Kinetic Molecular Theory and the Ideal Gas Laws

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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