# What is the partial pressure of gases?

Jul 19, 2018

In a gaseous mixture, the partial pressure is the pressure exerted by a component gas if it ALONE occupied the container.

#### Explanation:

The total pressure is the SUM of the individual partial pressures. Ans so the air we breathe (at approx. $1 \cdot a t m$) COULD be expressed as ${P}_{\text{ambient"=underbrace(P_"dioxygen"+P_"dinitrogen"+P_"other gases")_"0.21(atm)+0.78(atm)+0.1(atm)}}$.

So in a gaseous mixture:

${P}_{\text{Total}}$ $=$ ${P}_{1} + {P}_{2} + {P}_{3} + \ldots \ldots \ldots \ldots {P}_{n}$

Where ${P}_{i}$ is the partial pressure of a component. But we can assume ideality, and thus,

${P}_{1} = \frac{{n}_{1} R T}{V}$, etc. since $V$ and $T$ are common to all the gases.

Since the total pressure is the sum of the partial pressures,

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

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

And so the partial pressure of a component is proportional to the mole fraction of that component. The law of course presupposes that the individual gases do not react with each other.