# Chemistry: Boyle's Law: Why Compressed Gas Is Small

## Boyle's Law: Why Compressed Gas Is Small

Let's do a demonstration: Inflate a balloon and put it on your chair. Now, flop down on the chair as hard as you can, squishing the balloon.

When you did this demonstration, you probably found that the balloon popped when you sat on it. This wasn't really a surprise because it seems obvious that if you sit on a balloon, it will pop. My question for you: *Why* did the balloon pop?

I don't know if it's true, but I like to think that the British chemist Robert Boyle asked himself the same question back in 1662 after sitting on a balloon. In any case, he came up with a way of explaining why balloons pop when you sit on them.

##### You've Got Problems

Problem 1: If I compress 1,500 L of nitrogen at an initial pressure of 1.00 atm until the pressure reaches 450 atm, what will the new volume of this gas be?

For the sake of argument, let's say that your balloon had an initial volume of one liter, and that the pressure inside the balloon was initially one atmosphere. When you sat on the balloon, let's say that the force of your behind squished the volume of the balloon to 0.500 liters. What was the pressure inside the balloon after it had been squished?

##### Chemistrivia

If you live in a highly elevated area (such as Denver), you may have noticed the effects of Boyle's Law at the supermarket. Potato chips are frequently packaged near sea level, which has a higher air pressure than exists at high altitudes. As the atmospheric pressure outside the bag decreases, the volume of the gas inside the bag increases. As a result, prepackaged snack food bags are often highly inflated at high altitudes.

Boyle's Law allows us to solve this problem:

- P
_{1}V_{1}= P_{2}V_{2}

where P_{1} is the initial pressure of the gas, V_{1} is the initial volume of the gas, P_{2} is the final pressure of the gas, and V2 is the final volume of the gas. When using this equation, we assume that the temperature and number of moles of gas stay the same. Using the values from our example, we find that the pressure inside the balloon after we sat on it was:

- (1.00 atm)(1.00 L) = (x atm)(0.500 L)
- x = 2.00 atm.

The implication of this finding is clear. When you sat on the balloon, the pressure inside the balloon rose to 2.00 atm. Because the thin rubber of a balloon isn't strong enough to hold pressurized gas, it pops! The mystery of the popping balloon is now solved!

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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