The Foundations of Chemistry

The average kinetic energy of gaseous molecules is directly proportional to the

absolute temperature of the sample. The average kinetic energies of molecules of

different gases are equal at a given temperature.

For instance, in samples of H 2 , He, CO 2 , and SO 2 at the same temperature, all the mole-
cules have the same average kinetic energies. But the lighter molecules, H 2 and He, have
much higher average velocities than do the heavier molecules, CO 2 and SO 2 , at the same
temperature.
We can summarize this very important result from the kinetic–molecular theory.

Average molecular KEKET

or

Average molecular speedu



Molecular kinetic energies of gases increase with increasing temperature and decrease
with decreasing temperature. We have referred only to the averagekinetic energy; in a
given sample, some molecules may be moving quite rapidly while others are moving more
slowly. Figure 12-9 shows the distribution of speeds of gaseous molecules at two temper-
atures.
The kinetic–molecular theory satisfactorily explains most of the observed behavior of
gases in terms of molecular behavior. Let’s look at the gas laws in terms of the kinetic–
molecular theory.

T



molecular weight

A bar over a quantity denotes an

averageof that quantity.

12-13 The Kinetic–Molecular Theory 465

See the Saunders Interactive

General Chemistry CD-ROM,

Screen 12.11, Distribution of Molecular

Speeds.

Figure 12-9 The Maxwellian distribution function for molecular speeds. This graph shows
the relative numbers of O 2 molecules having a given speed at 25°C and at 1000°C. At 25°C,
most O 2 molecules have speeds between 200 and 600 m/s (450–1350 miles per hour). Some
of the molecules have very high speeds, so the distribution curve never reaches the
horizontal axis.

Fraction of moleculesat a particular speed

Very few

molecules

have very

low speeds

At 25°C more molecules are moving

at about 400 m/s than at any other speed

At 1000°C many,

many more molecules

are moving at

1600 m/s than at 25°C

O 2 at 25°C

O 2 at 1000°C

O 2 at 25°C O 2 at 1000°C

Molecular speed (m/s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000