Question Video: Calculating the Partial Pressure of a Gas at Equilibrium | Nagwa Question Video: Calculating the Partial Pressure of a Gas at Equilibrium | Nagwa

Question Video: Calculating the Partial Pressure of a Gas at Equilibrium Chemistry • Third Year of Secondary School

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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 atm.

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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.

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