Hg, and copper (cuprum) = Cu.(cf. the periodic table of
elements).
A chemical compound is represented symbolically by its chemical formula.
For example, water is represented by H2O, carbon dioxide by CO2, methane
(natural gas) by CH4, and aspirin by C9H8O4. The formula H2O, for instance,
describes a substance containing two hydrogen atoms for every oxygen atom.
Similarly, the compound CH4 contain one atom of carbon for every four atoms of
hydrogen.
Often, two or more atoms are able to join tightly together so that they behave
as a single particle called a molecule. If the atoms are of different elements, as in
water (H2O) or methane (CH4), it is a molecule of a compound. If the atoms of
the same element, it is a molecule of an element. Some common and important
elements that occur in nature as molecules composed of two atoms are, hydrogen,
H2; oxygen, O2, nitrogen, N2; fluorine, F2; chlorine, Cl2; bromine, Br2; and iodine,
I2.
A chemical equation is written to show the chemical changes that occur
during a chemical reaction. In a sense, it's a " before and after" description of the
reaction. For example, the equation
Z n + S Z n S
r e a c ta n ts p r o d u c t
describes the reaction between Zinc (Zn) and Sulfur (S) to produce zinc
sulfide (ZnS), a substance used on the inner surface of TV screens. The
substances on the left of the arrow are called reactants and are the chemical
present before the reaction takes place. Those on the right of the arrow are called
the products and are the substance present after the reaction is over. (In the
reaction above, there is only one product). The arrow is read as "react to yield" or
simply "yield". Thus, the equation above can be read as "zinc plus sulfur react to
yield zinc sulfide" or "zinc plus sulfur yield zinc sulfide", or "zinc recta with
sulfur to yield zinc sulfide."
Sometimes it is necessary to indicate whether the reactants and the products
are solids, liquids, gases, or dissolved in solvent such as water. This is done by
placing the letters s = solid, l = liquid, g = gas, or aq = aqueous (water) solution in
parentheses following the formula of substances in the equation. For instance, the
equation
C a C O 3(s) + H 2O ( l) + C O 2(g)C a (H C O 3)2(a q)
٢٨
Many of the equations that we write contain numbers, called coefficients,
preceding the chemical formulas. An example is the reaction of hydrogen (H2)
with oxygen (O2) to form water.
2 H 2+ O 22 H 2O
Such equation is said to be balanced because it contains the same number of
atoms of each element on both sides of the arrow. A coefficient of 1 is assumed if
none is written.
LAWS OF CHEMICAL COMBINATION
DALTON'S ATOMIC THEORY AND ATOMIC MASSES
POSTULATIONS OF DALTON'S ATOMIC THEORY AND ATOMIC
MASSES
1- Matter is composed of tiny indivisible particles called atoms.
2- All atoms of a given elements are identical, but differ from elements to
other elements.
3- A chemical compound is composed of the atoms of its elements in a
definite fixed numerical ratio.
4- A chemical reaction merely consists of a reshuffling (rearrangements)
of atoms from one set of combinations to another. The individual atoms
themselves however, remain intact and do not change.
Atomic masses
The law of definite proportions is easy to explain. Let's imagine that two
elements, say A and B , form a compound in which each molecule of the
substance is composed of one atom of A and one atom of B. Let's also suppose
that an atom of A is twice as heavy as atom of B, so if an atom of B were arbitrary
assigned a mass of 1 unit, then the mass of an atom A would be 2 units. Below we
see how the masses of A and B vary for various numbers of molecules.
Number of
Molecules
Number
of
Atoms of
A
Mass of A Number
of
Atoms
B
Mass of B Mass
Ratio,
(mass A/
(mass B)
1 1 2 units 1 1 unit 2/1
2 2 4 units 2 2 units 4/2 = 2/1
10 10 20 units 10 10 units 20/10 = 2/1
500 500 1000 units 500 500 units 1000/500 =
2/1
Now, notice that no matter how may molecules we have, each with the same 1- to
1- ratio by atoms, the ratio by mass is the same. This is exactly what the law of
٢٩
definite proportions says: In any sample of compound, regardless of sise, the
elements are always present in the same proportion (ratio) by mass.
Atomic masses
Because atoms are too small to be seen and too small to have their masses
measured individually on laboratory balance in a unit of grams, an atomic mass
scale was devised in which mass is measured in atomic mass units (the SI
symbol is u).
The atomic mass unit is defined as 1/12th of the mass of atom of carbon-
12 isotope. The atomic masses of elements are given along with the symbols of
the elements in the periodic table. The numbers in these table are relative average
atomic masses, expressed in atomic mass units.
The law of multiple proportions
The law of multiple proportions can be expressed as follows: " Suppose we have
samples of two compounds formed by the same two elements. If the masses of
one elements are the same in the two samples, then the masses of the other
elements are in a ratio of small whole numbers. This can be understand by the
following example. We know that carbon forms two different compounds with
oxygen called carbon monoxide and carbon dioxide. In 2.33 g of carbon
monoxide, we find 1.33 g of oxygen combined with 1.00 g of carbon. Notice that
the masses of oxygen that are combined with the same mass of carbon (1.00 g) are
in a ratio of 2 to 1 (a ratio of small whole numbers).
1
2
g 1.33
g 2.66
The result is consistent with the atomic theory if a molecule of carbon monoxide
(CO) contain 1 atom of C and 1 atom of O, and a molecule of carbon dioxide
(CO2) contain 1 atom of C and 2 atoms of O, so the ratio of the oxygen masses
has to be 2 to 1.
The mole concept
As we've learned, atoms react to form molecules in simple-whole-number ratio.
Carbon and oxygen atoms, for instance, combine in 2 to 1 ratio to form carbon
monoxide (CO)
1 a t o m C + 1 a t o m O 1 m o le c u le C O
We really can't work with individual atoms because they are so tiny., so
we must increase the sizes of the samples to the point where we can see them and
manipulate them, but we do this in a way that maintains the proper ratio of atoms.
One way we could enlarge amounts in a chemical reaction would be to
work with dozens of atoms instead of individual atoms.
٣٠
1 a t o m C + 1 a t o m O
1 d o z e n 1 d o z e n O a t o m s
( 1 2 a to m s C ) (1 2 a t o m s O )
1 m o le c u l e C O
1 d o z e n C O m o l e c u le
( 1 2 m o l ec u l e s C O )
A dozen atoms or molecules is still much too small to work with, so we
must find a larger unit. The " chemist's dozen" is called the mole or (mol, for
abbreviation) is a larger unit to be used instead of using a dozen atoms or
molecules.
1 dozen = 12 objects
1 mol = 6.022 x 1023 objects
The atomic weight of carbon to four significant figures is 12.01 atomic mass unit
(amu) or (u). How many atoms are in 12.01 g of carbon? Modern experimental
methods show that this number of atoms is 6.022 x 1023. This huge number is
called Avogadro's number, named in honor of Amadeo Avogadro, the brilliant
contemporary of Dalton. The weight of 6.022 x 1023 atoms of oxygen is 16.00 g;
the weight of 6.022 x 1023 molecule of carbon monoxide (CO), is 28.01 g; and the
weight of 6.022 x 1023 molecule of carbon dioxide (CO2), is 44.01 g. a mole or
(mol, for abbreviation) of a substance is the amount that contains 6.022 x 1023
units of substance.
Example: what is the mass of one atom of calcium?
Solution: we can restate the problem as
1 atom Ca = (?) Ca
We have the relationships
6.02 x 1023 atoms Ca = 1 mol Ca(to 3 significant figures)
1 mol Ca = 40.1 g Ca
The solution to the problem can be set up as
Ca atom10 x 6.02 23
1 a to m C a x x
1 m o l C a
6.02 x 102 3 a to m s C a
4 0 . 1 g C a
1 m o l C a = 6 .6 6 x 1 0 - 2 3 g C a
Example: How many moles of calcium (Ca) are required to react with 2.5 mole
of chlorine (Cl) to produce the compound CaCl2 (calcium chloride)?
Solution: we can restate the problem:
٣١
2.5 m o l C l (?) m ol C a
We know from the formula that 1 atom of Ca combines with 2 atoms of Cl. Thus,
1 ato m C a 2 ato m s C l
Because moles combine in the same ratio as atoms
1 m o l C a 2 m o l C l
We can obtain the answer as follows:
2 . 5 m o l C l X
1 m o l C a
2 m o l C l 1 .2 5 m o l C a
Example: How many grams of Ca must react with 41.5 g of Cl to produce CaCl2?
Solution:
1 m o l C a 2 m o l C l
1 m o l Ca = 4 1.1 g C a
Now we have all the information needed to solve the problem, but before we
actually go to the solution, let's diagram how it will work.
g ra m s C l
(l a b u n i t )
m o le s Cl
(c h e m ic al un i t ) m o l e s C a
(c h e m i ca l u n i t) g ra m s C a
(l a b u n i t )
we follow the outline above, being careful to set up the conversion factors so that
units cancel correctly.
4 1 .5 g C l X
1 m o l C l
3 5 .5 g C l 1 . 1 7 m o l C l
=
1 .1 7 m o l C l X
1 m o l C a
2 m o l C l 0 . 5 8 5 m o l C a
٣٢
0 .5 8 5 m o l C a X
4 0 . 1 g C a
1 m o l C a = 2 3 . 5 g C a
Usually, we put all the three steps together as follows.
41 .5 g C l X 1 m o l C l
3 5 .5 g C l
1 m o l C a
2 m o l C l
XX4 0 . 1 g C a
1 m o l C a 2 3 . 5 g C a
to m o le s o f C l
t o m o le s o f C a
t o g r a m s o f C a
Example: How many moles of silicon, Si, are in 30.5 g of Si?
Solution: we know from the table of atomic masses that
1 mol Si = 28.1 g Si
To convert from Si to moles, we must multiply 30.5 g Si by a factor that contains
the units "g Si" in the denominator, that is,
Si g 28.1
Si mol 1
Thus,
3 0 .5 g S i X 1 m o l S i
2 8 . 1 g S i = 1 .0 9 m o l S i
Therefore, 30.5 g Si = 1.09 mol Si
Example: How many moles of carbon atoms are needed to combine with 4.87
mol Cl to form the substance C2H6?
Solution: Let's restate the problem as follows:
٣٣
4 .8 7 m ol C l ? m ol C
We have conversion factors to choose from
2 m o l C
6 m o l C l
,
6 m o l C l
2 m o l C
Of course, we would also simplify these ratio to give
1 m o l C
3 m o l C l
,
3 m o l C l
1 m o l C
To get rid of the units " mol Cl" we must use the one on the left.
4 . 8 7 m o l C l X 2 m o l C
6 m o l C l
1 . 6 2 m o l C
We need 1.62 mol C.
Example: How many moles of are in 2.65 mol C2Cl6 ?
Solution: our problem can be stated as
2 .65 m o l C 2Cl6? m ol C
And then use it to construct the necessary conversion factor.
2 .6 5 m o l C 2C l 6X2 m o l C
1 m o l C 2C l 6
5 . 3 0 m o l C
Thus, 2.65 mol C2Cl6 contain 5.30 mol C.
Measuring moles of compounds:
Molecular mass and formula mass
The simplest way of obtaining the weight of one mol of a substance is merely to
add up the atomic masses of all the elements present in the compound. If the
substance is composed of molecules (for example, CO, H2O, or NH3), the sum of
the atomic masses is called the molecular mass (or molecular weight-the terms
are used interchangeably). Thus, the molecular mass of CO2 is obtained as
C 1 X 12.0 u = 12.0 u
2 O 2 X 16.0 u = 32.0 u
CO2
total 44.0 u
٣٤
Similarly , the molecular mass of H2O = 18 u and that of NH3 = 17.0 u.
The weight of one mol of a substance is obtained simply by writing its molecular
mass followed by the units, grams. Thus,
1 mol CO2 = 44.0 g
1 mol H2O = 18.0 g
1 mol NH3 = 17.0 g
One mole samples of several different compounds, contains the same number of
the formula units, although the number of atoms is different form sample to
sample. They differ because the number of atoms per formula unit is different for
each compound. Atoms or groups of atoms that have acquired an electrical
charge are called ions. Since solid NaCl is composed of Na+ and Cl+ ions, it is
said to be an ionic compound.
For ionic compounds, the sum of the atomic masses of the elements
present in one formula unit is known as the formula mass or formula weight.
For NaCl, this is 22.99 + 23.45 = 58.44.
Na 22.99 u
Cl 35.45 u
NaCl 58.44 u
One mole of NaCl ( 6.022 X 1023 formula units of NaCl) would contain 58.44 g
NaCl. Use of terms formula mass, of course, is not restricted to ionic compounds.
It can be applied to molecular substances, in which case the terms formula mass
and molecular mass mean the same thing.
Example: sodium carbonate, has molecular formula Na2CO3
(a) How many grams does 0.250 mol Na2CO3 ?
(b) How many moles of Na2CO3 are in 132 g Na2CO3?
Solution: we calculate the formula mass of Na2CO3 from the atomic masses of its
elements
2 Na
1 C
3 O
Total
2 X 23.0 = 46.0u
1 X 12.0 = 12.0 u
3 X 16.0 = 48.0 u
106.0 u
The formula mass is 106.0 u; therefore,
1 mol Na2CO3 = 106.0 g Na2CO3
This can be used to make conversion factors relating grams and moles of Na2CO3,
which we need to answer the questions
٣٥
(a) to covert 0.250 mol Na2CO3 to grams, we set up the units to cancel.
0 . 2 5 0 m o l N a 2C O 3X
1 0 6 . 0 g N a 2C O 3
1 m o l N a 2C O 3
= 2 6 .5 g N a 2C O 3
(b) Again, we set the units to cancel.
1 3 2 g N a 2C O 3X
1 m o l N a 2C O 3
1 0 6 .0 g N a 2C O 3
= 1 .2 5 m o l N a 2C O 3
Percentage composition: Percentage composition of a compound is that, the
percentage of the total mass (also called the percent by weight) contributed by
each element. The procedure to determine the percentage composition is
illustrated in the following example.
Example: What is the percentage composition of chloroform, CHCl3, a substance
once used as an anesthetic?
