# What is the equation for Dalton's law of partial pressure?

Dec 23, 2016

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

#### Explanation:

In a gaseous mixture, the partial pressure exerted by a component, is the same as the pressure it would exert if it ALONE occupied the container. The total pressure is the sum of the individual pressures. The mole fraction of a component gas is proportional to the partial pressure.

Clearly, the total number of moles of gas is..........

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

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

But given ideality, then ${P}_{i} = \frac{{n}_{i} R T}{V}$

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

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

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

It is worthwhile spending a bit of time on the equation, and checking problems where you use it .