hey it's professor Dave let's talk about ideal gases
let's recall our definition of a gas as the phase of
matter where atoms of a substance are in motion and fill their container
if we make a couple simplifying assumptions about gases
we can make some easy predictions those are that one
particles in the gas are dimensionless points in random motion
and the identity of the gas is irrelevant, could be anything, and two
that the particles don't interact apart from elastic collisions
bouncing off one another like balls on a pool table. these things aren't
completely true
but they make the math easy and surprisingly accurate
so these kinds of samples are called ideal gases
when examining an ideal gas we want to be able to discuss four variables
one: pressure, this is the force the gas is exerting on its container
or rather how much the particles are hitting the sites. two:
temperature, this is the amount of heat energy available to be transferred into
kinetic energy of motion
the higher the temperature the faster the particles move
3: volume, how big is the container
and four: moles, how many particles are there
in the container. so how many particles
how big is the container, how fast are the particles moving
and how often do they hit the sides. as it turns out these variables depend on
one another in interesting ways
that have been formulated into laws. let's look at a piston
while keeping the moles and temperature the same, in other words the same number
of particles moving at the same speed
if we compress the volume the pressure must go up
the particles will be hitting the sides more often because there is less
distance to travel to hit a side
that means that pressure and volume are inversely proportional
if one goes down the other goes up. this is expressed
in Boyle's law. P1V1 equals P2V2
if we double one variable we have to cut the other one in half
in order to keep this equation valid. volume and temperature are also related
if we have gas in a balloon and we heat it up, the particles will move more
quickly
in order to keep pressure constant
or hit the sides with the same frequency, the volume will have to expand
this means that volume and temperature are directly proportional
if one doubles the other must double. this is expressed
in Charles's law. when we do calculations with temperature
we must always use an absolute temperature scale called the Kelvin
scale
one degree kelvin is the same magnitude as one degree Celsius
but zero kelvin is absolute zero
the lowest temperature possible, a complete absence of heat energy
this helps us avoid weird mathematical issues that would arise
if we were doing a calculation involving a negative or zero temperature
to get Kelvin from celsius just add 273
to go the other way, subtract. the combined gas law
is like a combination of Boyle's and Charles's, avogadro's law says that equal volumes of
gas at the same temperature and pressure
contain the same number of molecules, specifically
that one mole of ideal gas occupies 22.4 liters
at standard temperature and pressure, regardless of the identity of the gas
lastly all the variables correlate in one equation
called the ideal gas law. this also contains the gas constant
R, which makes these calculations intelligible in our manmade units
there are a number of values for R depending on the units
we will predominately use this one. this equation is useful when we aren't
looking at a change
but just to know the value of all four variables at once
like in this case we could know the pressure
temperature and volume for a gas and quickly calculate how many moles of
particles
must be in the sample. so if you're looking at a sample of gas
and you have three of the four variables you can solve for the fourth
using the ideal gas law. if you are given some initial conditions as well as some
final conditions
you can use one of the other laws to find the other information
just plug in what you know and solve for what you don't. let's check comprehension
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