### Video Transcript

A mixture of gases in a closed
vessel at equilibrium contains three different gases: nitrogen, 20 moles; hydrogen,
45 moles; and ammonia, 25 moles. Calculate the partial pressure of
hydrogen at 40 atmospheres.

In this problem, we have a closed
vessel that contains a mixture of gases. The gas particles will collide with
the walls of the container, which exerts a pressure. If these gases are behaving
ideally, we can write the total pressure as the sum of the partial pressures of each
gas. The partial pressure is the
pressure that gas would exert if it was the only gas in the container.

In this problem, we need to
calculate the partial pressure of hydrogen gas. We can calculate the partial
pressure of a gas by multiplying the mole fraction by the total pressure. Before we can solve for the partial
pressure of hydrogen, we first need the mole fraction. To calculate the mole fraction of a
substance, we divide the amount of the substance in moles by the total amount of
substances in the mixture in moles. So the mole fraction for hydrogen
gas is the amount of hydrogen gas in moles divided by the total amount of gas in
moles.

The problem tells us there’s 45
moles of hydrogen in the mixture. Now we need to calculate the total
amount of gas in the mixture. There’s 20 moles of nitrogen, 45
moles of hydrogen, and 25 moles of ammonia. This gives us a total of 90 moles
of gas. The units of moles cancel, giving
us a mole fraction for hydrogen of 0.5.

Now that we have the mole fraction
for hydrogen, we can calculate the partial pressure. We calculated the mole fraction of
hydrogen to be 0.5. And the problem tells us the total
pressure is 40 atmospheres. Multiplying that out, we get our
final answer. So the partial pressure of hydrogen
in our mixture of gases at 40 atmospheres is 20 atmospheres.