# Ideal Gases

## Contents

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#### 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 T k = T C + 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 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 ( N A ) is

 N A = 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.
Units Value 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.