Question 10.4.3: Use mole fraction in calculations involving gases. A gas mix......
Use mole fraction in calculations involving gases.
A gas mixture contains the noble gases Ne, Ar, and Kr. The total pressure of the mixture is 2.46 atm, and the partial pressure of Ar is 1.44 atm. If a total of 18.0 mol of gas is present, what amount of Ar is present?
You are asked to calculate the amount of gas present in a mixture.
You are given the total pressure of the mixture, the total amount of gas in the mixture, and the partial pressure of one of the gases in the mixture.
The amount (in moles) of Ar is equal to the total moles of gas in the mixture times its mole fraction. The first step, then, is to determine the mole fraction of Ar in the mixture. Solving Equation 10.9 for mole fraction of Ar,
P_{A} = χ_{A}P_{total} (10.9)
P_{Ar}= χ_{Ar}P_{total}χ_{Ar}= \frac{P_{Ar}}{P_{total}} = \frac{1.44\text{ atm}}{2.46\text{ atm}} = 0.585
Use the mole fraction of Ar and the total amount of gases in the mixture to calculate moles of Ar in the mixture.
0.585 = \frac{n_{Ar}}{n_{total}} = \frac{n_{Ar}}{18.0\text{ mol}}
n_{Ar} = 10.5 mol