Using descriptions like “large” and “frequently” does not convey the nature of gases as well as specific numbers. Consider nitrogen molecules
(N 2 ), the most common molecule in our atmosphere. In one cubic meter of nitrogen molecules at 0°C and one atmosphere of pressure, there
are 2.69×10^25 molecules. They occupy just 0.07% of the space and move at an average speed of 454 m/s. The molecules run into one another
a lot: There are 9.9×10^34 collisions each second between molecules in that space. The condition of 0°C (273 K) at one atmosphere is called
standard temperature and pressure and is often used in calculations involving gases.
The molecules collide elastically with both each other and the container walls. The molecules only exert forces on one another when they
collide. Forces that they exert on one another at other distances are negligible.
Each molecule can be considered as a small, hard sphere. In elastic collisions, both kinetic energy and momentum are conserved. The
velocities of the molecules change after a collision, but the total momentum and kinetic energy of the molecules remain the same.
The walls of the container are rigid. When a molecule collides with a wall, its speed does not change although its velocity does (because its
direction changes). Newtonian physics can be used to analyze the collisions of the molecules with each other and with the walls of the
container.
19.2 - Gas pressure
Gas molecules not only collide with each other, but also with the walls of any container.
During these collisions, the molecules exert a force on the walls. Dividing the total
amount of force caused by these collisions by the surface area of the walls yields the
absolute pressure exerted by the gas.
In this section, we consider three factors that qualitatively influence gas pressure. If you
tried the simulation in the introduction section, some of this discussion should be
familiar to you. In this section, we show two containers of gas. For visual clarity, we
show only a small fraction of the actual number of particles in the containers. Each
particle in the simulation represents about 3.4×10^18 molecules. We have done the
calculations assuming that these are nitrogen molecules in a container about 10í^2 m
wide. In the container on the left in each diagram, the pressure is one atmosphere and
the temperature is 0°C. We vary one property at a time in each illustration.
Consider two containers of equal volume containing different numbers of gas particles
moving at the same speed. This is shown in Concept 1. The pressure will be greater in
the container on the right (the one that contains more molecules). Why? With everything
else equal, the collisions are more frequent in the container with the greater number of
molecules, which means the molecules collectively exert more outward force on the
walls of the container. Greater average force on the same amount of surface area
means the pressure is greater.
The relationship between molecular speed and pressure is shown in Concept 2. Now
each container contains the same number of molecules, but the container on the right
has faster moving molecules (at a greater temperature) and, thus, greater pressure.
Why does pressure increase with the speed of the molecules? There are two reasons
why this is the case. First, when molecules move faster, they collide more frequently
with the walls of the container. Second, when a molecule strikes the wall and rebounds,
the molecule exerts more force at greater speeds than at slower speeds. (Imagine the
force involved in a tennis ball rebounding off you when it is thrown at 1 m/s versus
20 m/s.) Since the average speed of molecules increases with temperature, this means
pressure also increases with temperature.
In Concept 3 the temperature and the number of molecules are the same for each
container. We change the volume of the container on the right. The pressure
decreases when the container volume increases; pressure is inversely proportional to
volume. In a larger container, the molecules collide less frequently with the walls. The
surface area of the container also increases, so pressure (force divided by area)
decreases for that reason, too.
Pressure increases with
Number of molecules
Pressure increases with
Speed of molecules (temperature)
Pressure decreases with
Volume of container