### Video Transcript

A mixture of gases at equilibrium contains 20 moles of SO2 gas, 40 moles of O2 gas, and 40 moles of SO3 gas. What is the mole fraction of SO2 at equilibrium?

The mole fraction, which is given the letter X, is very useful for expressing the relative amounts of substances in a mixture. The mole fraction for some substance we’ll call A is defined as the amount of substance A in moles divided by the total amount in moles. In this problem, we need to solve for the mole fraction of SO2. This will be equal to the amount of SO2 in moles divided by the total amount of gas in the mixture in moles. The problem says there’s 20 moles of SO2 gas in the mixture.

Now, we need to calculate the total amount of gas in the mixture. We already know there’s 20 moles of SO2 gas. There’s also 40 moles of O2 gas and 40 moles of SO3 gas. So the total amount of gas in our mixture is 100 moles. The units of moles in the top and bottom of our expression cancel, which means we’ll get a quantity with no units when we solve for the mole fraction. So the mole fraction of SO2 at equilibrium is 0.2.