Solution: the total mass of 1 mol of CHCl3 is obtained from the molecular mass
12,01 u + 1.008 u + 3 X 35.45 u = 119.37 u
Or for1 mol of CHCl3,
12,01 g + 1.008 g + 3 X 35.45 g = 119.37 g
In general,
100 X
wholeofweight
part ofweight
by weight %
Then,
100 X
CHClweight
carbonweight
C %
3
C % 10.06 100 X
CHCl g 119.37
C g 12.01
C %
3
٣٦
H % 0.844 100 X
CHCl g 119.37
H g 1.008
H %
3
Cl % 89.09 100 X
CHCl g 119.37
Cl g 106.35
Cl %
3
Total % = 100.00
Example on calculating the percentage composition of the compound (
percent mass)
Problem: Calculate the percentage composition of sodium sulfate whose formula
is Na2SO4 (Atomic mass Na = 23, S = 32, O = 16), or: find the mass percent of
each element of sodium sulfate (Na2SO4).
Solution:
100 X
compound ofor (wt.) massmolecular
atom)or (element ofweight
massPercent
Wt. of 2 Na = 2 X 23 = 46
Wt. of S = 32
Wt. of 4 O = 4 X 16 = 64
Molecular mass of Na2SO4 = 46 + 32 + 64 = 142
% 32.39 100 X
142
46
(Na) Sodium of Percentage
% 22.54 100 X
142
32
(S)Sulfur of Percentage
% 45.08 100 X
142
64
(O)Oxygen of Percentage
Total = 32.39 + 22.54 + 45.08 = 100.0
Calculation of the mass of an element in a sample of compound
Example: calculate the mass of iron in a 10.0 g sample of iron oxide, Fe2O3,
commonly refereed to as rust
Solution: In one mole of this compound, there are 2 mol Fe and 3 mol O.
Therefore,
٣٧
i s in
th i s m a s s o f F e
th is m a s s o f Fe 2O3
2 Fe : 2 X 55.8 5 g = 11 1.7 g Fe
3 O : 3 X 16 .00 g = 48.0 g O
1 m o l F e
2
O
3
= 1 5 9 .7 g F e
2
O
3
We can write
11 1.7 g F e 15 9.7 g F e 2O3
1 0 . 0 g F e 2O3X
1 1 1 .7 g F e
1 5 9 .7 g F e 2O36 . 9 9 g F e
Thus, in 10.0 g Fe2O3 there is 6.99 g Fe.
Chemical formulas
There are different kinds of chemical formulas, and each conveys certain kinds of
information. This include the elemental composition, the relative numbers of each
kind of atom present, the actual members of atoms of each kind in a molecule of
the substance, or structure of a molecule of the substance.
A formula that uses the smallest set of whole-number-subscripts to specify
the relative number of atoms of each element present in a formula unit is called
simplest formula. It is also called an empirical formula because it is normally
derived from the results of some experimental analysis. The formulas NaCl, H2O,
and CH2 are empirical formulas.
A formula that states the actual number of each kind of atom found in a
molecule is called a molecular formula. H2O is a molecular formula (as well as
an empirical formula) since a molecule of water contains 2 atoms of H and 1 atom
of O. The formula C2H4 is a molecular formula for a substance (ethylene)
containing 2 atoms of carbon and 4 atoms of hydrogen. The simplest formula
CH2 is not unique to C2H4, however. A substance whose empirical formula is
CH2 could have as a molecular formula CH2, C2H4, C3H8, and so on.
A third type of formula is a structural formula, for example,
C
H
H
H
C O H
O
A c e ti c a ci d (p r e s e n t i n v in e g a r )
٣٨
In a structure formula the dashes between different atomic symbols represent the
"chemical bonds" that bind the atoms to each other in the molecule. A structural
formula gives us information about the way in which the atoms in a molecule are
linked together and allow us to write the molecular and empirical formulas. Thus,
for acetic shown above, we can write its molecular formula (C2H4O2) and its
empirical formula (CH2O).
To calculate an empirical formula, we need to know the mass of each of the
elements in a given mass of the compound.
Problems on calculating an empirical formula
Problem: A sample of a brown-colored gas that is a major air pollutant is found
to contain 2.34 g of N and 5.34 g of O. What is the simplest formula of the
compound?
Solution: We know that
1 mol N = 14.0 g N
1 mol O = 16.0 g O
Therefore,
2 . 3 4 g N X
1 m o l N
1 4 .0 g N = 0 . 1 6 7 m o l N
5 . 3 4 g O X
1 m o l O
1 6 . 0 g O = 0 . 3 3 4 m o l O
We might write our formula N0.167O0.334. However, since the formula should have
meaning on a molecular level where whole numbers of atoms are combined, the
subscripts must be integers. If we divide each subscript by the smallest one we
obtain
5 .3 4 g O X
1 m o l O
1 6 .0 g O = 0 . 33 4 m o l O
2
0.167
0.334
0.167
0.167 NO ON
Example on calculating an empirical formula from percentage composition
٣٩
Problem: what is the empirical formula of a compound composed of 43.7% P and
56.3% O by weight?
Solution: We imagine having a 100-g sample of the compound. From the
analysis, this sample would contain 43.7 g P and 56.3 g O (notice that the percents
become grams of compound).We know that
1 mol P = 31.0g P
1mol O = 16.0 g O
We convert the masses to moles
P mol 1.41
P g 31.0
P mol 1
X P g 43.7
O mol 3.52
O g 16.0
O mol 1
X O g 56.3
The formula is
2.50
1.41
3.52
1.41
1.413.521.41 PO OPOP
Whole numbers can be obtained by doubling each of the subscripts. Thus, the
empirical formula is P2O5.
Problem on determining the empirical formula from a chemical analysis
Problem: 1.025-g sample of a compound that contains carbon and hydrogen was
burned in oxygen to give carbon dioxide and water vapor as products. These
products were trapped separately and weighed. It was found that 3.007 g of CO2
and 1.845 g H2O were formed in this reaction. What is the empirical formula of
the compound?
Solution: in 1 mol CO2 (44.01 g) , there is 1 mol (12.01 g) of C. In the 3.007 g of
CO2, therefore, the mass of carbon is
C g 0.8206
CO g 44.01
C g 12.01
X CO g 3.007
2
2
Similarly, in 1 mol of H2O (18.02 g), there are 2 mol (2.016 g) of H, so the mass
of H in the 1.845 g of H2O is
٤٠
H g 0.2064
OH g 18.02
H g 2.016
X OH g 1.845
2
2
Now we have the masses of C and H in the sample, so we can calculate the
number of moles of each,
and
C mol 0.06833
C g 12.01
C mol 1
X C g 0.8206
H mol 0.2048
H g 1.008
H mol 1
X H g 0.2064
Now we determine the subscripts:
C0.06833H0.2048
Dividing by the smallest value (o.06833)
0.06833
0.2048
0.06833
0.06833HC
gives C1H2.977. The empirical formula, therefore, is CH3.
Problem on determining the empirical formula from a chemical analysis
Problem: A 0.1000-g sample of ethyl alcohol, known to contain only carbon,
hydrogen, and oxygen, was burned completely in oxygen to form the products
CO2 and H2O. These products were trapped separately and weighed; 0.1910 g
CO2 and 0.1172 g H2O were found. What is the empirical formula of this
compound?
Solution: First we calculate the mass of carbon and hydrogen in the CO2 and
H2O.
C g 0.05212
CO g 44.01
C g 12.01
X CO g 0.1910
2
2
٤١
H g 0.0131
OH g 18.02
H g 2.016
X OH g 0.1172
2
2
When we add the masses of C and H, we get a total of 0.06523 g, so the mass of
oxygen in the sample must have been
Mass of O = (mass of sample)- (total mass of C and H)
= 0.1000 g – 0.06523 g = 0.0348 g O
Now we convert the masses of C, H, and O to moles of each of the element. Thus,
for carbon we have
C mol 0.04340
C g 12.01
C mol 1
X C g 0.05212
Similar calculation for other two elements give 0.0130 mol H and 0.00218 mol O.
This empirical formula is therefore
0.00218
0.00218
0.00218
0.0130
0.00218
0.04340.002180.01300.00434 O HC OHC
Dividing we get C1.99H5.96O1, which rounds to C2H6O.
Molecular formulas
It is possible for more than one compound to have the same empirical formula.
For example, the molecules C2H4, C3H6, and C5H10 all have a 1-to-2 ratio of
carbon to hydrogen atoms and the empirical formula CH2
Molecular formula = ( Empirical formula) X n
mass Empirical
(FM.)) mass (Formula massMolecular
n
Table : molecular masses as multiple
of the empirical formula mass
Formula Molecular mass
CH
2
14.0 = 1 X 14.0
C
2
H
4
28.0 = 2 X 14.0
C
3
H
8
42.0 = 3 X 14.0
٤٢
Ionic compounds don't have molecular formulas because they don't contain
molecules.
Example on determining the molecular formula of a compound
Problem: A colorless liquid used in rocket engines, whose empirical formula is
NO2, has a molecular mass of 92.0. What is its molecular formula?
Solution:
mass Empirical
(FM.)) mass (Formula massMolecular
n
The empirical mass of NO2 is 46.0. the number of times the empirical
formula, NO2, occurs in the compound is
2
46.0
92.0
The molecular formula is the (NO2)2 = N2O4 (dinitrogen tetroxide). N2O4 is the
preferred answer because (NO2)2 implies a knowledge of the structure of the
molecule (i.e., that two NO2 units are somehow joined together).
C
4
H
8
56.0 = 4 X 14.0
C
n
H
2n
n X 14.0
٤٣
CHAPTER 3
CHEMICAL REACTIONS
AND THE MOLE CONCEPT
3.1 Chemical Reactions and Chemical Equations
We recall that a chemical equation is written to show the chemical changes
that occur during a chemical reaction. In a sense, it's a " before and after"
description of the reaction. For example, the equation
Z n + S Z n S
r e a c ta n ts p r o d u c t
describes the reaction between Zinc (Zn) and Sulfur (S) to produce zinc sulfide
(ZnS), a substance used on the inner surface of TV screens. The substances on the
left of the arrow are called reactants and are the chemical present before the
reaction takes place. Those on the right of the arrow are called the products and
are the substance present after the reaction is over.
In order to write an equation, we must be able to write the formulas of the
reactants.
If an experiment has just been carried out, the equation might be meant to
describe what has just occurred in a chemical reaction. In this case, the reactants
are known because the chemist knows what chemicals were placed in the vessel.
The products, however, must be collected and identified (by a chemical analysis,
for example) before a valid equation can be written.
Often we write chemical equations to help us plan experiments. One way
that chemical equations are particularly useful in planning experiments is that
they allow us to determine the quantitative relationships that exist among the
amounts of reactants and products. To be helpful in this way, however, chemical
equations must be balanced, which means that they must obey the law of
conservation of mass by having the same number of atoms of each kind on both
sides of the arrow.
Balancing chemical equations
In order to minimize errors, writing a balanced equation should always be viewed
as two-step process.
٤٤
Step 1. First write an unbalanced equation, being careful to write the correct
formula for each substance involved.
Step 2. Balance the equation by adjusting the coefficients that precede the formula
of the reactants and products so that there are the same number of atoms
of each kind on both sides of the arrow.
It is very important to remember that in carrying out step 2, you must not alter the
formulas of the reactants or products
For example, consider the reaction between hydrochloric acid (HCl) and
sodium carbonate (Na2CO3). The product of the reaction are sodium chloride
(NaCl), gaseous carbon dioxide (CO2) and water.
To obtain the balanced equation for the reaction, we proceed as follows.
Step 1. Write the unbalanced equation, being sure to give the correct formulas for
the reactants and products.
2232 CO OH NaCl HCl CONa
Step 2. Place coefficients in front of chemical formulas to balance the equation.
Although there are no set rules to tell you where to start, it is often best
to seek out the most complex formula in the equation and begin there by
given it coefficient 1. in this case, we start with the Na2CO3. there are
two atoms of Na in this formula, so to balance the Na we need to place a
coefficient 2 in the front of NaCl on the right. This gives
2232 CO OH NaCl 2 HCl CONa
Although this balances the Na, it cause the Cl to become out of balance, but we
can correct this by placing a 2 in the front of HCl on the left.
2232 CO OH NaCl 2 2HCl CONa
Notice that this also brings hydrogen into balance, and a quick counts for
each elements reveals that the equation is now balanced.
Example on balancing an equation by inspection
Problem: Balance the following equation for the combustion of octane, C8H18,
which is a compound of gasoline:
OH CO O HC 222188
Solution: First, we assign C8H18 (the most complex formula) a coefficient of 1.
Next, we see that we need to have 8CO2 on the right to balance the carbon and 9
H2O on the right to balance the hydrogen (9 H2O contain 18 H atoms because
each H2O contains 2 H atoms). This gives
٤٥
OH 9 CO 8 O HC 222188
Now we can work on the oxygen. On the right there are 25 O atoms (2 X 8 + 9 =
25). On the left the oxygen (O) atoms come in pairs. This means that we must
have 2
1
12 pairs (O2 molecules)to have 25 O atoms on the left. This gives us
OH 9 CO 8 O
2
1
12 HC 222188
Finally, we can eliminate the fractional coefficient by doubling each coefficient.
OH 18 CO 16 O 25 HC 2 222188
3.2 Calculations based on chemical equations
A chemical equation can be interpreted in several ways. Consider, for example,
the balanced equation for the combustion of ethanol, C2H5OH, the alcohol that's
blensed with gasoline in the fuel known as gasohol.
OH 3 CO 2 O 3 OHHC 22252
On a molecular, submicroscopic level, we can view this as a reaction between
individual molecules. But we can just as easily scale this up to lab-sized amounts
by applying the same mole ratio.
The coefficient in a chemical equation provide the ratios by which moles of one
substance react with or form moles of another.
For example, the equation for combustion of C2H5OH gives six chemical
equivalents that we can use to form conversion factors for calculations.
O mol 3 OHHC mol 1 252
CO mol 2 OHHC mol 1 252
OH mol 3 OHHC mol 1 252
CO mol 2 O mol 3 22
OH mol 3 O mol 3 22
٤٦
OH mol 3 CO mol 2 22
Let's look at some examples that illustrate how we use this information in a
chemical calculation.
Example 3.2. using a chemical equation in a calculation involving moles
Problem: How many moles of oxygen are needed to burn 1.80 mol C2H5OH
according to the balanced equation
OH 3 CO 2 O 3 OHHC 22252
Solution: the coefficient of the equation gives us the relationship
O mol 3 OHHC mol 1 252
Which we can use for a conversion factor. We set up arithmetic so the units mol
C2H5OH cancel
2
52
2
52 O mol 5.40
OHHC mol 1
O mol 3
X OHHC mol 1.8
We need 5.40 mol O2.
