# Mole Fraction Formula

## What is Mole fraction?

Mole fraction represents the number of molecules of a particular component in a mixture divided by the total number of moles in the given mixture. It’s a way of expressing the concentration of a solution.

The molar fraction can be represented by X. If the solution consists of components A and B, then the mole fraction is,

$Mole&space;fraction&space;of&space;solute=\frac{Moles\;&space;of\;&space;Solute}{Moles\;of\;&space;Solute&space;+&space;Moles\;&space;of\;&space;Solvent}$

= $\frac{n_{A}}{n_{A}+n_{B}}$

$Mole&space;fraction&space;of&space;solvent=\frac{Moles\;&space;of\;&space;Solvent}{Moles\;of\;&space;Solute&space;+&space;Moles\;&space;of\;&space;Solvent}$

= $\frac{n_{B}}{n_{A}+n_{B}}$

Therefore, the sum of mole fraction of all the components is always equal to one.

Please note that mole fraction represents a fraction of molecules, and since different molecules have different masses, the mole fraction is different from the mass fraction.

Example 1

A tank is charged with a mixture of 1.0 x 103 mol of oxygen and 4.5 x 103 mol of helium. Calculate the mole fraction of each gas in the mixture.

Solution

The given parameters are

NHe = 4.5 x 103 mol and nO2 = 1.0 x 103 mol

Mole fraction can be calculated as

XHe = 4.5 x 103 mol / 4.5 x 103 mol + 1.0 x 103 mol

4.5 mol / 5.5 mol

= 0.82

XO2 = 2.0 x 103 mol / 4.5 x 103 mol + 1.0 x 103 mol

= 1.0 x 103 / 5.5 x 103

= 0.18

Example 2

Determine the mole fraction of methanol CH3OH and water in a solution prepared by dissolving 4.5 g of alcohol in 40 g of H2O. M of H2O is 18 and M of CH3OH is 32.

Solution

Moles of CH3OH = 4.5 / 32 = 0.14 mole

Moles of H2O = 40 / 18 = 2.2 moles

Therefore, according to the equation

mole fraction of CH3OH = 0.14 / 2.2 + 0.14

= 0.061

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