# Chemistry: Avogadro's Law and the Ideal Gas Law

## Avogadro's Law and the Ideal Gas Law

Let's go back to the Kinetic Molecular Theory for a moment. It states that the molecules in gases are infinitely tiny, and that at any given temperature, all gas molecules have exactly the same amount of kinetic energy. If you'll recall our discussion of rms velocity from The Kinetic Molecular Theory of Gases, that's why heavy gas molecules travel more slowly than light ones at any temperature.

##### Molecular Meanings

The volume of one mole of any gas at standard temperature and pressure is called the **molar volume**.

These properties of a gas lead us to an interesting conclusion. One mole of any gas has exactly the same volume under the same conditions of temperature as one mole of any other gas. The volume of one mole of a gas is called its *molar volume*.

It may not seem immediately obvious why all gases should have the same molar volumes at the same temperatures. Consider this: If the pressure of a gas is equal to the force exerted by gas particles pushing on the sides of whatever container it's stored in, and the volume of a gas depends on its pressure (Boyle's Law), then the molar volumes of every gas are the same. This principle was first understood by Amadeo Avogadro, and is usually referred to as Avogadro's Law.

Since all ideal gases have the same molar volumes, a single equation can be used to express the relationship between the number of moles of a gas present and the volume. This relationship shown below is called the ideal gas law, shown below:

- PV = nRT

##### You've Got Problems

Problem 4: If my oven has a volume of 1,100 L, a temperature of 250 C, and a pressure of 1.0 atm, how many moles of gas does it hold?

P denotes pressure (in either atm or kPa), V denotes volume in liters, n is equal to the number of moles of gas, R is the ideal gas constant, and T is the temperature of the gas in Kelvin. There are two possible values for R, 8.314 L kPa/mol K and 0.08206 L atm/mol K. The value used in each problem will depend on the unit of pressure given. For example, if pressure is given in atm, R will be 0.08206 L atm/mol K.

Let's see an example of how this works:

**Example**: My refrigerator has a volume of 1,100 L. If the temperature inside the refrigerator is 3.0 C and the air pressure is 1.0 atm, how many moles of air are in my refrigerator?

##### Chemistrivia

The ideal gas law explains why hot air balloons work. The number of moles of air inside the balloon will be less than the number of moles of air outside the balloon because the air inside the balloon is warmer than the outside air. Because there are fewer moles of air inside the balloon than outside, the mass of the air in the balloon is also less, causing the balloon to "float" above the surrounding cold air.

**Solution**: P = 1.0 atm, V = 1,100 L, R = 0.08206 L atm/mol L (because pressure was given as "atm" in the problem), and T = 276 K. Solve for n using the ideal gas law:

- (1.0 atm)(1,100 L) = n (0.08206 L atm/mol K)(276 K)
- n= 49 mol

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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