Charles’s Law
Recall that average kinetic energy is directly proportional to the absolute temperature.
Doubling the absolutetemperature of a sample of gas doubles the average kinetic energy
of the gaseous molecules, and the increased force of the collisions of molecules with the
walls doubles the volume at constant pressure. Similarly, halving the absolute tempera-
ture decreases kinetic energy to half its original value; at constant pressure, the volume
decreases by half because of the reduced vigor of the collision of gaseous molecules with
the container walls (Figure 12-12).
12-13 The Kinetic–Molecular Theory 467Piston10 gGas
sample3.0 L 1.5 L10 g600 K 300 KFigure 12-12 A molecular interpretation of Charles’s Law—the change in volume of a gas
with changes in temperature (at constant pressure). At the lower temperature, molecules
strike the walls less often and less vigorously. Thus, the volume must be less to maintain the
same pressure.
Kinetic–Molecular Theory, the Ideal Gas Equation, and Molecular
Speeds
In 1738, Daniel Bernoulli derived Boyle’s Law from Newton’s laws of motion applied to
gas molecules. This derivation was the basis for an extensive mathematical development of
the kinetic–molecular theory more than a century later by Clausius, Maxwell, Boltzmann,
and others. Although we do not need to study the detailed mathematical presentation of
this theory, we can gain some insight into its concepts from the reasoning behind Bernoulli’s
derivation. Here we present that reasoning based on proportionality arguments.
In the kinetic–molecular theory pressure is viewed as the result of collisions of gas mole-
cules with the walls of the container. As each molecule strikes a wall, it exerts a small impulse.
The pressure is the total force thus exerted on the walls divided by the area of the walls.
The total force on the walls (and thus the pressure) is proportional to two factors: (1) the
E
nrichment
See the Saunders Interactive
General Chemistry CD-ROM,
Screen 12.9, Kinetic–Molecular Theory
of Gases.