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Using the Ideal Gas Law: Calculate Pressure, Volume, Temperature, or Quantity of a Gas

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  • 0:07 The Ideal Gas Law
  • 0:59 Using the Ideal Gas Law
  • 3:02 Lesson Summary
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Lesson Transcript
Instructor: Sarah Friedl

Sarah has two Master's, one in Zoology and one in GIS, a Bachelor's in Biology, and has taught college level Physical Science and Biology.

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.

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 K

If 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 atm

The 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 * T

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