slightly less force than ideal gases. However, most gases (especially lighter ones
such as hydrogen and helium) under typical temperatures and pressures act
enough as an ideal gas to make the concept useful.
In order to succeed on this test, you’ve got to know the relationships that exist
among the temperature, volume, and pressure of an ideal gas.
Pressure and Temperature Suppose we start with a 3 L sample of gas at 200 K
and a pressure of 900 torr. If we raise the temperature to 400 K without changing
the volume of the container, what will happen? Because we doubled the
temperature, the pressure will double, too—to 1,800 torr. In other words, if
volume doesn’t change, then pressure is directly proportional to the temperature
in degrees Kelvin.
Why is that? The increased temperature provides the gas molecules with more
heat, which is converted to kinetic energy, which means, basically, movement.
The molecules start moving faster, and if they’re moving faster, they’re hitting
the walls of the container harder, and that increases the pressure.
The technical term for this phenomenon is kinetic molecular theory, which
states that the kinetic energy of a gas molecule increases proportionally with
temperature in degrees Kelvin. The mathematical formula that relates
temperature and pressure while volume is held constant is called Gay-Lussac’s
Law, and is represented as =
While any unit of pressure can be used as long as it’s consistent across both sides
of the equation, temperature must be measured in Kelvins to make use of this
law.
Pressure and Volume Now suppose we start with the same 3 L sample of gas at
200 K and 900 torr. Imagine that, without changing the temperature, we
suddenly increase the size of the container to 6 L. We’ve doubled the volume of
the gas, and we haven’t changed the temperature. What happens to the pressure
of the system? It goes down by one-half, to 450 torr. Here’s why. The gas
molecules have just as much kinetic energy as they had before, but they’ve got