Professor Dave here, let’s learn about kinetic
molecular theory. We have learned about different laws that
can be applied to ideal gases. Like any laws, these ideal gas laws are merely
summaries of observations, such as the way pressure and volume are inversely proportional,
or the way volume and temperature are directly proportional. We observe these relationships to always be
true, but again, just like any other law, it does not explain why. For that, we are going to need something more
powerful, we need a theory. And the theory that explains the behavior
of gases is called kinetic molecular theory. This theory consists of five postulates, and
from them all of the ideal gas laws can be derived, so let’s go through each postulate
and talk about what they mean. Number one. We make the assumption that a gas is made
up of particles, whether they are individual atoms or small molecules, and that these particles
are always in motion. Throughout their motion, these particles travel
in straight lines unless they collide with something, whether that is another gas particle
or the walls of whatever container they are in, at which point they will bounce off and
change directions. This vision of gas particles as moving around
like billiard balls on a pool table seems pretty intuitive, but it is an important one,
as it implies that tiny particles like atoms are subject to laws of motion just like macroscopic
objects are, and that they won’t just stop in their tracks and change direction without
cause. Number two. We can assume, under most sets of conditions,
that the gas is mostly empty space. This means that the fraction of the total
volume that is occupied by the particles of gas themselves is so close to zero that we
simply ignore it, regarding them as essentially dimensionless points. This is in stark contrast with solids and
liquids, which are non-compressible, because all the particles are pretty much right up
against one another, there is very little empty space between the particles. Number three. The phenomenon we refer to as pressure is
actually the gas particles in the sample imparting some of their kinetic energy of motion onto
the walls of the container every time they collide with it, just like a macroscopic object
would transfer energy onto some surface during a collision. It may seem like atoms are so tiny that they
can’t impart much force, and that’s true, but remember that in any sample of gas there
are trillions and quadrillions of particles, so all together, it can add up to a lot. If there are a lot of particles moving very
fast, there are many collisions, so the system has a lot of pressure. If there are very few particles moving very
slowly, there are very few collisions, and thus the system has very low pressure. Number four. We ignore the possibility that gas particles
could exert any kind of gravitational or electromagnetic influence on one another. Although they technically can interact slightly,
due to dispersion interactions or even dipole-dipole interactions if the molecules are polar, we
consider such interactions to be entirely negligible, so any collision will be purely
elastic, or occurring with no loss of kinetic energy. They will simply bounce off of one another,
once again, like balls on a pool table. And number five. The average kinetic energy of the particles
in the gas is proportional to the temperature of the gas in Kelvin. This means that if you increase the temperature,
you increase the kinetic energy, which means the particles will be moving faster. This means that in this specific context,
temperature is entirely indicative of average molecular velocity. So those are the five postulates of kinetic
molecular theory. These postulates are powerful in explaining
the behavior of gases, and to see how, let’s quickly review our understanding of some of
the ideal gas laws. For Boyle’s law, we can see that if we keep
temperature constant, meaning the molecules move at the same speed, increasing the volume
must decrease the pressure, because the particles have to move farther to reach the sides. And decreasing the volume must then increase
the pressure. This is why pressure and volume are inversely
proportional. For Charles’s law, if we increase the temperature,
in order to keep pressure constant, meaning the frequency of collisions stays the same,
the volume must expand, because if the particles move faster but also move farther, they will
hit the sides with the same frequency as before. This is why volume and temperature are directly
proportional. Looking at Amontons’s law, we can see that
increasing the temperature while keeping the volume constant, the pressure must increase,
as the particles are moving faster. This is why pressure and temperature are directly
proportional. All of these laws, which are simply statements
of observation, now make perfect sense in the context of kinetic molecular theory.
