Chapter 7. Gases
We are surrounded by an atmosphere composed of a mixture of gases
that we refer to as air. The behavior of air determines our weather, and the
oxygen, O2, in air supports our life. We also encounter gases in countless
other situations. For example, chlorine gas, Cl2, is used to purify drinking
water. Acetylene gas, C2H2, is used in welding. Nitrous oxide gas, N2O,
sometimes called laughing gas, is used as anesthetic in dentistry. Our goal
in this chapter is to develop a deeper understanding of the physical
properties of gases.
1. Properties of gases
Under appropriate conditions, substances that are ordinarily liquids or
solids can also exist in the gaseous state, where they are often referred to
as vapors. The substance H2O, for example, can exist as solid ice, liquid
water, or water vapor. Frequently, a substance exists in all three states of
matter.
The characteristic properties of gases arise because the individual
molecules are relatively far apart.
① A gas expands to fill its container. Consequently, the volume of the
gas is equal to the volume of the container in which it is held.
② Gases form homogeneous mixtures with one another regardless
of the identities or relative proportions of the component gases.
7–1
2. Gas pressure
Gases exert a pressure on any surface with which they are in contact.
For example, the gas in an inflated balloon exerts a pressure on the inside
surface of the balloon.
1) Pressure:
P = F/A
P: pressure, F: force, A: area
Unit: Pa (pascal), 1 Pa = 1 N/m2
2) Liquid pressure
P = F/A = mg/A = Vg/A = Ahg/A = gh ( = density)

h
A
3) Measurement of atmospheric pressure
The force experienced by any area exposed to Earth’s atmosphere is
equal to the weight of the column of air above it. It is the pressure exerted
by this column of air that we refer to as atmospheric pressure. The actual
value of atmospheric pressure depends on location, temperature, and
weather.
a) In 1643, Torricelli constructed a device to measure the pressure of
atmosphere.
 mercury (Hg) barometer
vacuum
air
pressure
76 cm
Hg
(a)
(b)
Figure. Measurement of atmospheric pressure with a mercury barometer. (a) The
mercury levels are equal inside and outside the open-tube. (b) A column of mercury 76
cm high is maintained in the closed-end tube.
7–2
b) Units of pressure
1 atm = 760 mmHg = 760 torr = 14.7 lb/in2 (psi)
= 1.0333 kg/cm2 = 101,325 N/m2 (Pa) = 101.324 kPa
What is the height of a water column, in meters, that could be
maintained by standard atmospheric pressure? ((Hg) = 13.6 g/cm3)
Solution:
1 atm = (H2O)·g·h(H2O) = (Hg)·g·h(Hg)

h(H2O) = (Hg)·h(Hg)/(H2O)
= [13.6 g/cm3 × 76 cm]/[1.0 g/cm3] = 1.03 × 103 cm = 10.3 m
c) Manometer
We use various devices to measure the pressure of enclosed gas.
i) An open-end manometer: An open-end manometer is usually
employed to measure gas pressures that are near atmospheric
pressure.
Patm
Pgas
Patm
Pgas
PHg
Hg
Patm
Pgas
Hg
(a)
Pgas = Patm
(b)
Pgas = Patm + PHg
7–3
(c)
Pgas = Patm - PHg
ii) A closed-end manometer: A closed-end manometer is usually
employed to measure gas pressures below atmospheric pressure
(5–300 mmHg). The pressure is just the difference in the heights
of the liquid levels in the two arms.
vacuum
P=0
PHg
Gas
AIr
(a)
(b)
Pgas = PHg
3. Ideal gas equation
Experiments with a large number of gases reveal that the four variables,
pressure (P), volume (V), temperature (T), and the quantity of matter (n) in
the gaseous samples are usually sufficient to define the state, or condition,
of a gas.
1)
V  1/P (at constant n and T)
V  T (at constant n and P)
V  n (at constant P and T)
Boyle's law:
Charle's law:
Avogadro's law:

V  nT/P
∴ V = RnT/P or PV = nRT (Ideal gas equation)
An ideal gas is a hypothetical gas whose pressure–volume–
temperature behavior can be completely explained by the ideal gas
equation. The molecules of an ideal gas do not attract or repel one another,
and their volume is negligible compared with the volume of the container.
