Ideal Gases II

Dalton's Law of Partial Pressures

Suppose we have a mixture of gases A, B, C, … in a container. We put them in one at a time and were able to measure the pressure of each in some way before introducing them into the container. Dalton's law of partial pressures states that the total pressure in the container is the sum of the partial pressures (which we measured prior to mixing them in the container) of the gases

At the same time, common sense demands that the same be true of the moles of each gas and the total number of moles

If we assume that each gas is ideal as well as the resulting mixture, we can write the ideal gas law for each gas

And so on. Note that the gases all occupy the same volume and are all at the same temperature. For a mixture of gases, the mole fraction of a component is defined as the moles of that component divided by the total number of moles:

For convenience, let's just work with a binary mixture of gases and only two components, A and B. Then,

Note that the mole fraction is a pure, unitless number. This means, in the case of component A that

Note that

So the sum of all the mole fractions is always 1.

Example

A 20.0L flask contains 0.232 moles of methane (A) and 0.545 moles of ethane (B) at 35oC. What are the mole fractions of each component? What is the total pressure? What are the partial pressures of each component?

Solution

The total moles are calculated

And so the mole fraction of A is

The mole fraction of B can either be calculated the same way,

Or by using

The result is the same. Now calculate the pressure using the ideal gas law with T = 35 + 273 = 308K

From this, we can get the partial pressures via

As a check on the calculations, calculate the total pressure