### Video Transcript

An equilibrium mixture contains
type M and N gas molecules. The mole fraction of gas M was
determined to be equal to 0.57. What is the mole fraction of gas
N?

The mole fraction of a substance is
equal to the amount of that substance in moles divided by the total amount of
substances in the mixture in moles. Say we have this container of gas,
where each dot represents one mole of gas. Let’s try calculating the mole
fraction of the pink gas. There are four moles of pink gas in
the mixture and 10 moles of gas in total. So the mole fraction of the pink
gas is 0.4. Notice the moles here cancel, so
the mole fraction is a unitless quantity.

In this problem, we need to find
the mole fraction of gas N, but the only information we’ve been given is the mole
fraction of gas M. So we can’t calculate the mole
fraction of gas N using this formula. However, since the mole fraction
represents a fraction of the total mixture, the mole fractions of each substance in
a mixture will sum to one. We can see this with our container
full of yellow and pink gas particles. Six moles out of the total 10 moles
of gas in the container is the gas represented by the yellow dots, giving us a mole
fraction of 0.6 for the yellow gas. The mole fraction of both gases in
the mixture should add to one. We can see that they do.

Now let’s apply this to finding the
mole fraction of gas N. The only gases in the mixture are
molecules of type M and N. So the mole fraction of these two
gases will add to one. We can isolate the mole fraction of
N on the left-hand side of the equation by subtracting the mole fraction of M from
both sides. Now all we need to do to solve the
problem is plug in the mole fraction of gas M. The problem states the mole
fraction of gas M is 0.57. Performing the calculation gives us
0.43. So the mole fraction of gas N is
0.43.