Ideal Gas Equation

Ideal Gas Equation

An ideal gas is an imagined version of a gas that is much simpler than a real gas. The reason for creating this is to have a model that is easy to calculate, yet not too different from the real thing.

Measurements on real gases have shown that they have the following behaviour:

Boyle's law: pV = constant, when T is constant.

Charles's law: V/T = constant, when p is constant.

The first one means that when pressure p is decreased, the volume V expands. The second one means that when temperature T is increased, volume V expands.

However, for a real gas, these laws are only true within a certain range of the variables. For example, if p is increased or T is decreased, the volume contracts up to a point. Beyond that, the gas condenses into a liquid, and the laws no longer hold. Even when the gas is not a liquid, the laws may only be approximately true.

If we imagine a gas for which these laws are exactly true, then we call this gas an ideal gas. For an ideal gas, the two equations above can be combined into one:

pV/T = another constant

To see that this is correct: If T is constant, it becomes Boyle's law. If p is constant, it reduces to Charles' law. So this new law indeed contains both the old ones.

For the same p and T, if we double the number of atoms in the gas, we would double the V, . This means that the above gas law can be written in the form

pV/T = n x new constant

where n is the number of moles of the atoms. Note that 1 mole is 6.022 x 10²³. This huge number is usually denoted N_A, and is called the Avogadro constant. The new constant in the equation is often denoted R. So the ideal gas law is

pV/T = nR

Measurements also show that R is the same even for different gases, with different atomic masses. The value is R = 8.31 J/K/mol, and is called the gas constant.

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