1 mole of all gases are assumed to occupy the same volume in space (24 000cm at room temperature and pressure).
The total pressure of a gaseous system is directly related to the number of moles in the system.
How much pressure one gas contributes to the total pressure of a system is called its partial pressure.
All partial pressures of gases in a system add up to give the total pressure of the system.
The mole fraction of a gas describes how many moles of a gas there are compared to all other gases in the system.
Mole Fractions and Partial Pressures
If an equilibrium mixture is made up of just gaseous substances, then the total pressure of the ‘system’ at equilibrium is directly related to the number of moles of each substance.
Remember the ideal gas assumption – we assume that 1 mole of any gas occupies the same volume as 1 mole of any other gas. 1 mole of hydrogen gas, (H ), is said to occupy the same volume as 1 mole of ethane (CH CH ), even though the individual gas molecules are a different size, the impact of the size of a molecule compared to the volume it occupies in space is negligible. At room temperature and pressure, 1 mole of a gas is assumed to occupy 24dm (24 000cm ).
Imagine a system that is made of 1 mole of A(g) and 1 mole of B(g), with a total pressure of 100kPa. We know there are 2 moles of gas in total and A + B are contributing the same amount of pressure to the system as they have the same number of moles.
Therefore, each gas is contributing 50kPa of pressure. This contribution is the partial pressure of each gas.
A partial pressure is the contribution that a gas makes towards the total pressure of a system.
Imagine a sealed box that contains 2 moles of A(g) and 1 mole of B(g), with a total pressure of 150kPa.
Each molecule of gas contributes to the overall pressure in the box. If three moles of gas cause a pressure of 150kPa, then one mole’s worth of gases must be contributing 50kPa of pressure.
There are two moles of A and one mole of B in the box. The partial pressure of A would be 100kPa (2 x 50kPa) and the partial pressure of B 50kPa (1 x 50kPa).
This shows that the number of moles of a gas compared to the total number of moles of all gases is linked to the partial pressure that the gas has in a system. This ‘comparison’ is called its mole fraction.
A mole fraction is just a way of representing, as a fraction or decimal, how much of a particular gas there is in a system compared to all gases present.
The partial pressure of a gas can then be calculated, by multiplying its mole fraction by the partial pressure of the system.
For example, in air 78% is nitrogen, 21% oxygen and 1% ‘other gases’. (Note – these actual percentages are not accurate!) Atmospheric pressure is 100 kPa.
Mole fraction of nitrogen = 79 /100
Mole fraction of oxygen = 20 /100
Mole fraction of ‘other gases’ = 1/100
Partial pressure of nitrogen = 79/100 x 100 kPa
Partial Pressure of oxygen = 20/100 x 100 kPa
Partial Pressure of ‘other gases’= 1 kPa