Example 3.3. Using a chemical equation in a calculation involving moles
Problem: How many moles of CO2 will be formed when 0.274 mol C2H5OH
burns?
Solution: Now we look at the coefficient for C2H5OH and CO2, which give us
CO mol 2 OHHC mol 1 252
Then we set up the arithmetic to get the proper units in the answer.
2
52
2
52 CO mol 5.48
OHHC mol 1
CO mol 2
X OHHC mol 0.274
Example 3.4. Using a chemical equation in a calculation involving moles
٤٧
Problem: How many moles of water will form when 3.66 mol CO2 are produced
during the combustion of C2H5OH?
Solution: the coefficients in the equation tell us that
OH mol 3 CO mol 2 22
Therefore,
OH mol 5.49
CO mol 2
OH mol 3
X CO mol 3.66 2
2
2
2
General way to tackle stoichiometry problems that involve a chemical
reaction.
g r a m s o f
su b s ta n ce
A
m ol s o f
su b s ta n c e
A
m o le s o f
su b s ta n ce
B
g r a m s o f
su b s ta n ce
B
U s e f o r m u l a
m a s s o f A
to c o n v er t
to m a s s
U s e r a ti o o f
c o ef i c ie n t s
to co n v e r t
m o l es o f A
to m o l e s o f
B
U s e f o r m u l a
m a s s o f B
to c o n v er t
t o g r a m s
L a b u n i t ch e m ic a l u n it ch e m i c a l u n i t L a b u n i t
A diagram showing in a general way to tackle
stoichiometry problems that involve a chemical reaction.
Example 3.5. Using a chemical equation in a calculation involving grams
Problem: Aluminum react with oxygen to aluminum oxide Al2O3, as shown
below
322 OAl 2 O 3 Al 4
How many grams of O2 are required to react with 0.300 mol Al?
Solution: we restate the problem as
٤٨
2
O g ? Al mol 0.300
The balanced equation provide a path between moles of Al and moles of O2.
2
O mol 3 Al mol 4
We know that
2
O g 32.0 O mol 1
2
2
22 O g 7.20
O mol 1
O g 32.0
X
Al mol 4
O mol 3
X Al mol 0.300
We need 7.20 g O2 to react with 0.300 mol Al.
Example 3.6. Using a chemical equation in a calculation involving grams
Problem: Aluminum react with oxygen to aluminum oxide Al2O3, as shown
below
322 OAl 2 O 3 Al 4
Calculate the number of grams of Al2O3 that could be formed if 12.5 g O2 react
completely with aluminum.
Solution: we can restate the problem in equation form
32OAl g ? O2 g 12.5
The central route we have to follow
322 OAl mol 2 O mol 3
The three relationships needed to solve the problem are
22 O g 32.0 O mol 1
322 OAl mol 2 O mol 3
3232 OAl g 102 OAl mol 1
٤٩
We use them to construct conversion factors and arrange them so that the units
cancel correctly.
32
32
32
2
32
2
2
2OAl g 26.6
OAl 1mol
OAl g 102
X
O mol 3
OAl mol 2
X
O g 32.0
O mol 1
X O g 12.5
The following diagram summarizes the steps involved.
X2 m o l A l 2O3
3 m o l O 2
X1 m o l O 2
3 2.0 g O 2
X2 m o l A l 2O3
3 m o l O 2
0 .3 9 1 m o l O 2
12 .5 g O 22 6. 6 g A l2O3
0 .2 6 0 m o l A l 2O3
N o d ir e c t
c a l c u la t i o n
3.3 Theoretical yield and percentage yield
The theoretical yield of a given product is the maximum yield that could be
obtained if the reactants gave only that product with no side reactions.
The actual yield: is the amount of product actually obtained in a given
experiment
The percentage yield is a measure of the efficiency of the reaction and is defined
as
100% X
yield ltheoretica
yield actual
yield percentage
Example: 3.48 g of CO2 was obtained when 1.93 g a mixture of ethylene (C2H4)
and 5.92 g O2 is ignited according to the following equation. Calculate the
percentage yield of CO2
OH 2 CO 2 O 3 HC 22242
Solution:
٥٠
% 64.1
100% X
CO g 5.43
CO g 3.48
CO of yield percentage
2
2
2
3.4 Reaction in solution
In many chemical reactions, one or more of the reactants are present in solution-
that is are dissolved in some fluid such as water. In bodies, for instance,
nutrients are dissolved in blood and are carried to our cells where they undergo
the complex chain of reaction called metabolism.
Terminology applied to solutions
Molar concentration: Molarity(M) this is defined as the number of
moles of solute in the solution divided by the volume of the solution expressed in
liters.
solution
of
liters
solute of moles
)(molarity M
M = mol / L or = mmol / L
Example: Calculate the molarity of 2.0 L solution that contains 10 moles of
NaOH.
Solution:
MM 5
2
10
)(molarity
Example: What is the molarity of a solution that has 18.23 g HCl in 2.0 L?
Solution:
a) Mol.wt. of HCl = 1.0 +35.5 = 36.5 g / mol
b) Number of moles of HCl = 18.23 g HCl / 36.5 = 0.5 mol
c) Molarity of HCl = 0.5 mol / 2.0 L = 0.25 M
Example: A 2.00-g sample NaOH, was dissolved in water to give a solution
with a volume of exactly 200 mL. What is the molarity of NaOH in solution?
Solution:
٥١
The formula mass of NaOH is 40.0 g/ mol, so
NaOH mol 0.0500
NaOH g 40
NaOH mol 1
X NaOH g 2.00
When expressed in liters, 200 mL becomes o.200 L. The molarity is therefore
NaOH 0.250
L / NaOH mol 0.25
sol L 0.200
NaOH mol 0.0500
molarity
M
Example: How many milliliters of 0.250 M NaOH solution are needed to
provide 0.0200 mol of NaOH?
Solution: We can restate the problem as
soln NaOH mL ? NaOH mol 0.0200
By choosing a conversion factor with "mol NaOH" IN denominator we get the
answer
soln mL 80.0
NaOH mol 0.250
soln mL 1000
X NaOH mol 0.0200
Thus, if we measure out 80.0 mL of this solution, it will contain the desired
0.0200 mol of NaOH
Example: How many grams of NaOH are in 50.0 mL of 0.400 M NaOH
solution?
Solution: We can restate the problem as
NaOH g ? soln mL 50.0
First, we have to translate 0.400 M to the corresponding ratio of moles to volume.
soln
mL
1000
mol 0.400
means 0.400 M
٥٢
Now we apply the ratio as a conversion factor to cancel " mL soln"
NaOH mol 0.0200
soln mL 1000
NaOH mol 0.400
Xsoln mL 50.0
The formula mass of NaOH is 40.0 g/mol. Therefore,
NaOH g 0.800
NaOH mol 1
NaOH g 40.0
X NaOH mol 0.0200
Thus, 50.0 ml of 0.400 M NaOH contains 0.800 g NaOH.
Molal concentration: (Molality) (m) this is defined as the number of
moles of solute in the solution divided by the volume of the solvent expressed in
kilograms.
Example: What is the molality of solution that contains 330 g of CaCl2 per
kilogram of solvent?
Solution:
Number of moles = wt./ mol.wt
= 330/ 110.98
= 3 mol
m = number of moles of solute/ Kg of solvent
= 3/1 = 3 molal solutiom CaCl2
Example: How many grams of NaOH are needed to make 2 molal solution?
Solution :
m = number of moles of solute/ Kg of solvent
Number of moles = wt/ mol.wt
Mol.wt of NaOH = 23 + 16 + 1 = 40
So,
1
40
wt
2
g 80 wt
Equivalent weight and normality (N)
The normality (N) of a given solution is the number of equivalents of solute per
one liter of solution.
٥٣
N = number of equivalents of solute/ liter of solution
N = equivalents / L
solution of (L)Liter 1
solute of wt.equvalent
solute of grams ofnumber
Normality
solution of (L)Liter 1
alancemol.wt / v
solute of grams ofnumber
Normality
Equivalents: are the amounts of replaceable H+ or OH- or valence
(n) valnce
mol.wt
wt)(eq. weight equivalent
In case of acids: e.g H2SO4 eq.wt = 98/2 = 49
In case of bases: e.g. Ba(OH)2 eq. wt = 171/2 = 85.5
In case of salts: e.g. NaCl eq.wt = 58.5/1 = 58.5
NaCO3 eq.wt = 106/2 = 53
Examples: (1) Calculate the normality of solution contaning 98.0 g of H2SO4 in
0.5 L solution?
Solution:
L / eq 0.4
0.5
98/49
Normality (N)
(2) How many grams of NaOH are required to prepare 2.00 L of 0.5 N
solution?
solution of (L)Liter 1
alancemol.wt / v
solute of grams ofnumber
Normality (N)
L
2
/40g ?
0.5
٥٤
g 40 g ?
Thus, the number of grams of NaOH that required to prepare 2.00 L of 0.5 N
solution is 40 g.
Interconversion between molarity and normality
N = normality
N = valance
M = Molarity
Example: What is the normality of 2.3 molar HCl solution?
Solution: The valance of HCl = 1, because, the number of replaceable H+ is 1
So,
N = 1 X 2.3 = 2.3
Mole fractions
Is the ratio of number of moles of one component to the total number of moles of
all components in the solution
nBA
A
An.....nn
n
X
XA = mole fraction of A
nA = number of moles of component A
nA + nB + ……..+ nn = total number of moles
Example: What is the mole fraction of ethyl alcohol (C2H5OH) and H2O if 0.5
mol of ethyl alcohol and 1.5 mol of H2O is mixed?
Solution:
75.0
1.5
0.5
1.5
X
OH2
25.0
1.5
0.5
0.5
X
OHHC 52
Dilution of solutions
N = n x M
٥٥
The process involves mixing a concentrated solution with additional solvent to
give larger final volume is known as dilution. Throughout this process, the
number of moles of the solute remains constant, and only the volume increases.
If we multiply a solution's molarity M by its volume V, we obtain the
number of moles of the solute
molL X
L
mol
VXM
Since the number of moles of solute stays the same during a dilution, the product
of the final molarity and volume (M1XV1) must be equal to the product of the final
molarity and volume (M2XV2). This give the useful equation
M1 X V1 = M2 X
V2
Example: What is the concentration of solution produced by diluting 100 mL of
1.5 M NaOH to 2 L?
Solution:
M1 X V1 = M2 X
V2
(1 = Initial, 2 = Final)
M1 = 1.5 M
M2 = ?
V1 = 100 mL
V2 = 2000 mL
1.5 X 100 = M2 X 2000
M2 = 0.075 M
Example: How many milliliters of concentrated H2SO4 (18.0 M) are required to
prepare 750 ml of 3.00 M H2SO4 solution?
Solution:
M1 X V1 = M2 X V2
M1 = 18.0 M M2 = 3.00 M
V1 = ? V2 = 750 ml
Solving for V1 gives
X
1
12
1M
V M
V
٥٦
M
M
V
18.0
mL) )(750 00.3(
1
mL 125
1V
To prepare the solution, we dilute 125 mL of the concentrated H2SO4 to a total
final volume of 750 mL.
Example: How much water must be added to 25.0 mL of 0.500 M KOH solution
to produce a solution whose concentration is 0.350 M?
Solution:
M1 X V1 = M2 X
V2
M1 = 0.500 M M2 = 0.350 M
V1 = 25.0 mL V2 = ? ml
Solving for V1 and substituting, we get
M
M
V
0.350
mL) )(25.0 500.0(
2
mL 37.5
2V
Since the initial volume was 35 mL, we must add 10.7 mL water to get final
volume 37.5 mL of 0.350 M concentration.
٥٧
CHAPTER 4
THE PERIODIC TABLE
AND SOME PROPERTIES OF THE ELEMENTS
4.1 Some properties of the elements
One of the simplest methods of classification of elements is to divide the
elements into three categories: metals, nonmetals and metalloids. The elements
in each of these categories have distinctive characteristics.
Metals
More than 70% of the elements are metals, some examples are iron (Fe),
aluminum (Al), copper (Cu). Chrome (Cr) gold (Au), lead (Pb), sodium (Na)---
etc. They have distinctive appearance, shiny with a luster. They have abilities to
deform without breaking when hit with hammer and to stretch when pulled. The
ability to deform when hammered is called malleability. The ability of metal to
stretch when pulled from the opposite directions is called ductility.
Metals are good conductors of electricity. They are also good conductors
of heat. Some metals are very reactive like sodium, while other like gold are very
unreactive. Some metal are very hard, and other are very soft. Chromium (Cr) and
iron (Fe) are example of hard metals; gold and lead are example of soft ones.
Sodium is also a soft metal. The extremes of melting point are even more
impressive. Tungsten has the highest melting point of any element, 3400 0C.
Mercury has the lowest point of any metal, -38 0C. Mercury is fluid at room
temperature, commonly used in thermometers.
Nonmetals
Just as the properties of metals cover a broad range, so do the properties of
nonmetals. As we've seen some, are gases, like oxygen (O), nitrogen (N),
hydrogen (H), fluorine(F), chlorine(Cl), helium (He), neon (Ne), argon (Ar). One
is liquid (bromine) (Br). Some are solid, like carbon C, and iodine (I).nonmetals
differ from each other in their chemical properties. Fluorine, for example, is
extremely reactive, while helium is inert (totally unreactive)
Metalloids
Metalloids (also called semimetals) are elements that have properties between
those of metals and those of nonmetals. The best-known example is the element
silicon. Two others are arsenic (As) and antimony (Sb).
Metalloids are typically semiconductors-they conduct electricity, but not
nearly as well as metals.
٥٨
4.2 The first periodic table
In 1869 a Russian chemist Dimitri Mendeleev and Lothar Meyer, a German
independently published arrangements of known elements that closely resemble
the periodic table of elements in use today. Mendeleev's classification was based
primarily on chemical properties of elements, while Meyer's classification was
based largely on physical properties. The tabulations were surprisingly similar
and both emphasized the periodicity, or regular periodic repetition, of properties
with increasing with atomic weight. Mendeleev discovered that if he arranged the
elements in order of increasing atomic mass, elements with similar properties
occurred at periodic intervals.
