# Why can you calculate the total pressure of a mixture of gases by adding together the partial pressures of the component gases?

May 15, 2016

Partial pressures are really just fractions of the total pressure. You can add any fraction together to achieve a new total, in accordance with Dalton's Law of Partial Pressures. So the math is valid; it's really in the measured pressures that you can go wrong.

Suppose a total pressure $\text{P"_"tot}$ was equal to $\text{10 bar}$ for a mixture of ideal, inert gases.

Then we could have a situation where the partial pressure "P"_("O"_2) of oxygen gas is $\text{2 bar}$, the partial pressure "P"_("Ne") of neon gas is $\text{5 bar}$, and the partial pressure "P"_("N"_2) of nitrogen gas is $\text{3 bar}$.

By summing each contributed pressure, you get the total contribution to the pressure, i.e. you get the total pressure.

This works fairly well so long as the gas itself can be assumed ideal without losing accuracy in terms of what its volume per $\text{mol}$ actually is.

But, there are characteristics that real gases have, and ideal gases don't:

• Some real gases are compressed more easily than an ideal gas, and those have smaller volumes per $\text{mol}$ than if they were ideal. These gases exert a smaller partial pressure at a given volume.
• Some other real gases are harder to compress than an ideal gas, so they have larger volumes per $\text{mol}$ than if they were ideal. These gases exert a larger partial pressure at a given volume.

The above two points also can blend together at extreme pressure amounts, as some gases can deviate drastically from ideality depending on the pressure and temperature of the system.

CONCLUSIONS

As long as every gas in a system is able to be assumed ideal, and as long as they don't react, we can treat contributions to the partial pressure with approximately equal weight.