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.