Chemistry: The Combined Gas Law

The Combined Gas Law

The three gas laws we've mentioned so far in this section show that the pressure, volume, and temperature of a gas are all related. Using these equations, we can determine what happens to a gas when we change any of these three variables.

What happens, however, if we want to change two variables at once? Well, we can either use two equations, one after the other, or we can find an equation that includes all three variables. As it turns out, somebody has already done that by formulating the combined gas law. The combined gas law is, straightforwardly enough, a combination of the three laws we just mentioned:

• ^P₁⁄T₁ = ^P₂V₂⁄_T2

To see how this works, let's do a practice problem:

Example: A child at the county fair has let go of her toy balloon. If the initial volume of the balloon was 2.50 L, the atmospheric pressure was 1.00 atm, and the temperature at the fairgrounds was 25º C, what will the volume of the balloon be when it reaches an altitude where the air pressure is 0.250 atm and the temperature is -15º C?

Solution: Simply by plugging these numbers into the combined gas law, we get:

• ^{(1.00atm)(2.50L)}⁄_(298K) = ^{(0.250atm)(V₂)}⁄_258K
• V₂ = 8.66 L