# How is partial pressure related to mole fraction?

Aug 2, 2017

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, ${P}_{\text{total}}$, is the SUM of the individual partial pressures, ${P}_{1} , {P}_{2} , {P}_{3.} \ldots \ldots \ldots . .$.

${P}_{1} = \frac{{n}_{1} R T}{V}$; ${P}_{2} = \frac{{n}_{2} R T}{V}$, ${P}_{3} = \frac{{n}_{3} R T}{V}$............where ${n}_{1}$, ${n}_{2.} \ldots \ldots \ldots {n}_{n}$ are the molar quantities of each component.

${P}_{\text{Total}} = \frac{R T}{V} \left\{{n}_{1} + {n}_{2} + {n}_{3} + \ldots \ldots \ldots {n}_{n}\right\} .$

And thus ${P}_{1}$ $=$ $\frac{R T}{V} \left\{{n}_{1} / \left({n}_{1} + {n}_{2} + {n}_{3.} \ldots \ldots \ldots \ldots + {n}_{n}\right)\right\}$...

and ${P}_{n}$ $=$ $\frac{R T}{V} \left\{{n}_{n} / \left({n}_{1} + {n}_{2} + {n}_{3.} \ldots \ldots \ldots \ldots + {n}_{n}\right)\right\}$...

And thus the partial pressure, ${P}_{1}$, is proportional to the mole fraction of ${n}_{1}$. The constant of proportionality is $\frac{R T}{V}$.