When Mendeleev constructed his table, not all the elements had yet been
discovered. He realized this because in order to always have similar elements in
the same column, or group, he was forced to leave occasional blanks in his table.
4.3 The modern view of the atom
Dalton's vision of atoms as indivisible particles in known now to be incorrect.
Experiments begun in the late of 19th.century and continued to the present day
have shown that atoms are themselves composed of still simpler subatomic
particles. Many such particles have been discovered. The principal ones-those
most important to us- are called protons, neutrons, and electrons.
Some properties of these subatomic particles are shown in the following
table
Table 4.1. Some properties of subatomic particles .
Mass Charge
Grams Atomic Mass
units (u)
Coulombs Electronic
charge
Proton 1.67 X 10
-
24
1.007276 + 1.602 X 10
-
19
1+
Neutron 1.67 X 10
-
24
1.008665 0 0
Electron 9.11 X 10
-
28
0.0005486 -1.602 X 10
-
19
1-
The concept of an atomic nucleus should be familiar to anyone. The
nucleus is the name given to the extremely small and very dense particle that
experiments have shown is located at the center of every atom.
Protons and neutrons are found in the nucleus at the center of an atoms.
Electrons fill the space around the nucleus.
The number of protons in the nucleus, which is referred to as an atom's
atomic number, determines the number of electrons that the atom must have in
order to be electrically neutral. The mass number of an atom is determined
primarily by the number of protons and neutrons in its nucleus, each of which
contributes approximately one atomic mass unit.
mass number = number of protons + number of neutrons
= atomic number + neutron number
٥٩
Mass number are always integral numbers.
Isotopes
As mentioned before, not all atoms of the same element have identical masses as
first suggested by Dalton. It is referred to these different kinds of atoms as
isotopes. The existence of isotope is a common phenomenon, and most of the
elements occur naturally as mixtures of isotopes.
A particular isotope of an element is identified by specifying its atomic
number given the symbol Z, and its mass number A.
We represent an isotope symbolically by writing its mass number as a
superscript and its atomic number as subscript, both preceding the atomic symbol.
X A
Z
For example, a carbon atom (Z = 6) that has 6 neutrons would be given the
symbol C
12
6. This is the carbon-12 isotope that is serves as the basis of the atomic-
mass scale.
The mass number (Z) of normal hydrogen is 1, for deuterium 2, and for
tritium 3, and the atomic number for each is 1, so, we can write their symbols as
follows
HH, H, 3
1
2
1
1
1
Atomic numbers and the modern periodic table
When the elements are arranged in the periodic table in order of their atomic
numbers, all the inconsistencies that had occurred in Medeleev's table disappear.
The periodic table that is used today is shown in the next separate sheet.
The numbers printed above the chemical symbols are atomic numbers, and those
below are atomic amass. Like Medeleev's table, it consists of a number of rows
called periods, which are identified by Arabic numerals. The vertical columns are
called groups, each containing a family of elements. The groups are identified by
Roman numeral and letter, either A or B.
The groups labeled with the letter A (Groups IA through VIIA) and Group
0 are referred to collectively as the representative elements. Those labeled with
the letter B (Groups IB through VIIB) plus Group VIII are called transition
element
Finally, there are two long rows of elements placed just below the main
part of the table. These elements, known as inner transition elements, actually
belong in the body of the table.
4.4 Reactions of metals with nonmetals; the formation of
ionic compounds
٦٠
The reaction between sodium (Na) and chlorine (Cl) atoms to form sodium
chloride (NaCl) is a clear example for the reactions of metals with nonmetals to
form ionic compounds.
(s)
(g)
2(s) NaCl 2 Cl Na 2
When the reaction occurs, each atom of sodium loses one electron, which
is transferred to chlorine atom. The loss of an electron leaves the particle with one
more positive charge than negative charge. As a result, the sodium ion carries
charge of 1+ and is written as Na+. When the chlorine atom gains an electron, it
acquires an additional negative charge, so the chloride ion carries a charge of 1-
and is written Cl-. Because NaCl contains these ions, it is called an ionic
compound.
Metal tend to react with nonmetals to form ionic compounds.
In these reactions, the metal atoms each lose one or more electrons and become
positive ions, or cations, and the nonmetal atoms each gain one or more electrons
and become negative ions, or anions.
The strong electrostatic forces of attraction among ions in ionic compounds
account for their relatively high melting points. According to Coulombs's Law,
the force of attraction, F, between two oppositely charged particles of charge
magnitude q is directly proportional to the product of the charges and inversely
proportional to the square of the distance separating them, r.
2
r
qq
F
Table 4.2 lists the ions formed by most of representative elements. Notice
first that the atoms in any particular group form ions with the same charge.
Table 4.2. Ions formed by the representative elements
Group number
IA IIA IIIA IVA VA VIA VIIA
Li
+
Be
2+
C
4
-
N
3
-
O
2
-
F1
-
Na
+
Mg
2+
Al
3+
Si
4
-
P
3
-
S
2
-
Cl
-
K
+
Ca
2+
Se
2
-
Br
-
Rb
+
Sr
2+
Te
2
-
I
-
Cs
+
Ba
2+
We can use the periodic table to help us remember the ions formed by the
nonmetals. The number of negative charges is just the number of step to the right
that you have to go in the table to get the noble gas column. Consider oxygen, for
example. It is in Group VIA, and to get the noble gas column requires moving
two steps to the right.
٦١
OF N e
12
Oxygen forms an ion with a negative two charge, O2-. Similarly, to move from
fluorine to the noble gas column is just one step, and fluorine forms the ion F-.
The ions formed by the transition metals is different from that formed by
representative elements, because the transition elements to form more than one
ion. Some of these ions are listed in Table 4.3.
Table 4.3. cations formed by some transition elements
Chromium Cr
2+
Gold Au
+
Cr
3+
Au
3+
Manganese Mn
2+
Zinc Zn
2+
Mn
3+
Cadmium Cd
2+
Iron Fe
2+
Mercury Hg
+
Fe
3+
Hg
2+
Cobalt Co
2+
Tin Sn
2+
Co
3+
Sn
4+
Nickel Ni
2+
Lead Pb
2+
Copper Cu
+
Pb
4+
Cu
2+
Bismuth Bi
3+
Silver Ag
+
Rules for writing formula for ionic compounds
1. The positive ion is always written first in the formula.
2. The ratio of positive ions to negative ions must be such that the total number of
positive charge equals the total number of negative charges; the formula unit
must be electrically neutral.
3. The smallest set of subscripts that give electrical neutrality is always chosen.
We always write empirical formulas for ionic compounds.
The reason for the third rule is that there are no molecules in an ionic compound.
Each positive ion is surrounded by and attracted equally to some number of
negative ions, and vice versa, so we can't say that any particular positive ions
belongs to any particular negative ion. All we can do is specify the ratio in which
the ions occur in the compound.
Let's look now at a few simple examples of how the rules are applied.
1. The compound formed from calcium and oxygen. Looking at the periodic table
we see that calcium is in Group IIA, soothe calcium ion is Ca2+. Oxygen is a
nonmetal in group VIA, so its ion is O2-.To make an electrically neutral
compound, we take the ions in a 1-to-1 ratio, and the formula is CaO.
2. The compound formed from zinc and chlorine. Zinc is a transition metal and it
forms the ion Zn2+. Chlorine is Group VIIA, so its ion is Cl-. To give an
٦٢
electrically neutral compound, we must have two Cl- for each Zn2+, so the formula
is ZnCl2.
3. The compound formed from of aluminum with oxygen. Aluminum forms Al3+
and oxygen forms O2-. In the compound, we need a ratio of ions that makes the
total positive and negative charges the same. This requires that we take two Al3+
ions for every three O2- ions, because
2 Al3+ have a charge of 2 X (3+) = 6+
3 O2- have a charge of 3 X (2-) = 6-
Total net charge = 0
There is a very simple shortcut that can use to obtain the formula of an ionic
compound. It involves exchanging superscripts for subscripts.
O
A l
2
O
3
2-
A l 3+
Ions that contain more than one atom
Some of most common polyatomic ions are given in table 4.4.
Table 4.4. Some common polyatomic ions
Cations
NH
4
+
H
3
O
+
Anions
(alternative names in parentheses)
CO
3
2
-
Carbonate ClO
2
-
Chlorite
HCO3
-
Hydrogen
carbonate
(bicarbonate)
ClO
-
(or OCl
-
) hypochlorite
C
2
H
4
2
-
Oxalate PO
4
3
-
Phosphate
CN
-
Cyanide HPO4
2
-
Hydrogen
phosphate
NO3
-
Nitrate H2PO4
-
Dihydrogen
phosphate
NO
2
-
Nitrite CrO
4
2
-
Chromate
OH- Hydroxide Cr
2
O
7
2
-
Dichromate
SO
4
2
-
Sulfate MnO
4
-
Permanganate
HSO4
-
Hydrogen sulfate
(bisulfate)
C2H3O
2
-
Acetate
SO
3
2
-
Sulfite
HSO3
-
Hydrogen sulfite
(bisulfite)
ClO
4
-
Perchlorate
٦٣
ClO
3
-
Writing the formula for a compound that contains a polyatomic ions
follows the same rules that we've applied in the previous discussion. The only
difference is that when two or more of the polyatomic ions occur in the formula,
the formula for the ion is enclosed in parentheses. Thus, the compound composed
of Ca2+ and PO43- has the formula Ca3(PO4)2:
P O 4
C a
3
(P O
4
)
2
3-
C a 2+
4.5. Reactions of nonmetals with each other; the formation of molecular
compounds
The nonmetals react not only with metals but also with each other. However,
when two nonmetals combine to form a compound, electrically neutral molecules
are formed instead of ions. An example of such a reaction occurs between oxygen
and hydrogen to form water.
)(2
)(
2
)(
2OH 2 O H 2 l
gg
The number of compounds formed among the nonmetals is enormous. There are
millions of organic compounds, for example, whose molecules are composed
chiefly of carbon and hydrogen, but that often contain other nonmetals as well
(principally oxygen, nitrogen, sulfur, and the halogens).
Table 4.5. Simple hydrogen compounds of the nonmetals
Group IVA Group VA Group VIA Group VIIA
CH
4
NH
3
H
2
O HF
SiH
4
PH
3
H
2
S HCl
GeH
4
AsH
3
H
2
Se HBr
SbH
3
H
2
Te HI
Simple compounds of the nonmetals with oxygen
Finding correlations between the formulas of nonmetal oxides and the positions of
the nonmetals in the periodic table isn't easy as with hydrogen compounds
because so many of these elements form more than one oxide. Nitrogen, for
example, forms N2O, NO, NO2, N2O3, N2O4, and N2O5. Nevertheless, there are
some similarities within groups of elements that are listed by oxides listed in
Table 4.6.
٦٤
Table 4.6. Empirical formulas of some oxides of nonmetals
Group IIIA Group IVA Group VA Group VIA
B
2
O
3
CO
2
N
2
O
3
-
N
2
O
5
SiO
2
P
2
O
3
SO
2
P
2
O
5
SO
3
GeO
2
As
2
O
3
SeO
2
As
2
O
5
SeO
3
Sb
2
O
3
TeO
2
Sb
2
O
5
TeO
3
Some of the properties associated with many simple ionic and covalent
compounds in the extreme cases are summarized Table 4.7 shown below.
Table 4.7 Some of the properties associated with many simple ionic
and covalent compounds
Ionic compounds Covalent compounds
1.High melting solids 1. Gases, liquids or low melting solids
2.Most are soluble in polar solvents
such as water
2. most are insoluble in polar solvents
3. Most are insoluble in nonpolar
solvents such as benzene or hexane
3. most are soluble in nonpolar solvents
4.Molten compounds conduct
electricity well because they contain
charged particles (ions)
4. liquid molten compounds do not
conduct electricity
5.Aqueous solutions conduct electricity
well because they contain charged
particles
5. aqueous solutions are usully poor
conductors of electricity because they
do not contain charged particles
4.5 Oxidation-reduction reactions
Oxygen reacts with most of elements to form compounds we call oxides, and
from the time that oxygen was discovered, the term oxidation has been associated
with that kind of reaction. For example iron is oxidized slowly in air and form
rust, which is composed of Fe2O3. it has also been known since the iron age that
the substance we now call iron oxide can be broken down, or reduced, to give the
free metal. Recovery of metal from its oxide therefore became known as
reduction.
In modern terms, oxidation and reduction have been given broader
meanings, which we can see if we analyze what happens when metal such iron is
oxidized and its oxide is reduced. Iron oxide, Fe2O3, is an ionic compound
composed of the ions Fe3+ and O2-. When iron reacts with oxygen,
٦٥
(s)
32
(g)
2(s) OFe 2 3O 4Fe
Iron begins as electrically neutral atoms that lose electrons to become Fe3+ ions.
When the oxide is reduced to give metallic iron, the reverse process must happen,
so Fe3+ ions must gain electrons to give Fe atoms. It is this loss and gain of
electrons, which occurs in many similar reactions, that is now associated with the
terms oxidation and reduction.
Oxidation is the loss of electrons by a substance.
Reduction is the gain of electrons by a substance.
Reactions that involve oxidation and reduction are called oxidation-reduction
reactions or redox reactions, for short.
Now, let's examine a reaction to see how we apply terms. Consider the
oxidation of magnesium .
(s)
(g)
2(s) MgO 2 O Mg 2
The product MgO is ionic and contains the ions Mg2+ and O2-, which are formed
by transfer of electrons from magnesium to oxygen.
)(oxidation 2e Mg Mg -2
)(reduction 2O 4e O -2-
2
Two terms that we often use in discussing redox reactions are oxidizing agent
and reducing agent.
The oxidizing agent is the substance that takes electrons from the substance that
is oxidized, thereby causing oxidation to take place. That's what O2 does in the
reaction between Mg and O2, it takes electrons from Mg and causes Mg to be
oxidized, so O2 is oxidizing agent. Notice that the oxidizing agent (O2) becomes
reduced in the reaction.
The reducing agent is the substance that gives electrons from the substance that
is reduced, thereby causing reduction to take place. That's what Mg does when it
reacts with O2; it gives electrons to O2 and causes O2 to be reduced. Notice that
the reducing agent (Mg) is oxidized.
Oxidation numbers
Oxidation numbers are numbers (either positive or negative) that we assign to
atoms in a compound so we can follow the changes that take place in redox
reactions. For the purposes of assigning oxidation numbers, we do this whether or
٦٦
not the compound is ionic or molecular, which means that for molecular
substances the oxidation numbers are really fictitious charges.
