# How can kinetic theory be used to verify Dalton's law of partial pressures?

I have been told Dalton's law of partial pressures can be proved from kinetic theory. This is my reasoning for why this might be:

Since in kinetic theory there are no forces of attraction between the particles, the only "force" on the container is the pressure exerted by the different gas species hitting on it, multiplied by the collision area, which will be different for the different species of gas. We thus consider the total pressure to be given by the sum of these individual pressures from the different gas species. This would also make sense since both kinetic theory and Dalton's law work on the assumption that the gas is an ideal one.

Is this too simplistic of an explanation? Many thanks.

Is this too simplistic of an explanation?

It is basically correct, since Dalton's law of partial pressures is based on ideal gas behavior of the individual gases as well as the mixture of gases. And ideal gas behavior is based on the kinetic theory of gases.

The partial pressure of the $$i$$ th gas in a mixture of gases in a volume $$V$$ is the pressure that that gas would alone exert if all the other gases were removed from the volume, and is given by the ideal gas equation

$$P_{i}=\frac{m_{i}R_{i}T}{V}$$

where $$m_i$$ and $$R_i$$ is the mass and gas constant for gas $$i$$.

Then $$P_{tot}=\sum P_i$$

Also

$$P_{i}=x_{i}P_{tot}$$

Where $$x_i$$ is the mole fraction of the $$i$$ th gas.

Hope this helps.