What are the partial pressures of the gases?

Nov 1, 2016

In a gaseous mixture, the partial pressure exerted by a component gas is the same as the pressure it would exert if it alone occupied the container.

Explanation:

The total pressure is the sum of the individual partial pressures:

And thus ${P}_{\text{total}} = {P}_{1} + {P}_{2} + \ldots \ldots \ldots {P}_{n}$

Assuming ideality,

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

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

And thus the partial pressure of any component gas is proportional to the mole fraction, the constant of proportionality $=$ $\frac{R T}{V}$.

Clearly, this law assumes a mixture of non-reacting gases. And thus now we breathe dioxygen gas at a pressure of approx. $0.20 \cdot a t m$.