 In this video, I'm going to go over one of the gas laws called Boyle's law. Boyle's law states that the pressure of a gas is inversely related to the volume when temperature and the amount of gas are held constant. The important term here is this inverse relationship between pressure and volume. What does it mean to have an inverse relationship? What that means is that when pressure of the gas is increased, the volume will decrease. If we increase the volume of the gas on the other hand, then we would expect for pressure to decrease. Graphically, we can show this relationship to look something like this. As we increase the pressure here along our x-axis, the volume decreases. The formula for Boyle's law is P1 times V1 is equal to P2 times V2. This is pressure and volume at condition number one. When they are multiplied, they are equal to the pressure and volume of the gas under condition number two. So how can we use this formula in a problem? If we look right here at this problem, we have a sample of nitrogen gas. This nitrogen gas has a volume of 4.2 liters, and it's at a pressure of one atmosphere. If we decrease the pressure to 0.75 atmospheres, we have no change in temperature and no change in the amount of gas, what will be the new volume? Before we solve it, we can use Boyle's law to predict what we expect to happen. If we decrease the pressure of the gas from one atmosphere to 0.75 atmospheres, then this inverse relationship indicates that the pressure or the volume of the gas should increase. Let's see if that holds true. So let's determine what variables the problem gives us. It tells us that this gas under condition one has a volume of 4.2 liters. It also tells us that the pressure of this gas at condition one is one atmosphere, and then it tells us that we're going to decrease the pressure to 0.75 atmospheres. So that's going to be our P2, and it's asking us to solve for the volume when we decrease the pressure. So we are going to solve for V2. In order to solve for V2, we just input the values given to us in the problem into our formula. So we've got P1, we're going to multiply that by V1, which is 4.2 liters, and that's going to be equal to 0.75 atmospheres multiplied by V2. In order to solve for V2, we need to get this pressure value on the left side of the equal sign. In order to do that, we use algebra and we just multiply by the inverse. The inverse of 0.75 atmospheres in the numerator is going to be 1 over 0.75 atmospheres. What that allows us to do is to cancel those values out. What we do to one side of the equal sign, we always have to do the other side, so we're going to multiply this side by 1 over 0.75 atmospheres. So when we clean this equation up, we find that V2 is equal to 1 multiplied by 1 multiplied by 4.2 liters, and all of that's going to be divided by 0.75 atmospheres. Let's make sure our units cancel out correctly to ensure that we've set up the problem correctly. Here we have atmospheres in the numerator, atmospheres in the denominator, those will cancel out. The only unit that we're left with is liters. We're solving for volume, which is measured in liters. When this is solved, we find that V2 is equal to 5.6 liters. So in fact what we see happening is when we decrease the pressure of our gas, we see that inverse relationship of our volume increasing when pressure decreases.