Partial pressure

John Dalton, an English chemist, experimented on the behaviour of gas mixtures in 1801 and concluded that:

The total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each gas.

This became the Dalton’s law of partial pressures. The law can be rationalised for an ideal gas, which is described by the ideal gas law, pV = nRT.

Consider a mixture of ideal gases in a rigid container at constant temperature. Since ideal gas particles are assumed to be point masses with elastic collisions and no intermolecular forces of interaction, they are expected to collide onto the walls of the container independently from one another in the mixture. The total pressure exerted by the gas mixture on the walls of the container is therefore proportional to the total number of particles of ideal gases in the container. The ideal gas law for a mixture of ideal gases then becomes:

p_T=\left ( n_1+n_2+...n_i \right )\frac{RT}{V}=\frac{RT}{V}\sum_in_i\; \; \; \; \; \; \; \; 16

where pT is the total pressure of the gas mixture and ni is the number of moles of gas i in the mixture. Expanding eq16, we have:

p_T=n_1\frac{RT}{V}+n_2\frac{RT}{V}+...+n_i\frac{RT}{V}=p_1+p_2+...p_i=\sum_ip_i\; \; \; \;\; \; \; \; 17

where pi is known as the partial pressure of gas i:

p_i=n_i\frac{RT}{V}\; \; \; \; \; \; \; \; 18

Dividing eq18 with eq16 and rearranging, we have

p_i=x_ip_T\; \; \; \; \; \; \; \; 19

where x_i=\frac{n_i}{\sum_in_i}, i.e. the mole fraction of gas i.

Even though eq17 and eq19 are derived from the ideal gas law, they are applicable to real gases in many situations.



What is the partial pressure of He in a balloon that is filled with He and 0.410 atm of N2, assuming atmospheric pressure is 760.0 mmHg?


Since 760.0 mmHg = 1.000 atm, pHe = 1.000 – 0.410 = 0.59 atm



Previous article: Ideal gas law
Content page of gas laws
Content page of Basic chemistry
Main content page

Leave a Reply

Your email address will not be published. Required fields are marked *