Lesson 2 - Gas Laws

Perhaps unknowingly, we have already defined above, the concept of partial pressure.

A partial pressure is the pressure which a single gas would exert if it alone occupied the volume of a mixture.

In the previous example, at a mixture pressure of 10 bar a, the partial pressures of CO₂ and N₂ would be 2 and 8 bar a, respectively. We can apply our universal gas law to this situation, namely, defining the partial pressures of 2 and 8 bar a for the CO₂ and N₂ gas mixture in a vessel of volume V and at temperature T.

The partial pressure of CO₂ p_CO2 is given by:

The partial pressure for N₂:

The mixture to give the mixture pressure P_T:

Where n_T is the total number of moles of CO₂ and N₂.

So, if we take the ratio of the partial pressure of CO₂ to the mixture pressure P_T:

Rearranging for the partial pressure of CO₂:

A similar expression can be derived for the partial pressure of nitrogen:

The ratio of the number of moles of either gas to the total number of moles of gas, i.e. n_CO2/n_T or n_N2/n_T is known as the molar fraction. Another way to think of this is the fraction of any individual gas component to the total number of moles of the mixture. We commonly give the molar fraction the symbol x:

If we summed both partial pressures, we would get the total mixture pressure P_T:

We can show that the sum of the molar fractions is one:

Dalton’s law states that in a non-reactive gas mixture, the total pressure of a mixture of gases is the sum of the individual partial pressures of the gases in the mixture at constant volume and temperature.

John Dalton (1766-1844) was an English chemist, physicist and meteorologist who made major contributions in chemistry, physics, and many other fields, including mountaineering. He was considered an authority in the heights of local mountains which he used to climb to take atmospheric readings from the summit. From these readings, he would estimate the height using the change in atmospheric pressure from the foot of the mountain to its summit.