Question

Determine the mole fractions and partial pressures of CO2, CH4, and He in a sample of gas that contains 1.25 mole of CO2, 1.59 moles of CH4, and 3.41 moles of He, and in which the total pressure is 5.78 atm.The mole fraction (x) of a component of a mixture is the number of moles of the component divided by the total number of moles in the mixture.The total number of moles in the mixture is:1.25 mol + 1.59 mol + 3.41 mol = 6.25 molCalculate the mole fraction of each component.XCO2 = _____ ? XCH4 = _______ ? xHe = _________ ?

Answer 1

xCO₂ = 0.2

xCH₄ = 0.2544

xHe = 0.5456

pCO₂ = 1.156 atm

pCH₄ = 1.470 atm

pHe = 3.154 atm

Step-by-step explanation:

The molar fraction is the number of moles of the component divided by the total amount of moles, which is 6.25 moles, so:

xCO₂ = 1.25/6.25 = 0.2

xCH₄ = 1.59/6.25 = 0.2544

xHe = 3.41/6.25 = 0.5456

By Dalton's law, the total pressure of a gas mixture is the sum of the partial pressures of the components of it. And, by the Raoult's law, the partial pressure is the mole fraction multiplied by the total pressure, so:

pCO₂ = 0.2*5.78 = 1.156 atm

pCH₄ = 0.2544*5.78 = 1.470 atm

pHe = 0.5456*5.78 = 3.154 atm