Rules for assigning oxidation numbers
1. The oxidation number of any element in its elemental form is zero,
regardless of the complexity of the molecule in which it occurs. Thus,
the atoms in Ne, F2, P3, and S8 all have oxidation number of zero.
2. The oxidation number of any monatomic ion (an ion composed of only
one atom) is equal to the charge on the ion. The ions Na+, Al3+, and S2-
have oxidation numbers equal to +1, +3, and -2, respectively.
3. The sum of all oxidation numbers of all the atoms in a compound is
zero. For polyatomic ions, the sum of oxidation numbers must equal
the charge of the ion.
In addition to these basic rules, we obey the following when assigning
oxidation numbers to specific atoms in a compound:
4. Fluorine has an oxidation number of -1.
5. Hydrogen has an oxidation number of +1.
6. Oxygen an oxidation number of -2.
When assigning oxidation numbers, you will sometimes encounter situations in
which these rules conflict with one another. When this happens, the rule higher up
takes precedence. Let's look at a few examples.
Example 4.1. Assigning oxidation numbers of atoms
Problem: Assign oxidation numbers of each of the atoms in the following: (a)
FeCl3, (b) KNO3, (c) H2O2, (d) Fe2(SO4)3, (e) Cr2O72-, (f) ClO3-, and (g)NaS4O8.
Solution: the oxidation number of the Fe can then be obtained by the summation
rule (rule 3).
(a) FeCl3
Cl 3 X (-1) = -3
Fe 1 X (x) = x
Sum = 0
For the sum to be zero, the oxidation number of the iron must be +3
(b) KNO3
potassium (Group IA) forms ions with a charge of 1+ (K+), so the
oxidation number of K must be +1 (rule 2). Oxygen is assigned an oxidation
number of -2 (rule 6). We get the oxidation number of N by applying rule 3.
K 1 X (+1) = +1 (rule 2)
O 3 X (-2) = -6 (rule 6)
N 1 X (x) = x
Sum = 0 (rule 3)
٦٧
(c) H2O2 is hydrogen peroxide compound formed between nonmetals, so we
expect it to be molecular. Since there is no ions, we can't use rule 2. Rules 5 and 6
refer to H and O, so we can use these, but there is a conflict. If we take H to be +1
according to rule 5, then O must be assigned an oxidation number of -1 in order
for the sum of oxidation numbers to be zero. On the other hand, if we take O to be
-2 according to rule 6, then H must be +2 for the sum to be zero. As mentioned
earlier, however, when two rules conflict, we apply the one higher up on the list.
Therefore, we take H to be +1 and the oxidation number of O in the compound is
-1.
(d) Fe2(SO4)3
Fe 2 X (+3) = +6 (rule 2)
S 3 X (x) = 3x
O 12 X (-2) = 24 (rule 6)
Sum = 0
3x + (+6) + (-24) = 0
3x = +18
x = + 6
The oxidation number of S must be +6 in this compound.
(e)For the Cr2O72- ion, the sum of oxidation numbers must equal the charge on the
ion. Therefore,
Cr 2 X (x) = 2x
O 7 X (-2) = -14 (rule 6)
Sum = -2 (rule 3)
2x + (-14) = -2
x = + 6
In this ion, the oxidation number of Cr is +6. However, you should keep in
mind that the atoms in a polyatomic ion are held together by the same kinds of
attractions that hold together atoms in molecules. There are really no Cr6+ ions
within the Cr2O72- ion. As in molecular substances, the oxidation numbers of
Cr and O here are not their actual charges.
(f) ClO3- ion is composed of two nonmetals, which means that the ion is held
together by the same kind of attractions that exist within molecules. This means
that we can't just assume that the Cl exist as Cl- ion within the ClO3- ion, so we
can't apply rule 2 in this case. However, rule 6 tells us that oxygen has an
oxidation number of -2, so we can calculate what Cl must be in order for the sum
of oxidation numbers to be equal to the charge on the ion.
Cl 1 X (x) = x
O 3 X (-2) = -6 (rule 6)
Sum = -1 (rule 3)
It's not hard to see that chlorine must have an oxidation number of + 5.
(g)NaS4O8,
٦٨
sodium is an alkali metal and must be Na+, so its oxidation number is +1.
oxygen is -2 according to rule 6. therefore,
Na 2 X (+1) = +2 (rule 2)
S 4 X (x) = 4x
O 6 X (-2) = -12 (rule 6)
Sum = 0
(+2) + (4x) + (-12) = 0
4x = 0
x = +5/2
The oxidation number of sulfur is +5/2. notice that oxidation numbers don't have
to be whole numbers (although they usually are).
Using oxidation numbers
In redox reaction, there is a change in the oxidation number or oxidation state (we
use the terms interchangeably) of two or more elements. Consider, for example
the reaction between magnesium and oxygen
2- 2 0 0
2
2MgO O 2Mg
The oxidation number of Mg changes from 0 to +2 and that of O changes
from 0 to -2. thus, the oxidation of Mg is accompanied by an increase in
oxidation number (become more positive). The reduction of O2, is
accompanied by a decrease in the oxidation number 9become less positive or
more negative)
Oxidation is increase in oxidation number.
Reduction is decrease in oxidation number.
To be in consistent with the earlier definitions, the oxidizing agent is the
substance that is reduced and the reducing agent is that substance oxidized.
By using these definitions, we can now see that the reaction between
sulfur and oxygen is also a redox reaction. Let's rewrite the equation with the
oxidation number below the symbols.
2- 4 0 0
22 SO O S
The oxidation number of sulfur (S) increase from 0 to +4, so the sulfur is
oxidized. The oxidation number of O decreases from 0 to -2, so O2 is reduced.
This means that O2 is oxidizing agent and S is reducing agent.
٦٩
Example 4.2. identifying oxidation and reduction in reaction
Problem: In the following reaction, which substance is oxidized and which is
reduced? Which substance is the oxidizing agent and which is the reducing
agent?
O7H 3Cl 2CrCl 2KCl OCrK 14HCl 223722
Solution: Let's begin by writing the oxidation numbers under each of the
chemical symbols.
2- 1 0 1- 3 1- 1 2- 6 1 1- 1
223722 O7H 3Cl 2CrCl 2KCl OCrK 14HCl
Now we look for changes in oxidation numbers. We see that the oxidation
number of Cl changes from -1 to 0. this is an increase in oxidation number, so
the substance oxidized is HCl. We also see that Cr changes from +6 to +3. this
is a decrease in oxidation number, so the K2Cr2O7 is reduced.
The oxidation agent is the substance that's reduced; it is K2Cr2O7. The
reducing agent is the substance that's oxidized is HCl.
٧٠
CHAPTER 5
CHEMICAL REACTIONS
IN AQUEOUS SOLUTION
When the reactants are dissolved in a solvent, we said that we have a
solution. One of the most important solvents for chemical reactions is water.
It is a common substance, and it is also a good solvent for many different
kinds of chemicals, both ionic and molecular.
5.1 Solution Terminology
Many terms that used in discussing solutions were introduced in previous
chapters. These include the terms solvent and solute. The solvent is generally
taken to be the substance present in solution in largest proportion, and all
other substances are considered to be solutes. In solutions that contain water,
however, water is almost always thought of as the solvent even if it is present
in relatively small amounts. For example, a mixture composed of 96% H2SO4
and 4% H2O by mass is called "concentrated sulfuric acid," which implies that
a large amount of sulfuric acid is dissolved in a small amount of water-water
is taken to be the solvent and H2SO4 the solute.
Another set of terms is concentrated and diluted. A concentrated solution
has a relatively large proportion of solute to solvent, and a dilute solution has
a relatively smaller proportion of solute to solvent.
A solution that contains as much dissolved solute as it can hold while in
contact with excess solute is said to be a saturated solution, and the amount
of solute needed to give a saturated solution with a given amount of solvent is
called the solubility of that particular solute. Thus, the solubility of sodium
chloride in water at 0 0C is 35.7 g of NaCl per 100 mL of water. Usually a
solute's solubility change with temperature. For example, at 100 0C the
solubility of NaCl is 39.1 g/ 100 mL of H2O. this means that we should
always specify the temperature when stating the solubility.
If a particular solution contains less solute than is needed for saturation, it
is said to be an unsaturated solution. An example would be a solution of 20
g of NaCl in 100 mL of H2O at 0 0C. An unsaturated solution is capable of
dissolving more solute-in this case, an additional 15.7 g of NaCl could be
dissolved in each 100 mL.
Finally, there are some substances that frequently form supersaturated
solutions, solutions that contain more solute than ordinary required for
saturation. Sodium acetate, NaC2H3O2, is an example. At 0 0C, this compound
is soluble in water to the extent of 119 g/ 100 mL, but its solubility increase
greatly with increasing temperature. If a hot unsaturated solution that contains
more than 119 g of NaC2H3O2 per 100 mL is cooled to 0 0C, the excess solute
should separate from the solution and settle to the bottom, but usually it does
not. The excess solute remains in the solution, and the solution is
supersaturated.
٧١
5.2 Electrolytes
Water is generally a good solvent for ionic compounds, and water solutions
(aqueous solutions) that contain these substances have some unusual
properties, one of which is that they conduct electricity. A compound such as
NaCl that gives an electrically conducting solution is said to be an electrolyte.
When an ionic compound dissociate in water, its ions are not really
entirely free. Instead, they become surrounded by water molecules and said to
be hydrated. We indicate this by writing (aq) after formulas of ions. For
example, the dissociation of sodium chloride (NaCl) that occurs when the
solid is dissolved in water can be represented by the equation
(aq)(aq)(s) -
Cl Na NaCl
The production of ions in solutions is not limited to ionic compounds.
There are many molecular substances that react with water to produce ions
and therefore qualify as electrolytes. Hydrogen chloride is a typical example.
When HCl gas is dissolved in water, the following reaction takes place:
(aq)(aq)(g) -
32 Cl OH OH HCl
This reaction is properly called an ionization reaction because it produces
ions where there was none before.(However, it is often referred to as
dissociation). The reaction occurs by the transfer of proton, or hydrogen ion
(H+), from the HCl molecule to water molecule to produce hydronium ion,
H3O+, and a chloride ion Cl-. We often speak of the H3O+ ion as the hydrogen
ion. By leaving out the H2O of H3O+ ion, we can write the dissociation of HCl
as
(aq)(aq)(aq) -
Cl H HCl
Strong and weak electrolytes-chemical equilibrium
The two examples of electrolytes discussed above, NaCl and HCl, are
essentially completely dissociated in aqueous solution. The electrolytes that
are completely dissociated in solution are called strong electrolytes.
There are also many molecular substances that have no tendency at all to
undergo ionization when dissolved in water. Sugar and ethyl alcohol, for
example, do not produce ions in solution, the solution doesn't conduct
electricity and these solutes are therefore called nonelectrolytes.
Between the extremes of strong electrolytes and nonelectrolytes exists a
large collection of compounds called weak electrolytes. These compounds
produce aqueous solution that conduct electricity, but only very weakly. An
example is acetic acid HC2H3O2.
In a solution of acetic acid, only a small fraction of all the acetic acid
molecules are present as ions, produced by the reaction
٧٢
(aq)(aq)(aq) -
23232232 OHC OH OHOHHC
For example, in a 1.0 M solution of HC2H3O2, only about 0.42% of the solute
has undergone this reaction. The rest of acetic acid exists as uncharged
molecules. In this solution there are two reactions occurring simultaneously,
(1) OHC OH OHOHHC -
23232232
(2) OH OHC HOH OHCOH 223232323
Such a state is called equilibrium. It said to be dynamic equilibrium because
things are continually happing in the solution-two reaction are taking place:
ions reacting to yield molecules and molecules reacting to produce ions.
To indicate chemical equilibrium in a reacting system, we use a set of
double arrows , in the chemical equation. Thus, the equilibrium that we
have been discussing is expressed as
H C
2
H
3
O
2
( aq) + H
2
OH
3
O+( aq) + C
2
H
3
O
2
-( aq)
Some additional examples of weak electrolytes are found in Table 5.1.
notice that water itself is included in this table because it is actually a very
weak electrolyte by virtue of the reaction.
H
2
O + H
2
OH3O+( aq) + O H -( aq)
Table 5.1 Some weak electrolytes
Substance
Dissociation Reaction Present
Dissociation
of the solute
in 1.00 M
Solution
Water -
322 OH OH OHOH 1.8 X 10
-
7
(55.5
moles of H2O per
liter)
Acetic acid OHC OH OHOHHC -
23232232 0.42
Ammonia -
423 OH NH OHNH 0.42
Hydrogen cyanide -
32 CN OH OHHCN 2.0 X 10
-
3
٧٣
5.3 Reactions between ions
Many of chemical reactions that carry out in the laboratory involve
electrolytes dissolved in water. Usually, these reactions take place between the
ions present in the solution and can therefore be called ionic reactions. A
typical reaction is the reaction occurs when solutions of sodium chloride and
silver nitrate are mixed, a white solid, silver chloride, is formed. The chemical
equation for this reaction is
(aq)(s)(aq)(aq) 33 NaNO AgCl NaClAgNO
This kind of reaction, in which cations and anions have changed partners, is
called metathesis or double replacement (Cl- has replaced NO3- and NO3- has
replaced Cl-).
The equation above is called a molecular equation, because all the
reactants and products are written as if they were molecules. (of course, we
know that ionic substances don't exist as molecules either in the solid state or
in solution. We just call this molecular equation because we haven't indicated
the presence of ions).
A more accurate representation of the reaction as actually occurs is
obtained if we take into account what happens to the solutes when they
dissolved in water. In water the NaCl exist as Na+ and Cl- ions. Similarly, in
its solution, the AgNO3 exists as Ag+ and NO3- ions. When the two solutions
are mixed, solid AgNO3 is formed by combination of the Ag+ and Cl- ions.
We call such a solid, formed in the solution as the result of a chemical
reaction, a precipitate. The solution that exist after the formation of AgCl
contains just Na+ and NO3- ions, and is therefore a solution of sodium nitrate.
To show those substance that are completely dissociated in the reaction, we
rewrite the equation as
)(Na AgCl )()(NO)(Ag 33 aqNO(aq)(s)aqClaqNa(aq)aq
This is called the ionic equation and is obtained by writing the formulas of
any soluble strong electrolytes in "dissociated form" and the formulas of any
insoluble substances in molecular form."
