# What rule states that the pressure exerted by a mixture of gases is equal to the sum of the individual gas pressures?

Nov 19, 2016

$\text{Dalton's law of partial pressures}$.

#### Explanation:

$\text{Dalton's law of partial pressures}$, which was established by experiment, holds that in a gaseous mixture, the pressure exerted by an individual component gas is the same as the pressure it would exert if it alone occupied the container.

And so, ${P}_{\text{Total}} = {P}_{A} + {P}_{B} + {P}_{C} \ldots \ldots \ldots$, where $A , B , C , e t c$ are the individual, component gases.

But if we assume ideality, ${P}_{A} = \frac{{n}_{A} R T}{V}$, where ${n}_{A}$ is the number of moles of $\text{component gas A}$.

And so, ${P}_{\text{Total}} = \frac{{n}_{A} R T}{V} + \frac{{n}_{B} R T}{V} + \frac{{n}_{C} R T}{V} \ldots \ldots \ldots$,

Equivalently, ${P}_{\text{Total}} = \frac{R T}{V} \left\{{n}_{A} + {n}_{B} + {n}_{C} \ldots . .\right\}$.

And thus the partial pressure, ${P}_{A}$, is proportional to the mole fraction:

${P}_{A} = \frac{R T}{V} \times {n}_{A} / \left({n}_{A} + {n}_{B} + {n}_{C} \ldots . .\right)$, the constant of proportionality is of course $\frac{R T}{V}$