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# 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:

• P1T1 = P2V2T2

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

##### You've Got Problems

Problem 3: I've decided to go deep sea exploring in a giant transparent balloon. If I start my voyage in a balloon with a pressure of 1.00 atm, a temperature of 20º C, and a volume of 5.00 × 103 L, what will be the pressure inside the balloon be when I reach a depth where the temperature of the balloon is 2º C and the volume of the balloon is 1,170 L?

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 Excerpted from The Complete Idiot's Guide to Chemistry © 2003 by Ian Guch. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.

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