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 (𝒳i) can be calculated by

𝒳i = nintot

ni = Mole of ith component of the solution
ntot = Mole of the solution

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

Mole fraction of component A (𝒳A) = nAnA + nB + nC

Mole fraction of component A (𝒳B) = nBnA + nB + nC

Mole fraction of component A (𝒳C) = nCnA + nB + nC

nA = Mole of component A
nB = Mole of component B
nC = Mole of component C

Since the solution contains only three components, two solutes, and a solvent, the total moles (ntot) of the solution will be equal to
ntot =  nA + nB + nC

Therefore above equation can also be written

Mole fraction of component A (𝒳A) = nAntot 

Mole fraction of component A (𝒳B) = nBntot 

Mole fraction of component A (𝒳C) = nCntot 

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
𝒳A + 𝒳B + 𝒳C = 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.

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