PlanetPhysics/Dalton's Law

The gases are mixable with each other in all proportions.\, Since the ideal gas law $$\begin{matrix} pV = nRT \end{matrix}$$ is valid for any ideal gas, one may think that it's insignificant whether the mole number $$n$$ concerns one single gas or several gases.\, It is true, which can be shown experimentally.

Let's think that we mix the volumes $$V_1$$, $$V_2$$, ..., $$V_k$$ of different gases having an equal pressure $$p$$ and an equal temperature $$T$$.\, If one measures the volume $$V$$ of the mixture in the same pressure and temperature, one notices that $$V = V_1\!+\!V_2\!+\!...\!+\!V_k.$$ Each of the gases satisfies an equation\, $$pV_i = n_iRT$$,\, and thus $$\begin{matrix} pV = pV_1\!+\!pV_2\!+\!...\!+\!pV_k = (n_1\!+\!n_2\!+\!...\!+\!n_k)RT. \end{matrix}$$ This is similar as the general equation (1).\, If we think that the same volume $$V$$ would be filled by any of the gases alone, we had an equation $$p_iV = n_iRT$$ for each gas; here the pressure $$p_i$$, i.e. $$n_i\frac{RT}{V}$$, is called the partial pressure of the gas $$i$$.\, By (2), we have $$p = (n_1\!+\!n_2\!+\!...\!+\!n_k)\frac{RT}{V} = n_1\frac{RT}{V}\!+\!n_2\frac{RT}{V}\!+\!...\!+\!n_k\frac{RT}{V} = p_1\!+\!p_2\!+\!...\!+\!p_k.$$ Accordingly we have obtained the

Dalton's law. \, The pressure of a gas mixture is equal to the sum of the partial pressures of the component gases.

This law was invented by J. Dalton in 1801.