download the script: Dalton’s Law and Partial Pressure

Assume that we have 2 rigid closed containers originally occupying the same volume V. One container (container 1) is filled with ideal gas A at a known pressure p_A. The other (container 2) is filled with ideal gas B at a known pressure p_B. Both gases have the same temperature T.

Now we mix both ideal gases A and B in a third container (container 3) with the same volume V and at the same temperature T. We suppose that the pressure of mixture A+B is then p_tot. It must be emphasized that A+B is a nonreacting mixture, and since gas A and gas B behave as ideal gases, their mixture A+B can also be regarded as ideal gas and follow the ideal gas law as well.

As mentioned above, A and B do not react with each other. Therefore, the conservation of moles for a nonreacting mixture can be used:

The mole n can be substituted by applying the ideal gas law:

• For gas A:

• For gas B:

• For mixture A+B:

Then we obtain:

 Now we can extend this conclusion to any number of ideal gases which is the well-known Dalton’s Law:

(where T=constant and V=constant)

Here we call:

• p_tot = the total pressure of the mixture
• p_i = the partial pressure of i-th gas

Hence, the Dalton’s Law, from the equation expressed above, states that the total pressure exerted by the mixture of nonreacting gases equals to the sum of partial pressure of every constituent.

For ideal gas, by using the ideal gas law, we can calculate the partial pressure as following:

(for more information about mole fraction, please see here: https://thermodynamics-engineer.com/mass-and-mole-fraction/)