The Foundations of Chemistry

Plan

(a) Ideal gases obey the ideal gas equation. We can solve this equation for P.

(b) To describe methane as a nonideal gas, we use the van der Waals equation and solve

for P.

Solution

(a) Using the ideal gas equation to describe ideal gas behavior,

PVnRT

P48.9 atm

(b) Using the van der Waals equation to describe nonideal gas behavior,

P (V
nb)nRT

For CH 4 , a2.25 L^2 atm/mol^2 and b0.0428 L/mol (see Table 12-5).

P 0.500 L
(1.00 mol)
0.0428 

(1.00 mol)
(298 K)

Combining terms and canceling units, we get

P9.00 atm

24

0

.5

.45

L

7

a

L

tm

53.6 atm

P 44.6 atm

You should now work Exercises 96 and 97.

Repeating the calculations of Example 12-23 with the volume twenty times higher

(V10.0 L) gives ideal and nonideal pressures, respectively, of 2.45 and 2.44 atm, a differ-

ence of only 0.4%.

Many other equations have been developed to describe the behavior of real gases. Each

of these contains quantities that must be empirically derived for each gas.

0.0821 Latm



molK

L



mol

(1.00 mol)^2 (2.25 L^2 atm/mol^2 )



(0.500 L)^2

n^2 a



V^2

(1.00 mol)


0.08

m

21

ol

L

K

atm

(298 K)



0.500 L

nRT



V

The pressure is 4.3 atm (8.8%) less
than that calculated from the ideal
gas law. A significant error would be
introduced by assuming ideal behavior
at this high pressure.

474 CHAPTER 12: Gases and the Kinetic–Molecular Theory

Key Terms

Absolute zero The zero point on the absolute temperature scale;

273.15°C or 0 K; theoretically, the temperature at which mol-
ecular motion is a minimum.
Atmosphere (atm) A unit of pressure; the pressure that will sup-
port a column of mercury 760 mm high at 0°C; 760 torr.
Avogadro’s Law At the same temperature and pressure,
equal volumes of all gases contain the same number of
molecules.
Barometer A device for measuring atmospheric pressure. See
Figures 12-1 and 12-2. The liquid is usually mercury.

Boyle’s Law At constant temperature, the volume occupied by

a given mass of a gas is inversely proportional to the applied

pressure.

Charles’s Law At constant pressure, the volume occupied by a

definite mass of a gas is directly proportional to its absolute

temperature.

Condensed states The solid and liquid states.

Dalton’s Law of Partial Pressures The total pressure exerted

by a mixture of gases is the sum of the partial pressures of the

individual gases.