The net ionic equation is obtained by removing the spectator ions Na+ and
NO3- as follows,
)(Na AgCl )()(NO)(Ag 33 aqNO(aq)(s)aqClaqNa(aq)aq
(s)aqClaq AgCl )()(Ag
5.4 Acid-Base Reactions
Among the kinds of substances are compounds that we call acids and bases.
Arrhenius also recognized these substance as electrolytes, and they include
for example, vinegar and lemon, acetic acid and citric acid, ascorbic acid
٧٤
(vitamin C), sulfuric acid (H2SO4), hydrochloric acid (HCl), nitric acid
(HNO3).
Among important bases are ammonia (NH3), sodium hydroxide (NaOH),
potassium hydroxide (KOH).
Acids and bases have certain properties that help us identify them, for
example, a solution of an acid has a sour taste. On the other hand, bases have
a bitter taste. (Caution: you should never test for acids and bases by tasting a
chemical in the laboratory. It might not be healthy). Another property of acids
and bases is their effect on indicators (chemicals whose colors depend on the
acidity or basicity of their solutions). A typical example is the dye called
litmus. Litmus is a chemical that has a blue color in a basic solution and a
pink color in an acidic solution.
Stated in modern terms, the Arrhenius definitions of acids and bases are as
follows: An acid is a substance that increases the concentration of hydronium
ion, H3O+, in an aqueous solution, and a base is a substance that increases
the concentration of hydroxide ion, OH-.
Acids
In general, acids are molecular substances that produce hydronium ion by
reaction with water. For example, hydrogen chloride (HCl) is an acid, because
when it is dissolved in water, it reacts with the solvent to produce H3O.
(aq)(aq)(aq) -
32 Cl OH OH HCl
If we use H+ as an abbreviation for the hydronium ion and leave out the
molecule of water that carries the H+, we can also express this reaction as
(aq)(aq)(aq) -
Cl H HCl
As it is known HCl is strong electrolyte, meaning that it is essentially 100%
dissociated in solution. Therefore, HCl is strong acid.
There are also many acids that are week electrolytes. Acetic acid,
HC2H3O2, is an example. Recall that this acid reacts with water according to
the equation
H C
2
H
3
O
2
( aq) + H
2
OH O 3+( aq) + C 2H3O2-( aq)
Or more simply
H C
2
H
3
O
2
( aq) H+( a q) + C
2
H
3
O
2
-( a q)
This is an equilibrium, and in a solution of HC2H3O2 only a small fraction of
the solute is dissociated into ions. This means that the concentration of H3O+
in the solution is low. As a result, acetic acid and other acids that are weak
electrolytes are called weak acids.
٧٥
Both HCl and HC2H3O2 are able to furnish only one hydrogen ion (one
proton) per molecule of the acid. Such acids are said to be monoprotic acids.
There are also many acids that are able to furnish more than one proton per
molecule of the acid. As a class, they are referred to as polyprotic acids. Two
examples are sulfuric acid, H2SO4, and phosphoric H3PO4.
Sulfuric acid is also called a diprotic acid because each molecule of it is
able to give up two protons. This happens in two distinct steps
(aq)(aq)(aq) -
442 HSO H SOH
H S O
4
-( aq) H+( aq) + S O
4
2 - ( aq)
Similarly, phosphoric acid, which is an example of a triprotic acid, dissociates
in three separate steps.
H
3
PO
4
( a q) H+( aq) + H
2
PO
4
-( aq)
H
2
PO
4
-( aq) H+( aq) + H P O
4
2 - ( aq)
H P O
4
2 - ( aq) H+( a q) + P O
4
3 - ( aq)
Notice that the second step in dissociation of H2SO4 is an equilibrium
(only about 10% of HSO4- is actually dissociated). Despite this, sulfuric acid
is considered a strong acid because the first dissociation step is complete.
Phosphoric acid, is a weak acid because all three of its dissociation steps are
equilibria that do not proceed very far toward completion.
There are substances that do not contain hydrogen, yet still produce acidic
solutions when dissolved in water. A common example is carbon dioxide
(CO2). When dissolved in water, it reacts as follows:
C O ( g) + H
2
OH
2
C O
3
( aq)
The compound H2CO3 is called carbonic acid; it is a weak diprotic acid that is
dissociated in two steps, the first of which is
H
2
C O
3
( aq) H+( aq) + H C O
3
-( aq)
Bases
There are two principal kinds of bases: ionic hydroxides and molecular
substances that react with water to produce OH-. Sodium hydroxide (NaOH),
٧٦
and calcium hydroxide (Ca(OH)2) are typical ionic hydroxides. In the solid
state they consist of a metal ion and hydroxide ion, and when they dissolve in
water, they dissociate.
(aq)(aq)(s) -
OH Na NaOH
(aq)(aq)(s) -2
22OH Ca Ca(OH)
As is typical ionic compounds when they dissolve in water, this dissociation is
complete, so ionic metal hydroxide are strong bases.
The most common molecular substance that is base is ammonia, NH3. It
reacts with water in an equilibrium.
N H 3(a q) + H 2ON H 4 +( a q) + O H -( aq)
In this case, a proton is transferred from a water molecule to an ammonia
molecule. After the H2O loses an H+, the particle left behind is a hydroxide
ion OH-.
The reaction of NH3 with water is an equilibrium, and only a small
fraction of the NH3 placed into the solution is present as NH4+ and OH- ions.
Ammonia is a weak electrolyte, and because its solution have relatively few
OH- ions, it is also said to be a weak base. In general, molecular bases are
weak bases.
Table 5.2 Some acids and bases
Acids (Those followed by an asterisk(*) are strong electrolytes and are completely
ionized in aqueous solution.)
Monoprotic acids
XHHX
HF
Hydrofluoric
acid
HClO3
Chloric acid*
HCl
Hydrochloric
acid*
HClO4
Perchloric
acid*
HBr
Hydrobromic
acid*
HIO4
Periodic acid*
HI
Hydroiodic
acid*
HNO3
Nitric acid*
HOCl
Hydrochlorous
acid
HNO2
Nitrous acid
HClO
2
Chlorous acid
HC
2
H
3
O
2
Acetic acid
Diprotic acids
2
2
XHHX
HXHXH
H2SO4
Sulfuric acid*
H2S
Hydrosulfuric
acid
H2SO3
Sulfurous acid
H3PO3
Phosphorous
acid (only two
٧٧
hydrogen can
be removed as
protons)
H
2
CO
3
Carbonic acid
H
2
C
2
O
4
Oxalic acid
Triprotic acids
3
-2
2
2
23
XHHX
HXHXH
XHHXH
H3PO4
Phosp
horic acid
(orthophosphoric
acid)
Typical acidic oxides
(nonmetal oxides)
SO2 3222 SOHOHSO
SO3 4223 SOHOHSO
N2O3
2232 HNO2OHON
N2O5
3252 HNO2OHON
P4O6
33264 POH4OH6OP
P4O10
432104 SOH4OH6OP
Bases
Molecular bases
(weak bases)
NH3 Ammonia
( N H 3+ H 2ON H
4
++ O H -)
N2H4 Hydrazine
( N
2
H
4
+ H
2
O N
2
H
5
++ O H -)
NH2OH Hydroxyl amine
( N H
2
+ H
2
O N H
2
O H ++ O H -)
Ionic bases
(strong bases)
Metal
hydroxides
NaOH
Ca(OH)
2
-
OHM(OH) nM n
n
Typical basic oxides
(metal oxides) OH2OHO
OK
ONa
22
2
2MM
22 OH)(OHO
BaO
SrO
CaO
MM
Neutralization
The most important reaction that acids and bases undergo is their reaction
with each other, a reaction called neutralization. In aqueous solutions the
٧٨
neutralization reaction between a strong acid and strong base takes the form of
the net ionic equation
O2H OH OH 2
-
3
(aq) (aq)
Or if we use H+ as an abbreviation for the hydronium ion,
OH OH H 2
-
(aq) (aq)
If we examine the molecular equation for a typical acid-base reaction, the
reaction between sodium hydroxide and hydrochloric acid,
OH NaCl HCl NaOH 2
(aq)(aq)(aq)
we can arrive at another generalization. The products of a neutralization
reaction in aqueous solution are a salt and water.
THE BRØNSTED-LOWRY ACID AND BASES THEORY
In 1923 BrØnsted and Lawry independently presented logical extensions of
Arrhenius theory.
An acid is defined in this theory as a proton donor, H+, and a base is
defined as a proton acceptor.
When an acid gives up a proton, the remaining species is a base and is referred
to as the conjugate base of the acid.
The relationship between an acid and its conjugate base can be
represented in general terms as:
H++ A -
H A
a c i d p r o to n c o n j u g a te b a s e
Water itself is both BrØnsted acid and base.(Has amphoteric behavior, act as
acid and base). Careful measurements have shown that pure water ionizes ever
so slightly to produce equal numbers of hydrated hydrogen ions and
hydroxide ions:
H
2
O + H
2
OH3O
+
+ H O
-
Or in simplified notation,
H
2
O H
+
( a q ) + H O
-
( a q)
The autoionization of water is an acid-base reaction according to Brønsted-
lowry acid and bases theory. One H2O molecule (the acid) donates a proton to
another H2O molecule (the base). The H2O molecule that donates a proton
becomes an OH- ion, which s called the conjugate base of water. The H2O
molecule that accepts a proton becomes an H3O+. Examination of the reverse
٧٩
reaction (right-to-left) shows that H3O+ (an acid) donates a proton to OH- (a
base) to form two H2O molecules. in the notation under the equation:
H2O + H 2OH3O
+
+ H O
-
a c i d 1a c i d
2
b a s e
2
b a s e 1
The subscripts refer to conjugate acid-base pairs. Note that each acid differs
from its conjugate base by a proton.
H2O + H 2OH3O
+
+ H O
-
a c i d c o n ju g a t e a c i d
b a s e c o n ju g a t e b a s e
The following equations provide specific examples of this relationship.
Acid1 Base2 Acid2 Base2
HCl +
H
2
O
H
3
O
+
+
Cl (1)
HC
2
H
3
O
2
+ H
2
O
H
3
O
+
+ C
2
H
3
O
2
-
(2)
NH
4
+
+
H
2
O
H
3
O
+
+ NH
3
(3)
Relative strengths of conjugate acids and bases pairs
The stronger the acid the weaker the conjugate base and the stronger the base
the weaker the conjugate acid. Acid and bases are ranked in order of their
comparative strengths as shown in Table 5.3.
Table 5.3 Relative strengths of conjugate acids and bases pairs
Acid
stro n g
aci d s
d e cr e a sin g
st re n g t h
w eak
aci d s
Conjugate base
w ea k
b as e s
in c re asi n g
st re ng t h
stro n g
b as e s
HClO
4
ClO
4
-
HCl
Cl
-
H
2
SO
4
HSO
4
-
HNO
3
NO
3
-
H
3
O
+
H
2
O
H
2
SO
3
HSO
3
-
HSO
4
-
SO
4
2
-
H3PO
4
HPO
4
-
HF
F
-
HC
2
H
3
O
2
C
2
H
3
O
2
-
H
2
CO
3
HCO
3
-
H
2
S
HS
-
HSO
3
-
SO
3
2
-
HCN
CN
-
NH
4
+
NH
3
HCO
3
-
CO
3
2
-
HS
-
S
2
-
H
2
O
OH
-
NH
3
NH
2
-
OH
-
O
2
-
٨٠
LEWIS ACIDS AND BASES; COMPLEX ION OF METALS
The American chemist Gilbert N. Lewis provide a further extension for the
acid-base concept. Thus, in the Lewis definition of acid and base: A base is
defined as a substance that can donate a pair of electrons to the formation of
covalent bond. An acid is a substance that can accept a pair of electrons to
form the bond.
A simple example of a Lewis acid-base reaction is the reaction of a
hydrogen ion with a hydroxide ion
OH
..
..
..
-
+
H+
O
HH
The hydroxide ion is the Lewis base because it furnishes the pair of electrons
that become shared with the hydrogen. The hydrogen ion, on the other hand, is
the Lewis acid because it accept a share of pair of electrons when the O-H
bond is created.
Another example is the reaction between BF3 and ammonia,
N
H
H
H
+B
F
F
FN
H
H
H
B
F
F
F
In this case, the NH3 functions as the base and BF3 serves as the acid.
Compounds elements with incomplete valence shells, such as BF3 or AlCl3,
tend to be Lewis acids, while compounds or ions that have lone pairs of
electrons can behave as Lewis bases. When the Lewis acid-base reaction
occurs, a coordinate covalent bond is formed.
Some common Lewis bases are amines and alcohols.
٨١
The Ionization of Water
As we've known in earlier chapter that water itself is a very weak electrolyte
because of the reaction
H
2
O + H
2
OH3O
+
( a q) + H O
-
( a q)
This kind of reaction, in which two molecules of the solvent react with each
other to form ions, is called autoionization. Since autoionization is an
equilibrium, we can write an equilibrium expression for it as follows
OH OH
OH OH
22
3
c
K
The molar concentration of water, which
appears in the denominator of this
expression, is very nearly constant (=55.6 M)
in both pure and dilute aqueous solutions.
Therefore, [H2O]2 can be included with the
equilibrium constant, Kc, on the left side of
the equation. This gives
]][OHO[HO]X[H 3
2
2
c
K
The left side of this expression is the
product of two constants which, must also a
constant. This combined constant is written
as
2
2O][H
cw KK
The equilibrium law therefore becomes
]][OHO[H -
3
cw KK
Because [H3O+][OH-] is the ion
concentration, Kw is called ion product
constant for water, or simply the ionization
constant or dissociation constant of water.
At 250C, Kw= 1.0 X 10-14, and is one
equilibrium constant that you should be
memorize.
