Calculating the Mole Fraction of Xe in a Gas Mixture

How do you calculate the mole fraction of Xe in a gas mixture?

Given a 565 cm3 vessel containing a mixture of Ar and Xe with a mass of 2.580 g at 25.0 ∘C and 760 Torr pressure, how can we determine the mole fraction of Xe in the mixture?

Calculating the Mole Fraction of Xe

To calculate the mole fraction of Xe in the mixture, follow these steps:

1. Use the ideal gas law to determine the number of moles of the gas mixture.
2. Calculate the moles of Xe using the mass and molar mass of Xe.
3. Divide the moles of Xe by the total moles of the gas mixture to get the mole fraction of Xe.

When dealing with gas mixtures, it's essential to understand the concept of mole fraction. The mole fraction of a particular gas component in a mixture is the ratio of the number of moles of that gas to the total number of moles of all gases present.

In the given scenario, we first need to find the number of moles of the gas mixture using the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. Once we have the total moles of the gas mixture, we can calculate the moles of Xe by using its molar mass.

By dividing the moles of Xe by the total moles of the gas mixture, we can determine the mole fraction of Xe in the mixture. Express the mole fraction to three significant figures for accuracy in the calculation.