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A gas mixture used for anesthesia contains 2.83 moles oxygen, O₂, and 8.41 moles nitrous oxide, N₂O.
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The total pressure of the mixture is 192 kilopascals.
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What are the mole fractions of O₂ and N₂O?
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So in this question, we have a mixture of two different gases in the same container, oxygen and nitrous oxide.
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The total pressure of the mixture is 192 kilopascals, which is about 1.9 times atmospheric pressure.
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Our job is to take the amounts of oxygen and nitrous oxide and work out the mole fractions.
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A mole fraction of a chemical X is equal to the amount of X in moles divided by the total amount in moles.
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In this question, the total amount refers to the amount of oxygen plus the amount of nitrous oxide.
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So we can start off working out the total amount of substance in the container.
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Here, we’re counting discrete gas particles, O₂ or N₂O.
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This gives us 11.24 moles of gas molecules.
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Mole fraction is sometimes given the symbol X.
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So that’s what I’ll use going forward.
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The mole fraction of oxygen, O₂, is equal to the amount of O₂ in moles divided by the total amount, which equals 2.83 moles divided by 11.24 moles.
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This gives us a mole fraction of oxygen of 0.25.
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And we can do exactly the same with nitrous oxide.
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Where the mole fraction of nitrous oxide is equal to the amount of nitrous oxide in the mixture divided by the total amount in the mixture in moles.
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This gives us 8.41 moles divided by 11.24 moles and a mole fraction for N₂O of 0.75.
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All the values in our calculation are given to three significant figures.
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So we should give our answers to the same precision.
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So the final mole fractions for O₂ and N₂O in this mixture is oxygen 0.252 and nitrous oxide 0.748.
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I’m going to store away the prerounded numbers for the next part of the question.
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You could use the rounded figures for future calculations.
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But since we’ve got a higher precision value, we should use this to reduce the error in the final calculation.
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What are the partial pressures of O₂ and N₂O?
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The term partial pressure can be confusing.
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It’s not the contribution of the component to the total pressure.
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It’s actually the pressure of that component if it was the only thing in the same container in the same amount.
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Fortunately, from the ideal gas law, we know that all else being equal, the pressure of a gas is proportional to the amount of gas.
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So for mixtures of ideal gases, the partial pressure of anyone component is equal to its mole fraction multiplied by the total pressure.
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This can be written in symbols as 𝑝 of X is equal to 𝑥 of X times the total pressure, 𝑝.
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From part a), we already have the accurate mole fractions for the two gases.
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The partial pressure of O₂ is equal to its mole fraction times the total pressure, which is equal to 0.251779 times 192 kilopascals.
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Meaning that the partial pressure of oxygen in this system is about 48 kilopascals.
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So we can move on to do the same for nitrous oxide.
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The partial pressure of nitrous oxide is equal to the mole fraction of nitrous oxide multiplied by the total pressure.
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Which is equal to 0.7482 to one times 192 kilopascals.
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Which is equal to about 144 kilopascals.
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The original data for this question was still given to three significant figures.
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So we should give our final answer to three significant figures also.
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So our final answer for the partial pressures of O₂ and N₂O in this mixture is O₂ 48.3 kilopascals and N₂O 144 kilopascals.
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As a result of the way gases behave, we have 25 mole percent oxygen in our mixture.
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And about 25 percent of the total pressure is because of oxygen.
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If the ratios of mole fractions don’t translate into the partial pressures for a gas mixture, there’s been a mistake.