# Boyle's Law

let's take a look at the relationship between pressure and volume of a gas to do this we're going to imagine that we have a container similar to ones that we've looked at before where I've got a plunger on one end this container is filled with gas particles which I'll indicate as usual by these red circles here right now the pressure on this gas sample is relatively low P stands for pressure but as we've learned previously because gas is compressible I can put pressure on
this piston and I can push it further into the container and what's eventually going to happen after I've increased the pressure there is I'm going to have all these gas particles squeezed into a much smaller area so over here the pressure is much higher let's look at what happens to volume during this change volume right here relatively speaking is pretty high these gas particles have a good amount of room to move around in on the other hand the volume over here is pretty low
we've squeezed them into a much smaller space so as pressure goes up from low to high volume goes down what this means is that the relationship between pressure and volume is an inverse relationship as pressure goes up volume goes down they move in different directions on the other hand if pressure were to go down the volume would be able to go up you're familiar with an inverse relationship because you see this a lot with the cost of things you buy as something becomes more expensive
fewer people want to buy it on the other hand as the price of something lowers more and more people want to buy it so that's an example of an inverse relationship to things moving in different directions pressure and volume also move in different directions because they have an inverse relationship let's look at how we can actually plug numbers into an equation and use this relationship to solve math problems the relationship between pressure and volume of a gas is described by

## Boyle

's law which is named after the scientist who figured out what the relationship between pressure and volume of a gas was all this law can be stated that p1 times v1 equals p2 times v2

## Boyle

's law assumes that we have a gas and it experiences some sort of a change maybe we increase or decrease the pressure change the volume in some sort of a way so p1 v1 means that the pressure and the volume before the change multiplied together so here we have before equals the pressure and the
volume after the change multiplied together so let's move right into an example of a math problem that we might do to see how we can use this I think it'll make a lot more sense here is a sample problem we say here at 1.70 atm a sample of gas takes up four point two five liters if the pressure on the gas is increased to two point four atm what will the new volume be so as we said before there's a change that takes place we increase the pressure we now want to look at the before of
the gas and after the gas figure out which of these variables we need to solve for okay at one point seven atm a sample of gas takes up four point two five liters so we have the before pressure one point seven zero ATM and we have the before volume four point two five liters we now say if the pressure on the gas increased to two point four atm what will the new volume be so we have P 2 we have the second pressure after the change we don't have the volume so it's going to be V two that
we're going to be solving for we'll want to rearrange this by moving P two under under this other thing so we're going to get P 1 V 1 divided by P 2 equals v2 and now let's go ahead and plug in our numbers initial pressure is 1.70 ATM times initial volume which is 4.25 liters divided by the second pressure which is two point four zero atm now let's take a look at how we set this up ATMs up here ATMs down here which means that the atmospheres are going to cancel out we're
left with leaders and our final answer is going to be three point zero one liters before we before we call it quits let's see if this makes sense well we started at four point two five liters and we increase the pressure on the gas which means that we squeezed it into a smaller space so three point zero one liters is less than four point two five liters this makes sense that we have a smaller volume after increasing the pressure now if you need to learn more about

's law how

## Boyle

figured out this relationship in the first place or want to look at graphs or seen something in our textbook that says P times V equals K go ahead and look at the the more complex

## Boyle

's law video otherwise you can just move on to the next gas law videos