The density of H2O is 1.00 g/ml,
so 1.00 L has a mass of 1.00X
103g. therefore,
X
L
1.00
OH g1.00X10
O][H 2
3
2
O/LH mol 6.55
OH 18.0g
OH 1mol
2
2
2
Kw varies with temperature. At
370C(body temperature)
Kw = 2.42 X 10-14
The equation for autoionization of water is often simplified by omitting the
water molecule that picks up the H+ and abbreviating the hydronium ion as
H+. The chemical equation becomes
H
2
O
H
+
+
H
O
-
٨٢
When we use this simplified equation, the expression for the ionization
constant for water is
]][OH[H -
w
K
This equation can be used to calculate the molar concentration of both H+ and
OH- ions in pure water. From the stoichiometry of dissociation, we see that for
each 1 mol of H+ formed 1 mol of OH- is also produced. This means that at
equilibrium, [H+] = [OH-]. If we let x equal the hydrogen ion concentration,
then
][OH][H x
Therefore,
2
.xxxKw
Or, because Kw = 1.0 X 10-14,
142 10 X 0.1
x
Taking the square root yields
7
10 X 0.1
x
Which means that the concentration of hydrogen ion and hydroxide ion in
pure water are
[H+] = [OH-] = 1.0 X 10-7 M (at 250C)
The pH concept
Hydrogen ion and hydroxide ion enter into many equilibria in addition to the
dissociation of water, so it is frequently necessary to specify their
concentrations in aqueous solutions. The concentrations may range from
relatively high values to very small ones (for example, 10 M to 10-14), and a
logarithmic notation has been devised to simplify the expression of these
quantities. In general, for some quantity X, the pX is defined as
logX
X
1
logpX
For example, if we wish to specify the hydrogen ion concentration in a
solution, we speak of pH. This is defined as
]log[H
][H
1
logpH
In a solution where the hydrogen ion concentration is 10-3 M, we therefore
have
٨٣
3 pH
-(-3)]log[10
][10
1
logpH 3-
3-
Notice that logs to the base 10
(common logs) are used here,
not natural logs.
Similarly, if the hydrogen ion concentration is 10-8 M, the pH of the solution is 8
Following the same approach for the hydroxide ion concentration, we can
define the pOH of a solution as
]log[OH
][OH
1
logpOH -
Just as the H+ and OH- ion concentration in as solution are related to each other,
so also are the pH and pOH. From the equilibrium expression for the dissociation
of water, we obtain the following by taking the logarithm of both sides.
]log[OH ]log[H log -
w
K
Multiplying through by -1 gives
])(-log[OH ])log[H ( ) (-log -
w
K
By definition, -logKw = pKw, therefore,
pOH pH p
w
K
Since Kw = 1.0X 10-14, pkw = 14.00. this gives the useful relationship
14.00 pOH pH
14.00
)10X0.1log(
logK- pK
14
ww
In a neutral solution, [H+] = [OH-] = 1.0 X 10-7 M, and pH = pOH = 7.00. In an
acidic solution the hydrogen ion concentration is greater than 1.0 X 10-7 M ( for
example, 10-3 M) and the pH is less than 7.00. By the same, in basic solution the
[H+] is less than 1.0 X 10-7 M (for example, 10-10 M) and the pH is greater than
7.00. this is summarized as follows:
[H
+
] [OH
-
] pH pOH
Acidic
solution
>(1.0 X 10
-
7
) <(1.0 X10
-
7
) <7.00 >7.00
Neutral
solution
1.0 X 10
-
7
1.0 X 10
-
7
7.00 7.00
Basic solution <(1.0 X 10
-
7
) >(1.0 X 10
-
7
) >7.00 <7.00
٨٤
Measuring pH; acid-base indicators and pH meters
One of the earliest ways of judging the acidity or basicity of solution was the use
of substances called acid-base indicators. These are organic compounds whose
color depends on the pH of the solution in which they're dissolved. A typical
example is litmus, which is pink in an acidic solution and blue in a basic solution.
It is quite common today to find instruments called pH meters in labs of
all kinds. These are electronic devices that enable the pH of a solution to be
measured with a high degree of precision and accuracy.
Example: calculating the pH of a solution of strong acid
Problem: What is the ph of a 0.0020 M solution of HCl?
Solution:
2.70 pH
)10 X log(2.0- pH
]log[HpH
3
-
Example: calculating the pH of a solution of strong base
Problem: What is the ph of a 5.0 X 10-4 M solution of NaOH at 250C?
Solution: We know that
]][OH[H -
w
K
Therefore,
M 10 X 2.0
10 X 5.0
10 X 1.0
][H
11-
4-
-14
From this we calculate the pH
10.70 pH
)10 X log(2.0- pH 11
-
Another solution: By definition
M 10 X 5.0][OH
]log[OHpOH
4--
-
٨٥
3.30
4)-10 X log(5.0pOH
Therefore,
10.70
3.30-14 pH
Example: Calculating [H+] and [OH-] from pH
Problem: A sample of orange juice was found to have a pH of 3.80. what were the
H+ and OH- concentrations in the juice?
Solution:
]log[HpH
The antilogarithm of this gives the following relationship:
-pH
10][H
For the sample of orange juice, therefore,
4
-3.80
10X6.1
10][H
Once we have obtained [H+], we can calculate [OH-] from Kw.
M 10 X 6.3
10 X 1.6
10 X 1.0
][OH
11-
4-
-14
Alternatively, we could first calculate pOH from pH and the take the
antilogarithm.
10.20 3.8-14.00
pH-14 pOH
10 X 6.3
10
10 ][OH
11-
10.20-
-pH-
M
٨٦
Conjugate acid-base systems in aqueous solutions
The most important equilibrium in aqueous solutions is the ionization of water. If
we look at this equilibrium in BrØnsted-Lowry terms and consider one water
molecule the acid and the other the base, we have
H2O+ H 2OH3O++H O -
a c i d a c i d
b a s e b a s e
c o nj u g a t e p a ir s
c o nj u g a te p a ir s
Equilibrium constant expressions for acids in water
For strong acid, such as HCl, we never bother to write an equilibrium law because
the dissociation is taken to be complete. Acetic acid, however, is a weak acid and
its reaction with water is in equilibrium., thus
-
32 Cl OH OH HCl
H C
2
H
3
O
2
+ H
2
O H
3
O++ C
2
H
3
O
2
-
Cl
-
is the conjugate base of HCl.
C2H3O2- is the conjugate base of
HC2H3O3
]OHO][HC[H
]OH][CO[H
2322
-
2323
c
K
The concentration of water in diluted aqueous solution is constant, and it can
incorporated into the equilibrium constant to give a new constant that we call Ka.
This constant is called ionization constant or dissociation constant for the acid.
]OH[HC
]OH][CO[H
O][H X
232
-
2323
2
ac KK
We can also simplify this somewhat by using H+ in place of H3O+ and writing the
simplified equation as
H C
2
H
3
O
2
H
+
+ C
2
H
3
O
2
-
From which we obtain the simplified expression
]OH[HC
]OH][C[H
232
-
232
a
K
٨٧
Some anions, such as the bisulfate ion, HSO4-, are also acids. This anion is formed
in the first step in the ionization of H2SO4, reacts with water as follows.
H S O
4
-+ H
2
O H
3
O++ SO
4
2-
Acids can even be cations, such as the ammonium ion, NH4+, which undergo
reaction.
N H
4
++ H
2
O H
3
O++ N H
3
We can write similar equilibrium laws for acids such as HSO4- and NH4+
][HSO
]][SOO[H
-
4
-
2
43
a
K
The simplified equation for the reaction is
H S O
4
-H++ SO
4
2-
For which we write the equilibrium expression
][HSO
]][SO[H
-
4
-
2
4
a
K
Similarly, for ammonium ion, we have
][NH
]][NHO[H
4
33
a
K
The simplified equation for the equilibrium and the corresponding equilibrium
law are
N H
4
+H++ N H
3
][NH
]][NH[H
4
3
a
K
Usually, it is easier to write everything in the abbreviate simpler form
HAH++A-
][H
]][[H
A
A
K
-
a
٨٨
Where Ka is called ionization constant or dissociation constant for the acid, A- is
the conjugate base
Equilibrium constant expressions for bases in water
As with acids, bases also undergo the same kinds of reactions with water. An
example is ammonia (the conjugate base of NH4+).
N H
3
+ H
2
O N H
4
++ O H -
The equilibrium law for this reaction is
]O][NH[H
]][OH[NH
32
-
4
c
K
Once again, the concentration of water appearing in the denominator is essentially
a constant that we incorporate into the equilibrium constant kc to give a new
constant that we will call kb.
][NH
]][OH[NH
O]X[H
3
-
4
2
bc KK
Many anions are bases and produce hydroxide ion in water just as ammonia does.
For example, acetate ion, C2H3O2-, which is conjugate base of acetic acid, reacts
with water as follows.
C
2
H
3
O
2
-+ H
2
O H C
2
H
2
O
2
+ O H -
We write the equilibrium expression as
]OH[C
]][OHOH[HC
-
232
-
232
b
K
There is general equation that we can write for the reaction of base with
water. If we use the symbol B to stand for a base, then
B-+ H
2
O H B + O H -
And the equilibrium law is written as
٨٩
[B]
]][OH[HB
-
b
K
You can apply this equation to solve equilibrium problems that involve weak
bases in water.
The relationship between ka and kb for an acid-base conjugate
pair
Ka X Kb = Kw
Example : using the pH of a solution of an acid to calculate ka
Problem: A student prepared a 0.1 M acetic acid solution and measured its pH to
be 2.88. calculate Ka for acetic acid.
Solution: the chemical equilibrium and equilibrium constant are
H C
2
H
3
O
2
H++ C
2
H
3
O
2
-
]OH[HC
]OH][C[H
232
-
232
a
K
To evaluate Ka, we need to have all the equilibrium concentrations to substitute
into the mass action expression. They are obtained from the information given in
the problem as follows:
pH = 2.88
[H+] = 10-pH = 1.3 x 10-3 M
At equilibrium , the concentrations of ions must be equal, thus
[H+] = [C2H3O2-] = 1.3 X 10-3 M
Equilibrium concentration
H
+
1.3 X 10
-
3
M
C
2
H
3
O
2
-
1.3 X 10
-
3
M
HC
2
H
3
O
2
1.0 X 10
-
1
– 0.013 X 10
-
1
= 1.0 X 10
-
1
M
Note that when we compute the acetic acid concentration rounded to the proper
number of significant figures, the amount that has dissociated is negligible
compared tom the amount initially present. Thus,
0.10 M – 0.0013 M = (0.0987 M) = 0.1 M (rounded)
٩٠
Substituting the equilibrium concentrations into the expression for ka, we have
5-
1-
-3-3
10 X 1.7
]10 X [1.0
]10 X ][1.310 X [1.3
a
K
Percent dissociation or percent ionization
The percent dissociation or percent ionization is given by the following
relation
100X
available baseor acid of mol/L
ddissociate baseor acid of mol/L
ondissociatipercent
For the acetic acid in the preceding example, the mol/L dissociate equals the
mol/L of H+ formed, which is 1.3 x 10-3 M. the mol/L available is the original
concentration, 0.01 M. Therefore,
%3.1100 X
10
.
0
10 x 3.1
ondissociatipercent
3
M
M
Example: Using the percent dissociation to calculate an
equilibrium constant
Problem: A 0.010 M NH3 solution was prepared and it was determined that the
NH3 had undergone 4.2% ionization. Calculate the ka for NH3.
Solution: Ammonia ionizes in water according to the reaction
N H
3
+ H
2
O NH
4
++ O H -
For which we write
][NH
]][OH[NH
3
-
4
b
K
At equilibrium
[NH4+] = [OH-]
Since the 0.010 M solution undergoes 4.2 % ionization, the number of moles per
liter of these ions at equilibrium is
٩١
[NH4+] = [OH-] = 0.042 X 0.010 M = 4.2 X 10-4 M
The number of moles per liter of NH3 at equilibrium would be
[NH3] = 1.0 X 10-2 – 0.042 X 10-2 = 0.958 X 10-2 M = 1.0 X 10-2 M (rounded)
The amount ionized per liter is 4.2% of 0.010 mol/L
Equilibrium concentration
NH
4
+
4.2 X 10
-
4
M
OH
-
4.2 X 10
-
4
M
NH
3
1.0 X 10
-
2
M
By substitution for kb, we have
5-
2]-
-4-4
10 X 1.8
10 X [1.0
]10 X ][4.210 X [4.2
b
K
Example: Using ka to calculate the concentration of the species in
a solution of a weak acid
Problem: What are the concentrations of all the species present in a 0.50 M
solution of acetic acid. For HC2H3O2, ka = 1.8 x 10-5.
Solution: The chemical equation and the equilibrium law are
H C
2
H
3
O
2
H++ C
2
H
3
O
2
-
5
232
-
232 10 X 8.1
]OH[HC
]OH][C[H
a
K
We assign the initial [C2H3O2-] a value of zero. We also expect the initial
concentration of H+ to be zero.
In reaching equilibrium, some of HC2H3O2 will dissociate, so its
concentration will decrease. We don't know how much, so let's say that the
change in HC2H3O2 concentration is x. Since all the coefficient in the equation are
equal to 1, the concentrations of H+ and C2H3O2- will increases by x. this gives us
the quantities in the center column of the table. The quantities corresponding to
the equilibrium concentrations are obtained by adding the "change" to the initial
concentration algebraically
Initial Molar
Concentration
Change Equilibrium Molar
concentration
H
+
0.0 +x x
٩٢
C
2
H
3
O
2
-
0.0 +x x
HC
2
H
3
O
2
0.50 -x 0.50 - x
.
Substituting these values into the equilibrium expression gives us
5
10 X 8.1
- 0.50
x
xx
Let us assume that x will be negligible compared to 0.50; that is
0.50 - x = 0.50
Our equation the becomes
5
2
10 X 8.1
50
.
0
x
3
10 X 0.3
x
If we look back on our assumption, we see that x is in fact small compared to 0.50
and that, when rounded to the proper number of significant figures,
0.50 – 0.0030 = 0.50 (rounded)
Equilibrium concentration (M)
H
+
3.0 X 10
-
3
C
2
H
3
O
2
-
3.0 X 10
-
3
HC
2
H
3
O
2
0.50
Therefore, the equilibrium concentrations of the species involved in the
dissociation of the acid are those given in the previous table. Since the question
asks for all concentrations, we must also calculate the concentration of OH-,
which comes from the dissociation of water. Here we use kw.
M
Kw
10 X 3.3
10 X 3.0
10 X 1.0
]H[
][OH
12-
-3
14
-
Example: Calculating the pH of a solution that contains a weak
acid and strong acid
Problem: What is the pH of a solution that contains 0.10 M HCl and 0.10 M
HC2H3O2? For acetic acid ka = 1.8 x 10-5.
