 In this video, I want to talk about the ideal gas law and how we can use this law in specific calculations that deal with gases. First of all, let's talk about the definition of the ideal gas law. And basically the ideal gas law simply relates the four variables that we use to describe a gas. Those four variables being pressure, volume, temperature, and the amount of gas. And it relates these variables in a closed system. So the ideal gas law works a little bit differently than the combined gas law, Boyle's law, Charles law, and Galusex law. All of those laws deal with an open system where a variable changes or you have multiple conditions that these gases are under. The difference with the ideal gas law is it's a closed system. So the ideal gas law is useful when you're given three of the four variables and you're just asked to solve for that fourth and last variable. So the ideal gas law formula is pv is equal to nrt. So the p is the pressure of the gas, v is equal to the volume, n, or the lowercase n, refers to the amount of gas present, r is a constant value. This is known as our ideal gas constant. The r value can have two different numbers. Alright, let's look at these numbers. First of all, we've got 0.0821 liters times atmospheres over moles per Kelvin. Or we have 62.4 liters times millimeters of mercury over moles per Kelvin. We have to choose the correct ideal gas constant depending on the pressure value that we're given in the problem. We'll go over that a little bit in just a second. The fourth variable is T which stands for temperature. Now let's look at an example of how we're going to use the ideal gas law in order to solve a problem. So here we have 0.250 moles of a gas. We place this gas into a container and it's at room temperature, or 25 degrees Celsius. This gas inside of this container exerts a pressure of 726 millimeters of mercury. What we want to know is how big the container is or the volume of the container that this gas is residing in. We can solve this problem using the ideal gas law. Look at the variables that are given to us in the problem. First of all, it tells us the amount of gas present. So N is equal to 0.250 moles. Then it tells us that we put this gas in a container at 25 degrees Celsius. So that's the second variable that we're given is temperature. However, the temperature is measured in Celsius. And we should know that anytime we're using any type of gas law to solve an equation, our temperature value must be converted to Kelvin first. So in order to convert Celsius value to Kelvin, we simply add 273. So that makes our temperature 298 Kelvin. The problem tells us that the pressure of this container is 726 millimeters of mercury. And it wants us to solve for volume. So here we've got four variables. Well, we're given three of the four and asked to solve for volume. Now we come to the R value. Which R value do we pick to solve this problem? We've got two R constant values. How do we pick the correct one? In this problem, our pressure is measured in millimeters of mercury. So therefore we're going to choose the R value that includes that unit in its unit. This R value uses atmospheres as its measure of pressure. Where the 62.4 liters per or multiplied by millimeters of mercury is the R value that we want to use because it contains the correct unit. Now that we have four of the five variables in the ideal gas law, we can solve for that last variable. So let's input the variables into the formula. Pressure times volume is equal to amount times our R value multiplied by our temperature. We said our temperature was 25. We converted that to Kelvin to give us 298 Kelvin. So we've inputted all of our variables. We want to solve for volume. In order to solve for volume, we've got to get all of the variables on the same side of the equal sign as the variable that we want to solve for, in this case volume, over to the other side. So we need to get this 726 millimeters of mercury over to the right side of the equation. In order to do that, we are going to multiply by the inverse. Here 726 is in the numerator. It's on top. So the inverse is putting 726 millimeters of mercury on the bottom. What we do to one side, we have to do the other side. On the left side of the equation, our 726 will cancel out. So now we know that volume is equal to 0.250 multiplied by 62.4 multiplied by 298. Then we're going to divide that by 726. When we solve for volume, we find that it is equal to 6.40 liters. Whenever we put this gas into a container and it exerts its pressure of 726 millimeters of mercury, it's at room temperature or 25 degrees Celsius and it contains 0.250 moles of gas. The volume of that container that that gas is in must be 6.40 liters.