How to Calculate Mole Fraction of a Gas?

To calculate the mole fraction of a gas in a mixture, divide the number of moles of that specific gas by the total number of moles of all gases present in the mixture.

Here's a breakdown of the process:

Steps to Calculate Mole Fraction

1. Determine the Number of Moles for Each Gas: This is often done using the ideal gas law (PV = nRT) or by converting from mass to moles using the gas's molar mass. The formula to calculate moles (n) from mass (m) is:

   n = m / M

   where M is the molar mass of the gas.

2. Calculate the Total Number of Moles: Add up the number of moles of each gas in the mixture:

   n_total = n₁ + n₂ + n₃ + ...

   where n₁, n₂, n₃, etc., are the number of moles of each individual gas.

3. Calculate the Mole Fraction: Divide the number of moles of the gas of interest (n_i) by the total number of moles (n_total):

   χ_i = n_i / n_total

   where:

   • χ_i is the mole fraction of gas i.
   • n_i is the number of moles of gas i.
   • n_total is the total number of moles of all gases in the mixture.

Example

Let's say you have a mixture of 2 moles of nitrogen (N₂) and 3 moles of oxygen (O₂).

1. n_N2 = 2 moles
2. n_O2 = 3 moles
3. n_total = 2 moles + 3 moles = 5 moles

To calculate the mole fraction of nitrogen:

χ_N2 = 2 moles / 5 moles = 0.4

Therefore, the mole fraction of nitrogen in the mixture is 0.4.

To calculate the mole fraction of oxygen:

χ_O2 = 3 moles / 5 moles = 0.6

Therefore, the mole fraction of oxygen in the mixture is 0.6.

Important Note: The sum of the mole fractions of all the gases in a mixture must equal 1. In this example, 0.4 + 0.6 = 1.