# Boyle's Law

**Boyle s Law** states that volume of a given amount of gas held at a constant temperature varies inversely the with pressure. The relationship between pressure and volume of Boyle s Law is expressed in mathematical terms as *P1V1=P2V2*.

So have you ever come home from a long plane ride only to open your suitcase to find your shampoo and toothpaste explode all over your clothes? It's happened to me a few times and I kind of wanted to know why. And the reason is, it's due to Boyle's law. Boyle's law was discovered by Robert Boyle, coincidentally, in the 1600s he was in Ireland. He did some Chemistry back then and he discovered that the volume of a given amount of gas held at a constant temperature varies inversely with the pressure.

Alright, so what does that mean? Let's look at this picture and this'll actually help us describe that. Alright, let's say you have a canister of gas, ten litres of gas inside and at a pressure of one atmosphere on there. If I multiply if I take my constant and multiply pressure times the volume, I find that if we have a constant of 10 atmosphere litres. Okay, fair enough. Let's say I pushed out on that canister. I pushed on it with twice as much pressure. So now pressure is two atmosphere. What's going to happen to the volume? Well, you guessed it. It's going to half there is a relationship between the pressure and the volume of the container as long as the temperature is constant. So if we were to multiply these we get the same thing as we did before, 10 atmosphere litres. So notice that p1v1=p2v2. These two sides are the same. Great. okay. So let's go over here.

The relationship between the pressure and the volume, what is that? Well, we notice that as pressure goes up so does the volume goes down. They have an inverse relationship to each other. And also pressure goes down volume will then go up. They're completely inverse of each other.

How do we graph that. Well, if we have volume on the y axis and pressure on the x axis, it will have a graph and we will graph all our points, it would have a graph that looks similar to this. Notice that this will never reach, volume will never reach zero and the pressure will never reach zero. That is because you will never have a volume that's nothing and you'll never have a pressure that's nothing. So we're going to have a curved graph that looks similar to this. Notice it's also a negative slope because the relationship is inverse.

Alright. If we were to mathematically look at Boyle's law, we would let's reiterate the fact that pressure one times volume one equals to pressure two times volume two as we demonstrated earlier. That's our mathematical relationship. Okay. So let's actually put this into practice. Let's say you have sample of neon gas that occupies 0.22 litres at 0.86 atmospheres. What will be its new volume at 29.2 kilo pascals? Well, this first thing you should notice is that when we're dealing with pressure, we want to make sure that the pressure is always in the same unit. In this case, pressure is in atmospheres in the first, in the first scenario and the second one it's in kilo pascals. I don't like that. So I'm going to put them in the same unit. I'm just going to randomly choose odd atmospheres. It doesn't matter if you choose atmospheres or kilo pascals, it will give you the same answer. But I like atmospheres.

So I know that one atmosphere equals 101.3 kilo pascals. Okay? So I'm going to change 29.2 kilo pascals to atmospheres. So I know that 101.3 kilo pascals equals one atmosphere. So 29.2 divided by 101.3 give me 0.2, 0.288 atmospheres. Okay. So let's start off with this. So instead of using this number, I'm going to use this number. The sample of neon gas occupies this is my v1 and this is my p, my p1. So 0.860 atmospheres times 0.220 litres equals, when our new volume and our second pressure is 0.288 atmospheres and we don't know our new volume. That's what we're looking for.

Now, before we even solve this, let's predict what our volume should be. Our atmosphere actually goes from 0.8 down to 0.2 or 0.3. So it drops. What's going to happen to our volume? Our volume should increase according to our relationship that we discovered earlier. So let's see if that happens. 0.86 times 0.22 will give me, I don't know that 0.86 times 0.22 gives me 0.1892. Equals 0.288v2. So we're going to divide by 0.288. Divided by 0.288. And we get 0.66 litres. Our second volume is 0.66. So that the volume with 0.220 not 0.66. It did go up which is what we predicted. So we just proved Boyle's law.

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