7–4
2) Some remarks
a) STP (Standard Temperature and Pressure)
i) For an ideal gas: 0 ℃ and 1 atm
ii) Volume of 1 mol of gas at STP = 22.4 L)
b) R (gas constant)
= 0.082 (L·atm)/(K·mol) = 1.987 cal/(K·mol) = 8.314 J/(K·mol)
c) K (Kelvin temperature or absolute temperature)
K = ℃ + 273.15
d) Molecular weight (Mw) determination: PV = nRT = (m/Mw)RT
e) At constant n,
 P1V1/T1 = P2V2/T2
P1V1 = nRT1, P2V2 = nRT2
A glass vessel weighs 40.1305 g when clean, dry, and evacuated;
138.2410 g when filled with water at 25 ℃ (density of water = 0.9970
g/cm3); and 40.2959 g when filled with propylene gas (C3H6) at 740.4
mmHg and 25 ℃. What is the molecular weight of propylene?
7–5
4. Mixtures of gases
1) Dalton's law
① Dalton's assumption: In a mixture of gases, each gas expands to fill
the container. Each gas exerts the same pressure, called its partial
pressure, that it would if it were alone in the container.
② The total pressure of a mixture of gases equals the sum of the
pressures that each gas would exert if it were present alone.
Ptot =  Pi =  (ni/V)RT (at constant V and T)
i) Pi (partial pressure of the ith gas) = (ni/ntot)Ptot = XiPtot
ii) Xi (mole fraction) = ni/ntot = ni/ ni
 Xi = 1
iii) Pi/Ptot = niRT/V = ni = Xi
ntotRT/V
ntot
The major components of air are N2, 78.08%; O2, 20.95%; Ar, 0.93%,
and CO2, 0.03% by volume. What are the partial pressures of these four
gases in a sample of air at 1 atm?
2) Collecting gases over water
An experiment that often comes up in the course of the laboratory work
involves determining the number of moles of gas collected from a chemical
reaction. Sometimes this gas is collected over water.
a) Gases insoluble in H2O: N2, Ar,…(wet gas): Ptot = Pgas + PH2O = Patm
Pgas + PH2O
Gas
Patm
Patm
water
Figure. Collecting a gas over water.
7–6
b) Vapor pressure of water (PH2O) depends only on the temperature of
water.
Table. Vapor pressure of water at various temperatures
T (℃)
PH2O (mmHg)
T (℃)
PH2O (mmHg)
0
4.6
27
26.7
5
6.5
28
28.3
10
9.2
29
30.0
11
9.8
30
31.8
12
10.5
35
42.2
13
11.2
40
55.3
14
12.0
45
71.9
15
12.8
50
92.5
16
13.6
55
118.0
17
14.5
60
149.4
18
15.5
65
187.5
19
16.5
70
233.7
20
17.5
75
289.1
21
18.7
80
355.1
22
19.8
85
433.6
23
21.1
90
525.8
24
22.4
95
633.9
25
23.8
100
760.0
26
25.2
105
906.1
Suppose that 0.20 L of oxygen gas is collected over water. The
temperature of the water and gas is 26 ℃, and the atmospheric
pressure is 750 mmHg.
a) How many moles of O2 are collected?
b) What volume would the O2 gas collected occupy when dry, at the
same temperature and pressure?
7–7
5. Kinetic theory of gases
The ideal gas equation describes how gases behave, but it does not
explain why they behave as they do. For example, why does a gas expand
when heated at constant pressure? Or why does its pressure increase
when the gas is compressed at constant temperature? To understand the
physical properties of gases, we need a model that helps us picture what
happens to the gas particles as experimental conditions such as pressure
or temperature changes. Such a model is referred to as the kinetic
molecular theory.
1) Assumptions
①
A gas consists of a very large number of extremely small particles
(atoms, molecules, or ions) in constant, straight-line motion.
②
Molecules of a gas are separated by great distances. (Point mass
model: it has mass but no volume.)
③
Molecules frequently collide with one another and with the wall of
their container. However, these collisions occur very rapidly and most
of the time molecules are not colliding.
④
Attractive and repulsive forces between gas molecules are negligible.
(No intermolecular forces)
⑤
Energy can be transferred between molecules during collisions, but
the average kinetic energy of the molecules does not change with
time, as long as the temperature of the gas remains constant. (Due to
elastic collisions between molecules, the total energy remains
constant.)
⑥
The average kinetic energy of the molecules is proportional to
absolute temperature. At any given temperature the molecules of all
gases have the same average kinetic energy.
The average kinetic energy of a molecule is
EK = 1/2mv2 = CT (C: constant)
v2 (the mean square speed)
= (v12 + v22 + v32 + + … + vN2)/N
N : the total number of molecules
7–8
2) Distribution of molecular speeds
① The absolute temperature of a gas is a measure of the average kinetic
energy of its molecules.
i) If two different gases are at the same temperature, the molecules
have the same average kinetic energy.
ii) If the temperature of a gas is doubled (say from 200 K to 400 K), the
average kinetic energy of its molecules is also doubled. Thus,
molecular motion increases with increasing temperature.
