Mole fraction is the amount of moles of particular component in the mixture to the total number of moles of all the components in the mixture. The symbol for mole fraction is X with the component being studied written as subscript.

**Mole Fraction Formula** of solute is

Mole fraction has no units.

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Example problems are given below based on mole fraction concept.

### Solved Examples

**Question 1: **A gaseous solution contains 3.5 $\times$ 10^{-3} moles of N_{2} and 1.5 $\times$ 10^{-3} moles of CO_{2}. What is the mole fraction of each component present?

** Solution: **

Moles of N_{2} = 3.5 $\times$ 10^{-3}

Moles of CO_{2} = 1.5 $\times$ 10^{-3}

Total number of moles = 3.5 $\times$ 10^{-3} + 1.5 $\times$ 10^{-3}

Total number of moles = 5 $\times$ 10^{-3}

Mole fraction of N_{2} = $\frac{3.5 \times 10^{-3}}{5 \times 10^{-3}}$ = 0.7

Mole fraction of CO_{2} = $\frac{1.5 \times 10^{-3}}{5 \times 10^{-3}}$ = 0.3

**Question 2: **What is the mole fraction of CH_{3}OH in an aqueous solution which is simultaneously 3.5m C_{2}H_{5}OH and 2m CH_{3}OH?

** Solution: **

3.5 m C_{2}H_{5}OH means 3.5 moles of C_{2}H_{5}OH in 1 kg water 2m CH_{3}OH means 2 moles of CH_{3}OH in 1 kg water. In 1 Kg of H_{2}O we have

$\frac{1000\ gm}{18.016\ gm\ mole}$ = 55.5 moles of H_{2}O

Total moles in the solution = 3.5 + 2 + 55.5

Total moles in the solution = 61 moles

Mole fraction of CH_{3}OH = $\frac{2\ moles}{61\ moles}$ = 0.0328

Moles of N

Moles of CO

Total number of moles = 3.5 $\times$ 10

Total number of moles = 5 $\times$ 10

Mole fraction of N

Mole fraction of CO

3.5 m C

$\frac{1000\ gm}{18.016\ gm\ mole}$ = 55.5 moles of H

Total moles in the solution = 3.5 + 2 + 55.5

Total moles in the solution = 61 moles

Mole fraction of CH