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Chapter 5: Problem 57

A mixture of gases contains \(\mathrm{CH}_{4}, \mathrm{C}_{2} \mathrm{H}_{6},\) and \(\mathrm{C}_{3} \mathrm{H}_{8}\). If the total pressure is 1.50 atm and the numbers of moles of the gases present are 0.31 mole for \(\mathrm{CH}_{4}\) 0.25 mole for \(\mathrm{C}_{2} \mathrm{H}_{6},\) and 0.29 mole for \(\mathrm{C}_{3} \mathrm{H}_{8},\) calculate the partial pressures of the gases.

Short Answer

Expert verified
The partial pressures of the gases are approximately \(0.5470 \, atm\) for \(CH_{4}\), \(0.4411 \, atm\) for \(C_{2}H_{6}\), and \(0.5118 \, atm\) for \(C_{3}H_{8}\)

Step by step solution

01

Calculate the total number of moles

First, it is important to calculate the total number of moles present in the mixture. This is done by adding the moles of each individual gas. So, it will be \(0.31 + 0.25 + 0.29 = 0.85 \, moles\)
02

Calculate the proportion of each gas

Next, we need to calculate the proportion of each gas. This is done by dividing the moles of each individual gas by the total moles calculated in Step 1. So for \(CH_{4}\) it is \(0.31/0.85 = 0.3647\), for \(C_{2}H_{6}\) it is \(0.25/0.85 = 0.2941\) and for \(C_{3}H_{8}\) it's \(0.29/0.85 = 0.3412\)
03

Calculate the partial pressures of each gas

Here we use these calculated proportions (from step 2) to work out the actual pressures. This is achieved by multiplying the mole ratio of each gas by the total pressure (1.50 atm). Therefore, the partial pressure of \(CH_{4}\) is \(0.3647 * 1.50 = 0.5470 \, atm\), the partial pressure of \(C_{2}H_{6}\) is \(0.2941 * 1.50 = 0.4411 \, atm\), and the partial pressure of \(C_{3}H_{8}\) is \(0.3412 * 1.50 = 0.5118 \, atm\)

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Most popular questions from this chapter

Write the van der Waals equation for a real gas. Explain clearly the meaning of the corrective terms for pressure and volume.

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