In another lesson, you learned that the ideal gas law is expressed as PV = nRT. In this video lesson, we’ll go one step further, examining how to rearrange the equation to solve for a missing variable when the others are known.

## The Ideal Gas Law

In another lesson, you learned about ideal gases and the ideal gas equation. Ideal gases are just what they sound like – ideal. But since real gases behave similarly to ideal gases at normal temperatures and pressures, we can use the ideal gas equation to predict the behavior of real gases under these conditions.First, let’s review the ideal gas law, PV = nRT. In this equation, ‘P’ is the pressure in atmospheres, ‘V’ is the volume in liters, ‘n’ is the number of particles in moles, ‘T’ is the temperature in Kelvin and ‘R’ is the ideal gas constant (0.0821 liter atmospheres per moles Kelvin).

Just like any equation, if we know three of those four variables (other than R, which we already know because it is a constant), we can rearrange the equation to calculate the unknown.

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## Using the Ideal Gas Law

Let’s start with a very simple example to see how this works. Say we want to calculate the volume of 1 mole of gas at 273 K (which is the same as 0 ;C) and 1 atmosphere of pressure.

Here’s what our equation looks like when we fill in the variables we do know:1 atm * V = 1 mol * 0.0821 atm L / mol K * 273 KIf we want to find the volume (V), we simply rearrange the equation to get this variable by itself. We do this by dividing by the pressure, 1 atm (atmosphere). So, now our equation looks like this:V = (1 mol * 0.0821 atm L / mol K * 273 K) / 1 atmThe moles cancel out, as do atmospheres and Kelvin. All we’re left with in terms of units is liters, and then to get our volume, we simply do the math.

Our final answer is 22.4 L. Make sense?Let’s try another example, this time solving a real-life example. Suppose you want to calculate the temperature of the gas in your bike tire. As long as you know the other variables, you can do this quite easily! In this case, the pressure is 1.14 atm, the volume of the tire is 5.

00 L, and we have 0.225 moles of gas. So, our original equation looks like this:1.14 atm * 5.00 L = 0.

225 mol * 0.0821 atm L / mol K * TTo get temperature alone, we simply divide by n and R to get:(1.14 atm * 5.00 L) / (0.225 mol * 0.0821 atm L / mol K) = TOnce we do the math, we end up with 310 K, because all of our other units cancel out.

And what exactly is 310 K? Well, that’s about 37 ;C, or about 98.6 ;F. That’s pretty warm!The best part about this equation is that you can find any variable as long as you have the other three! So, if you know temperature, pressure and number of moles, you can easily find the volume. Likewise, if you know the volume and also know the temperature and pressure, you can solve the equation to calculate how many moles there are. This makes the ideal gas law ‘ideal’ to work with!

## Lesson Summary

We know that ideal gases are just that – ideal.

But since real gases can behave like ideal gases under the right conditions, this allows us to use the ideal gas law to predict their behavior. The ideal gas law states that PV = nRT, or, in plain English, that pressure times volume equals moles times the gas law constant R times temperature. As long as you know three of the four variables, you can easily rearrange and calculate the missing one, no matter which one that may be!

## Learning Outcomes

Once you’ve completed this lesson, you’ll be able to:

• Define the ideal gas law and identify its formula
• Calculate a missing variable using the ideal gas law equation when you are provided the other required variables