# Ideal Gas Law Introduction

so here I have a tank filled with gas and these little dots represents some of the gas particles it would be in this tank the arrows I put in here because all of these particles are in constant random motion they're like a bunch of hyperactive little kids running into each other all the time banging into the sides of the container and so forth so we got this tank of gas let's think about the characteristics that we could use to describe it all right so one of the things that we can do is we could say what its temperature is the higher the temperature remember the faster these gas particles are moving around so temperature is very important when we talk about gas temperature for gases should always be reported in Kelvin so we can say for example that the temperature of this guy here is 313 Cal and that's how hot these gas particles and sample are when you talk about gas another important characteristic is pressure all right how hard are these gas particles bouncing it against the side of the tank how much pressure are they exerting on them and we could measure these with you know a pressure gauge or something like that on the top of this tank we could say I don't know the pressure for this is is three point one eight atm all right that might be a pressure and another thing that we spent a lot of time talking about when it comes to gas is volume and again I have these letters here that are how each one of these things are abbreviated volume V the volume of this...

tank might be something like ninety five point two liters and finally look at these particles that I've drawn right there's a certain amount of gas that's in here and the amount of gas which is abbreviated by the letter little letter n is usually reported in moles which is a convenient measure of how much of something we have so we could say that the amount of gas in this tank is I don't know seven point five volts now whenever we have a sample of gas like this you know a tank or it's in a balloon or wherever it is we can describe we can give it these various characteristics and it turns out that also for any sample of gas if we know three of these characteristics we can figure out what the fourth is all we need to do is know three and in order to do that we use an equation that's a representation of the

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gas law and it's written as P times V pressure times volume equals n the amount of gas times R times T temperature I'll get to our in a second don't worry about it for right now it's going to be a number that we know okay so let's say for example that we didn't know what pressure was but we still knew the temperature volume and the amount of gas no big deal we can take the equation PV equals NRT and rearrange it divide both sides by V get rid of the V and then we'd have P equals NRT divided by V plug these values in and we could figure out what the pressure was okay or let's say that we knew what the pressure was...of a particular gas sample we know the temperature wasn't the volume but we didn't know what the amount of gas was we didn't know how much we had we could figure out that fourth characteristic by rearranging the

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gas law for n cancelling out R and T on one side rearranging it to solve for N and then we could plug in the pressure the volume and the temperature and we can figure out the amount of gas so in other words if we know three of these characteristics we can always figure out what the fourth is so you may be asking yourself okay so our what's our R is what we call a constant it's a number that we know ahead of time that doesn't depend on the variables and our property the R that I'm going to be using most the time for the videos is 0.0821 liters times atm / Kelvin times mol now notice that this is a fraction it has both the top and a and it also is not just a number but it has units and check this out the units on our match the units in my problem they match the characteristics that I'd be using right so I have leaders here leaders there ATM ATM Kelvin Kelvin and moles moles you always want the the the units on our to match the units of the characteristics in your## ideal

gas problem okay so because you always want the units to match there are also different values of our although I'm going to be using this mostly for the videos up doing for example let's say that instead of atm I was using a pressure that was in millimeters of...mercury in this case I wouldn't want to use this R here I want to use this R here so that the unit's match millimeters of mercury here millimeters of mercury here and the numbers different 62.4 so again that's what I use here let's say that instead of millimeters of mercury my pressure was given to me in kPa I would then use this value of R so that the unit's match I've got kPa here kPa here and all the others are the same so 8.314 that now as i keep saying in most of the videos that i've been that i'm going to be doing i'm going to be using this top arm with atm but you may be asked by your teacher to use a different r it's no big deal that's probably just because they're giving you problems that have different pressure units and they want the pressure units to match so don't worry at all if you're using one of these other r's setting up and solving the