٩٣
Solution: The 0.10 M solution of HCl contains 0.10 mol/L of H+, because HCl is a
strong acid. This is the concentration of H+ before the HC2H3O2 is added. Then
we place 0.10 M HC2H3O2 into it, but we imagine that none of it dissociates. This
gives us the initial concentrations of H+ and HC2H3O2.
[H+]initial = 0.10 M
[HC2H3O2]initial = 0.10 M
Now, we have to consider the ionization of acetic acid. The chemical equilibrium
and equilibrium law are the same as in preceding problem.
H C
2
H
3
O
2
H++ C
2
H
3
O
2
-
5
232
-
232 10 X 8.1
]OH[HC
]OH][C[H
a
K
Since there is no C2H3O2- present initially, some of it must form by the
dissociation of the HC2H3O2. Therefore, we let the concentration of HC2H3O2
decrease by x and the concentrations of H+ and C2H3O2- increases by x and then
add the initial concentrations and the changes to get the equilibrium quantities.
Initial Molar
Concentration
Change Equilibrium Molar
Concentration
H
+
0.10 + x 0.10 + x ≈ 0.10
C
2
H
3
O
2
-
0 + x x
HC
2
H
3
O
2
0.10 - x 0.10 – x ≈ 0.10
We expect x to be small, so we've assumed 0.10 ± x ≈ 0.10 . substituting into the
ka expression, we get
]OH[HC
]OH][C[H
10 X 8.1
232
-
232
5-
a
K
5-
5-
5-
10
X
1.8
)10.0(
)(0.10)(
10 X 1.8
0.10
0.10
10 X 8.1
x
x
x
We see that x is indeed small compared to 0.10, so the solution [H+] = 0.10 M.
This gives a pH of 1.00.
٩٤
Example: Calculating the pH of a solution of a weak base
Problem: What is the pH of a 0.010 M solution of the weak base diethylamine
(C2H5)2NH, for which kb = 9.6 X 10-4?
Solution: Since the solute is a base, the equilibrium is
( C
2
H
5
)
2
N H + H
2
O (C
2
H
5
)
2
N H
2
++ O H -
Therefore,
4
252
-
252 10 X 6.9
NH])H[(C
]][OH)NHH[(C
b
K
We take the (C2H5)2NH concentration specified in the problem as its
initial concentration and the concentration of (C2H5)2NH2+ to be zero. As usual,
we assume the solvent makes no contribution to [OH-]. Therefore, we take the
initial OH- concentration to be zero, too. This gives us the entries for the initial
concentration column in the concentration table. Next, we realize that some of the
diethylamine must react, so we let its concentration decrease by x, and we
increase the concentrations of (C2H5)2NH2+ and OH- by x. adding the "changes" to
the initial concentrations gives the equilibrium quantities.
Initial Molar
Concentration
Change Equilibrium Molar
Concentration
(C
2
H
5
)
2
NH
2
+
0.0 x x
OH
-
0 x x
(C
2
H
5
)
2
NH 0.010 - x 0.010- x
Substituting these into the mass action expression gives
4
10 X 6.9
- 0.010
x
xx
Now let's see what happens if we assume that x is negligibly small compared to
0.01o M. This gives the equation
4
10 X 6.9
010
.
0
xx
x2 = 9.6 X 10-6
x = 3.1 X 10-3
If we aren't careful, we might accept this as the answer. However, if we check our
assumption, we find that x is not negligible compared to 0.010. In decimal form, x
= 0.0031, so 0.010-0.0031 = 0.007(rounded to the correct number of significant
figures). Certainly 0.007 is not the same as 0.010. in this problem, it was not safe
٩٥
to assume that the initial concentration of (C2H5)2NH is the same as its
equilibrium value.
0031 M is about 30% of the initial value of 0.010 M, so it is certainly not
negligible.
The next question, of course, is what do we do now? There are actually two
choices. One is to expand the equation into a quadratic equation and apply the
quadratic formula to it.
The quadratic formula:
a
acbb
x
2
42
Although tedious, the solution is relatively straightforward. It gives two values for
x because of the "±" sign before the radical. These turn out to be
x = 2.7 X 10-3
x = -3.6 X 10-3
we can discard the second value because the concentration of (C2H5)2NH2+ and
OH- can't be negative and also because 0.010- (- 3.6 X 10-3) = 0.014 (rounded),
which is impossible. Therefore, we are left with x = [OH-] = 2.7 X 10-3 M. This
gives a pOH of 2.57 and a pH of 11.43.
Buffers: the control of pH
If a solution contains both a weak acid and a weak base, it has the ability to
absorb small additions of either a strong acid or strong base with very little
change in pH. When a small amount of strong acid is added, its H3O+ is
neutralized by the weak base, and when a small amount of strong base is added,
its OH- is neutralized by the weak acid. Such solutions are said to be buffered and
the mixture of solutes that produces the effect is called a buffer.
Buffers usually consist of a weak acid and its conjugate base. An example
is acetic acid and acetate ion, and a solution buffered with this pair is prepared by
dissolving HC2H3O2 and acetate salt such as NaC2H3O2 in some appropriate
amount of water. In this case, the buffer has pH lower than 7 because the acid,
HC2H3O2, is stronger than the base C2H3O2-. (For HC2H3O2, ka = 1.6 X 10-5 and
for C2H3O2-, kb = 5.6 X 10-10.) If a small amount of strong acid is added to this
buffer, its H3O+ can react with acetate ion,
OH OHHC OHC OH 2232
-
2323
Or more simply,
OHHC OHC H 232
-
232
٩٦
Notice that this reaction removes H+ and changes the base into its conjugate acid.
A similar reaction occurs if a strong base is added. The OH- supplied by the
strong base reacts with the acetic acid and converts it to its conjugate base.
OHOHC OH OHHC 2232
-
232
Buffers with a ph higher than 7 can be prepared by using a base that is
stronger than its conjugate acid. A common basic buffer is formed by mixing
ammonia with an ammonium salt such as NH4Cl and contains the conjugate acid-
base pair NH4+ and NH3. If a strong acid is added to the buffer, it reacts as
follows,
OH NH NH OH 2433
d)(simplifie NH NH H 43
And if a strong base is added, the reaction is
OH NH NH OH 234
-
Buffer calculations
Example: Calculating the pH of a buffer solution
Problem: What is the pH of buffer solution prepared by dissolving 0.10 mol of
NaC2H3O2 and 0.20 mol of HC2H3O2 in enough water to give 1.00 L solution?
Solution: There is only one equilibrium here that we must concerned with
H C
2
H
3
O
2
+ H
2
O H ++ C
2
H
3
O
2
-
5
10 X 1.8
]OH[HC
]OH][C[H
232
232
When NaC2H3O2 dissolves, it is completely dissociated. It is important to
remember that virtually all salts are 100% dissociated in solution. Therefore, 0.10
mol/ L of NaC2H3O2 gives 0.10 mol/ L of Na+ and 0.10 mol/ L of C2H3O2-. We
are interesting only in the C2H3O2-; the Na+ is simply a spectator ion and we
ignore it. The initial concentration of the C2H3O2- is therefore 0.10 M. As usual,
we take the initial concentration of the weak acid to be the value specified in the
problem; in this case [HC2H3O2]initial = 0.20 M. We also ignore the contribution
that solvent makes to [H+], so we set this value to zero. These are the values that
go into the first column of concentration table.
Next, we enter the changes in the center column. Since no H+ is present,
some HC2H3O2 must ionize; so let's allow x to equal the number of moles per liter
٩٧
of HC2H3O2 that dissociates to give H+ and C2H3O-. This will increase [H+] and
[C2H3O2-] by x and decrease [HC2H3O2] by x. The equilibrium concentration are
then found in the last column for our table.
Initial Molar
Concentration
Change Equilibrium Molar
Concentration
H
+
0.0 x x
C
2
H
3
O
2
-
0.10 x 0.10 + x≈ 0.10
HC
2
H
3
O
2
0.20 - x 0.20- x ≈ 0.20
As before, we look at ka and see that x will probably be small. We will therefore
assume that 0.10 + x ≈ 0.10 and 0.20 – x ≈ 0.20. substituting into the expression
for ka gives
5
10 X 1.8
0.20
0.10
x
5
10 X 3.6
x
Now let's check our assumption. If 3.6 X 10-5 is added to 0.10 and the result
rounded to the correct number of significant figures, the sum is 0.10. If 3.6 X 10-5
is subtracted from 0.20, the difference is 0.20 when rounded correctly. This means
that we were correct in our assumption that x was small compared to 0.10 and
0.20. the equilibrium concentrations are therefore
[H+] = 3.6 X 10-5 M
[C2H3O2-] = 0.10 M
[HC2H3O2] = 0.2 M
Since we are interested in the pH, we use the H+ concentration.
pH = -log[H+] = -log(3.6 X 10-5)
= 4.44
Example: Preparing a buffer with a specified pH
Problem: What ratio of acetic acid to sodium acetate concentration is needed to
form a buffer whose pH is 5.70?
Solution:
a
K
H
]OHC[
OHHC
232
232
The H+ concentration when the pH is 5.70 is
[H+] = 2.0 X 10-6 M
٩٨
ACID-BASE TITRATIONS
Titration is useful way of determining the concentrations of solutions of acids and
bases, provided that the equivalence point can be detected. The equivalence point,
you should remember, occurs when equal numbers of equivalents of acid and base
have been combined.
Titration of a strong acid with a strong base
The titration of 25.00 mL of 0.10 M with 0.10 M NaOH is a typical example of
the titration of a strong acid with base. We can mathematically determine the ph
throughout the titration by calculating the H+ concentration present in the flask
each time a quantity of NaOH is added to the HCl. For example, the number of
moles of H+ present in the mL of a 0.1 M HCl solution is
H of mol 10 X 2.5 mL 25 X
mL 1000
mol 10.0 3-
When 10 ml of the 0.10 M NaOH is added, we in fact have added
OH of mol 10 X 2.5 mL 25 X
mL 1000
mol 10.0 3-
The neutralization reaction
OH OH H 2
-
Table: Titration of 25 ml of 0.1 M HCl with a 0.1 M NaOH solution
Volume
of HCl
(mL)
volume
of
NaOH
(mL)
Total
volume
(mL)
Moles
of H+
Moles of OH
-
Molarity of Ions in
Excess
pH
25.00 0.00 25.00
2.5 X 10
-
3
0 0.10 (H
+
) 1.00
25.00 10.00 35.00 2.5 X 10
-
3
1.0 X 10
-
3
4.3 X 10
-
2
(H
+
) 1.37
25.00 24.99 49.99 2.5 X 10
-
3
2.499 X 10
-
3
2.0 X 10
-
5
(H
+
) 4.70
25.00 25.00 50.00 2.5 X 10
-
3
2.50 X 10
-
3
0 7.00
25.00 25.01 50.01 2.5 X 10
-
3
2.501 X 10
-
3
2.0 X10
-
5
(OH
-
) 9.30
25.00 26.00 51.00 2.5 X 10
-
3
2.60 X 10
-
3
2.0 X10
-
3
(OH
-
) 11.30
25.00 50.00 75.00 2.5 X 10
-
3
5.0 X 10
-
3
3.3 X10
-
2
(OH
-
) 12.52
Occurs, and the amount of H+ remaining is
(2.5 X 10-3) – (1.0 X 10-3) = 1.5 X 10-3 mol of H+
٩٩
The molar concentration of H+ is now
M
2
-3
10X3.4
L
0.035
mol 10 X 1.5
][H
And the pH is calculated to be 1.37. the concentrations of H+ after further
additions of NaOH have occurred are summarized in the previous table.
Our calculations show that the pH increases slowly at first, then rises
rapidly near the equivalence point, and finally levels off gradually after the
equivalence point is reached.
If a graph is drawn of pH versus the volume of base added, we obtain the
plot shown in the following figure. The equivalence point occurs in this case, at a
pH of 7. at the equivalence point the solution is neutral because neither of the ions
of the salt that is left in solution (NaCl) undergoes hydrolysis.
Example: How many mL of 0.025 M H2SO4 are required neutralize 525 mL of
0.06 M KOH. What is the pH of neutralized solution?
Solution:
N of KOH = n H = 1 X 0.06 = 0.06 N
N of H2SO4 = NH = 2 X 0.025 = 0.05 N
Na X Va = Nb X Vb
0.05 X Va = 0.06 X 525
Va = 630 mL
Therefore, the pH of neutralized solution = 7
Acid-Base Indicators
Indicators are usually weak organic acids or bases that change color over a
range of ph values. Not all indicators change color at the same ph, however.
If we denote an indicator by the general formula HIn, we have the
dissociation reaction
١٠٠
H In H ++ I n -
Table: some common indicators
Indicator Color change pH Range in which color
change occurs
Thymol blue Red to yellow 1.2-2.8
Bromophenol blue Yellow to blue 3.0-4.6
Congo red Blue to red 3.0-5.0
Methyl orange Red to yellow 3.2-4.4
Bromocresol green Yellow to blue 3.8-5.4
Methyl red Red to yellow 4.8-6.0
Bromocresol purple Yellow to purple 5.2-6.8
Bromothymol blue Yellow to blue .0-7.6
Cresol red Yellow to red 7.0-8.8
Thymol blue Yellow to blue 8.0-9.6
phenolphthalein Colorless to pink 8.2-10.2
Alizarin yellow Yellow to red 10.1-12.0
Buffers and blood
Oxygen is transported primarily by hemoglobin in the red blood cells
CO2 transported both in plasma and the red blood cells
C
O
2
+
2
H
2
O
H
2
C
O
3
CO
2
H
3
O++ H C O
3
-
The amount of CO2 helps control blood pH
Too much CO2- Respiratory arrest (Hypoventilation)
pH goes down, acid level goes up-acidosis
Reduced in rate and depth of breathing
Solution: ventilate and give bicarbonate via IV
Too little CO2-anxiety (hyperventilation)
The pH goes up, acid level goes down-alkalosis
Increase in rate and depth of breathing
Solution: rebreath CO2 in paper bag to raise level
Normal blood pH is from 7.35-7.45
Going outside of this range can be very dangerous or deadly
Acidosis and Alkalosis
١٠١
Metabolic acidosis
Can be caused by uncontrolled diabetes mellitus, diarrhea, aspirin overdose and
after heavy exercise.
Metabolic alkalosis
Caused by prolonged vomiting, excessive use of bicarbonate for treating an upset
stomach.