How is the partial pressure of a gas in a mixture calculated?

Nov 22, 2015

A law of partial pressures pertains.

Explanation:

In a gaseous mixture, the pressure exerted by a component is the same it would exert if this gas alone occupied the container. The total pressure is the sum of the individual partial pressures.

${P}_{T O T A L} = {P}_{1} + {P}_{2} + \ldots \ldots \ldots . . {P}_{N}$

$=$ $\frac{{n}_{1} R T}{V} + \frac{{n}_{2} R T}{V} + \ldots \ldots \ldots . . \frac{{n}_{n} R T}{V}$

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

Thus the pressure exerted by any component is proportional to the mole fraction:

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

The constant of proportionality is $\frac{R T}{V}$.