Boyle's Law

Let's take a look at the relationship between the pressure and volume of a gas. To do this, let's imagine that we have a container similar to the ones we have seen before, where I have a plunger at one end of this container. It's full of gas particles, which I'll indicate as usual with these red circles here at this point, the pressure in this gas sample is relatively low. P stands for pressure, but as we learned earlier, because gas is compressible, I can put pressure on this piston. and I can push it further into the container and what will eventually happen after the pressure has increased.

I'm going to have all of these gas particles compressed into a much smaller area, so the pressure here is much higher, let's see. What happens to the volume during this change? The volume here, relatively speaking, is quite high, these gas particles have a good amount of space to move around, on the other hand, the volume here is quite low, we have compressed them into a much smaller space. so as the pressure increases from low to high the volume decreases what this means is that the relationship between pressure and volume is an inverse relationship as the pressure increases the volume decreases they move in different directions, On the other hand, if the pressure went down the volume could increase, you are familiar with an inverse relationship because you see this a lot with the cost of the things you buy, as something becomes more expensive the fewer people want to buy it, on the other hand, as the price of something falls further. and more people want to buy it, so that is an example of an inverse relationship between things moving in different directions, pressure and volume also move in different directions because they have an inverse relationship.

Let's see how we can actually plug numbers into an equation and use this. relationship to solve mathematical problems the relationship between the pressure and volume of a gas is described by Boyle's law, named after the scientist who discovered the relationship between the pressure and volume of a gas. This whole law can be stated that p1 multiplied by v1 is equal to p2 multiplied by v2 Boyle's law assumes that we have a gas and it undergoes some type of change, maybe we increase or decrease the pressure and change the volume in some way, so that p1 v1 means that the pressure and volume before the change were multiplied together so here we have before is equal to the pressure and volume after the change multiplied together, so let's jump right into an example of a math problem that we could do to see how can we use this.

I think it will make a lot more sense here. a sample problem that we say here at 1.70 atm a sample of gas occupies four point two five liters if the pressure on the gas is increased to two point four atm what will be the new volume, as we said before, a change occurs we increase the pressure, now we want to see the before the gas and after the gas find out which of these variables we need to solve for. Well, at one point seven atm, a sample of gas occupies four point two five liters, so we have. the previous pressure one point seven zero ATM and we have the previous volume four point two five liters now we say if the pressure of the gas increased to two point four atm what will be the new volume then we have P 2 we have the second pressure after the change we do not have the volume, so let's solve for V two.

We want to rearrange this by moving P two under this other thing, so we'll get P. 1 V 1 divided by P 2 equals v2 and now let's go ahead and plug in our numbers: the initial pressure is 1.70 ATM times the 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 the atmospheres will cancel out We stick with the leaders and our final answer will be three point zero one liter before we're done, let's see if this Makes sense, well, we start at four point two five liters and we increase the pressure of the gas, which means we compress it into a smaller space, so that three point zero a liter 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 Boyle's law, how Boyle discovered this relationship in the first place or want to see graphs or have seen something in our textbook that says P multiplied for V equals K, go ahead and watch the most complex video on Boyle's law; Otherwise, you can skip to the next video on the gas law.