② Although the molecules of a gas have the average kinetic energy and
hence an average speed, the individual molecules move at varying
speeds. At one instant, some of them are moving rapidly, others slowly.
0 oC
Relative number
of molecules
500 oC
0
1
2
3
4
3
5 (x 10 )
Figure. Distribution of molecular speeds. The distribution of speeds of H2 molecules
are shown for 0 ℃ and 500 ℃. Note that maximum in the curve increases with
temperature.
7–9
3) Application to the gas law
①
Gas pressure is the result of collisions between molecules and the
wall of the container.
② Compressibility of gases. Because molecules of a gas are separated
by great distances, gases can be compressed easily to occupy smaller
volumes,
③ Boyle’s law. Decreasing the volume of a given amount of a gas
increases its density and therefore increases its collision rate.
④ Charles’ law. Because the average kinetic energy of gas molecules is
proportional to the sample’s absolute temperature, raising the
temperature increases the average kinetic energy. Consequently, gas
molecules with the wall of the container more frequently and thus the
pressure increases. The volume of gas will expand until the gas
pressure is balanced by the external pressure.
⑤ Dalton’s law of partial pressure. If molecules do not attract or repel
one another, then the pressure exerted by one gas is not affected by
another gas. Consequently, the total pressure is given by the sum of
individual gas pressres.
4) Graham’s laws of diffusion and effusion
① Gas diffusion, the gradual mixing of molecules of one gas with
molecules of another by virtue of their kinetic properties, provides a direct
demonstration of random motion.
V1/v2 = (M1/M2)1/2
V1, v2: diffusion rates of gases 1 and 2
M1, M2: molar masses
③
Effusion is a process by which a gas under pressure escapes from
one compartment of a container to another by passing through a small
opening.
7 – 10
6. Nonideal gases (Real gases)
Although the ideal gas equation is a very useful description of gases, all
real gases fail to obey this relationship to some extent. The extent to which
a real gas deviates from ideal behavior may be seen by slightly rearranging
the ideal gas equation. For a mole of ideal gas (n = 1), the quantity PV/(RT)
equals 1 at all pressures and temperatures.
PV/(RT) = n
1) The deviation from ideal behavior depends on pressure.
① At high pressures, the deviation from ideal behavior [PV/(RT)] is large
and different for each gas.
② At low pressures (usually below 10 atm), however, the deviation from
ideal behavior is small, and we can use the ideal gas equation without
generating serious error.
2.0
1.5
H2
PV/RT
1.0
ideal gas
N2
CH 4
0.5
CO 2
0
2
4
6
8
2
10 (x 10 )
Figure. PV/(RT) versus pressure for 1 mol of several gases at 300 K. The data for CO 2
pertain to a temperature of 313 K because CO 2 liquefies under high pressure at 300 K.
2) The deviation from ideal behavior also depends on temperature.
① As temperature increases, the properties of a gas more nearly
approach those of the ideal gas.
② In general, gases deviate significantly from ideal behavior at
temperatures near their liquefaction points; that is, the deviations
7 – 11
increase as temperature decreases, becoming significant near the
temperature at which the gas is converted into a liquid.
3.0
300 K
500 K
2.0
1000 K
PV/RT
1.0
ideal gas
CO 2
0
3
6
9
(x 102)
P (atm)
Figure. PV/(RT) versus pressure for 1 mol of nitrogen gas at different temperatures. As
temperature increases, the gas more closely approaches ideal behavior.
Ideal gas
gas
Volume
liquid
solid
0
Real gas
Temperature
Figure. Volume change as a function of temperature of ideal and real gases.
7 – 12
3) We can understand the pressure and temperature effects on nonideality
by considering two factors that are considered negligible in the kinetic
molecular theory
① The molecules of a gas possess finite volumes.
② At short distances of approach, they exert attractive forces upon one
another.
(P + n2a/V2) (V – nb) = nRT
i) n2a/V2: correction for intermolecular forces of attraction
ii) nb: correction for the volume of gas molecules
Table. Van der Waals constants for gas molecules
Substance
a (L2·atm/mol2)
b (L/mol)
Substance
a (L2·atm/mol2) b (L/mol)
He
0.0341
0.0237
N2
1.39
0.0391
Ne
0.211
0.0171
O2
1.36
0.0318
Ar
1.34
0.0322
Cl2
6.49
0.0562
Kr
2.32
0.0398
H2O
5.46
0.0305
Xe
4.19
0.0510
CH4
2.25
0.0428
H2
0.244
0.0266
CO2
3.59
0.0427
CCl4
20.4
0.1383
7 – 13