Mole Fraction

Mole fraction refers to the fraction of a component of a solution when the amounts (component and solution) are expressed in moles. In other words, the Mole fraction of a component is the ratio of moles of that particular component to the total moles of the solution.

Mole fraction (𝒳_i) can be calculated by

${𝒳}_i = \frac{n_i}{n_{tot}}$

n_i = Mole of ith component of the solution
n_tot = Mole of the solution

Suppose a solution contains 3 components (two solutes, A and B, and a solvent C)

$Mole fraction of component A \left({𝒳}_A\right) = \frac{n_A}{n_A + n_B + n_C}$

$Mole fraction of component A \left({𝒳}_B\right) = \frac{n_B}{n_A + n_B + n_C}$

$Mole fraction of component A \left({𝒳}_C\right) = \frac{n_C}{n_A + n_B + n_C}$

Where
n_A = Mole of component A
n_B = Mole of component B
n_C = Mole of component C

Since the solution contains only three components, two solutes, and a solvent, the total moles (n_tot) of the solution will be equal to
n_tot =  n_A + n_B + n_C

Therefore above equation can also be written

$Mole fraction of component A \left({𝒳}_A\right) = \frac{n_A}{n_{tot} }$

$Mole fraction of component A \left({𝒳}_B\right) = \frac{n_B}{n_{tot} }$

$Mole fraction of component A \left(𝒳C\right) = \frac{n_C}{n_{tot} }$

Properties of Mole Fraction:

1. Mole fraction is dimensionless: 
Since the value of mole fraction is obtained by dividing the mass of a component by the total mass of solution, it is dimensionless. However, sometimes it is written as mole/mole.
The sum of all Mole fractions is equal to 1.

In above example
𝒳_A + 𝒳_B + 𝒳_C = 1

2. Mole fraction is independent of temperature
In contrast to density, the Mole fraction is independent of temperature i.e., if temperature changes, the value of the Mole fraction does not change.