Question

How is partial pressure related to mole fraction?

Answer 1

The partial pressure exerted by a gas in a mixture is directly proportional to its mole fraction........This is an experimental result, known since the time of Dalton, who formulated the following expression.

Explanation:

The total pressure, `P_"total"`, is the SUM of the individual partial pressures, `P_1, P_2, P_3............`.

`P_1=(n_1RT)/V`; `P_2=(n_2RT)/V`, `P_3=(n_3RT)/V`............where `n_1`, `n_2..........n_n` are the molar quantities of each component.

`P_"Total"=(RT)/V{n_1 + n_2 + n_3+.........n_n}.`

And thus `P_1` `=` `(RT)/V{n_1/(n_1+n_2+n_3.............+n_n)}`...

and `P_n` `=` `(RT)/V{n_n/(n_1+n_2+n_3.............+n_n)}`...

And thus the partial pressure, `P_1`, is proportional to the mole fraction of `n_1`. The constant of proportionality is `(RT)/V`.