# Ideal Gases

## Charles, Avogadro, and the Ideal Gas Law

### Charles' Law

Charles' law states that, at a constant pressure, the volume of a mixed amount of gas is directly proportional to its absolute temperature: = k

Where k is a constant unique to the amount of gas and pressure. Just as with Boyle's law, Charles' law can be expressed in its more useful form: = The subscripts 1 and 2 refer to two different sets of conditions, just as with Boyle's law.

Why must the temperature be absolute? If temperature is measured on a Celsius (non absolute) scale, T can be negative. If we plug negative values of T into the equation, we get back negative volumes, which cannot exist. In order to ensure that only values of V≥ 0 occur, we have to use an absolute temperature scale where T≥ 0. The standard absolute scale is the Kelvin (K) scale. The temperature in Kelvin can be calculated via Tk = TC + 273.15. A plot of the temperature in Kelvin vs. volume gives : Figure %: Temperature vs. Volume
As you can see from , Charles' law predicts that volume will be zero at 0 K. 0 K is the absolutely lowest temperature possible, and is called absolute zero.

### Avogadro's Law

Avogadro's law states that the volume of a gas at constant temperature and pressure is directly proportional to the number of moles of gas present. It's mathematical representation follows:

 fracVn = k

k is a constant unique to the conditions of P and T. n is the number of moles of gas present.

1 mole (mol) of gas is defined as the amount of gas containing Avogadro's number of molecules. Avogadro's number (NA) is

 NA = 6.022×1023

1 mol of any gas at 273 K (0_C) and 1 atm has a volume of 22.4 L. The conditions 273 K and 1 atm are the standard temperature and pressure (STP). STP should not be confused with the less common standard atmospheric temperature and pressure (SATP), which corresponds to a temperature of 298 K and a pressure of 1 bar.

The numbers 22.4 L, 6.022×1023, and the conditions of STP should be near and dear to your heart. Memorize them if you haven't already.

### The Ideal Gas Law

Charles', Avogadro's, and Boyle's laws are all special cases of the ideal gas law:

 PV = nRT

T must always be in Kelvin. n is almost always in moles. R is the gas constant. The value of R depends on the units of P, V and n. Be sure to ask your instructor which values you should memorize.
UnitsValue of R 0.08206 8.314 8.314 1.987 62.36
You can think of R as a converter that changes the units on the right side of the above equation to the units on the left side of the "=" sign. The values 0.0821 and 8.314 get the most use. Memorizing them will make your life easier.