 In this video, I'm going to talk about another one of the gas laws being Avogadro's law. Avogadro's law states that the volume of a gas is directly related to the number of moles of that gas when we hold pressure and temperature of the gas constant. Alright, so the important term here is this direct relationship between volume and number of moles. What does it mean to have a direct relationship? If we increase the number of moles of a gas then we would expect the volume that that gas occupies to also increase. If we decrease the number of moles then we would expect the volume of that gas to decrease. This can be shown graphically graphing volume and number of moles like this. So if our number of moles increase our volume should also increase. The formula for Avogadro's law is stated V1 over N1, N being number of moles is equal to V2 over N2. The 1 and 2 subscripts indicate a gas under condition number 1 and condition number 2. Let's use Avogadro's law this formula here to solve this problem. We have a sample of helium gas and we know that we have 0.75 moles of this gas and it occupies a volume of 1.5 liters. What will the volume be if we increase the number of moles of this helium gas to 1.2 moles? In order to solve for V2 then we need to determine what values, what variables are given to us in the problem. So we are told the number of moles under condition 1 is 0.75 moles. We are also told that V1 the volume of this 0.75 moles is 1.5 liters and the problem tells us that we are going to increase the number of moles of gas so this is going to be N2 our gas under condition number 2 to 1.2 moles. And then the problem asks us to solve for V2. How do we solve for V2? Well we are going to use this formula for our Avogadro's law. What we are going to do is input in our variables V1, 1.5 liters divided by N1 which is 0.75 moles. This is equal to V2 what we are trying to solve for divided by N2 which is 1.2 moles. In order to solve for V2 we first need to move our 1.2 moles to the left side of the equal sign so that we have our one variable that we are solving for by itself on one side of the equals sign. In order to do that we are going to multiply by the inverse which is 1.2 moles over 1 this allows us to cancel out these values. What we do to one side we have to do the other side of the equal sign we are going to multiply this side by 1.2 moles over 1. So what this tells us is that V2 the variable that we are solving for is going to be equal to 1.2 moles multiplied by 1.5 liters and then we are going to divide that all by 0.75 moles. In order to ensure that we set up our problem correctly we can determine what units can cancel out. You see here we have moles over moles those units will cancel out. The only unit that we are left with is liters and that is what we expect because volume is measured in liters. So we input this and we solve for V2 which comes out to be 2.4 liters now does this agree with Avogadra's law? Well Avogadra's law tells us that number of moles and volume have a direct relationship. If we increase the number of moles of our gas we would expect the volume holding that gas to also increase and that is exactly what we saw the volume increase from 1.5 liters to 2.4 liters.