Partial Pressures


Like so many things in nature, gases too come to us in mixtures. As was previously pointed out in section 2.1, air is a mixture of gases with the primary ones being nitrogen, oxygen, and argon. Because the behavior of gas molecules is universal - meaning they ALL behave exactly the same way, we can treat a mixture of gases as just one big collection of gas molecules or moles. So the ideal gas law works even when all the moles of gas are really different gases. If you want to calculate the total overall pressure of a mixture of gases, just count all the moles and use the ideal gas law:

Ptotal = ntotalRTV

Realize that pressure is the "total" pressure which means all the different gases in the mixture contribute to the overall pressure. The concept of partial pressure comes from the fact that each specific gas contributes a part of the total pressure and that part is the partial pressure of that gas. It is really pretty much like taking a percentage or fraction of the total to describe all the parts. Let me illustrate this with numbers for what we call dry air (remember, from section 2.1).

N2 gas is 78% of the air we breath which is on average 1 atm total pressure.

PN2 = 0.78(1 atm) = 0.78 atm

So the partial pressure of N2 of air at 1 atm pressure is 0.78 atm. If we do the same for O2 and Ar we get 0.21 atm for O2 and 0.01 atm for Ar. We also recognize a rather obvious math fact as well... those three pressure must add up to equal the total pressure of 1 atm.

Ptotal = PN2 + PN2 + PAr = 1 atm

This is known as Dalton's Law of partial pressures (check out those external links). The more generic way of writing it is

Ptotal = PA + PB + PC ···


Use Partial and Total Pressures to get Mole Fraction

We also discover that because pressure is directly proportional to the number of moles, we calculate the mole fraction of a gas in a mixture using the ratio of the partial pressure and the total pressure.

XA =  PA    Ptotal   *

And a friendly reminder that mole fraction is just a part vs whole thing where you count the part in moles and the whole in moles. If you multiply mole fraction by 100% you'd have percent mole fraction. Here is the basic formula (a repeat from section 1.7).

XA =  moles of A total moles

Now note that that simple calculation at the top of the page - the 78% nitrogen times the 1 atm to give 0.78 atm, is just using the mole fraction equation from above * with partial pressures rearranged like this.

PA = XA·Ptotal



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