It is a unit less and dimension less quantity.

## Example Questions based on Mole Fraction Formula

**Question 1**
Find the mole fraction of Methanol CH

_{3}OH and water in a solution prepared by dissolving 4.5 g of alcohol in 40 g of H

_{2}O.

Molar Mass of H

_{2}O is 18gm/mole and Molar mass of CH

_{3}OH is 32gm/mole

**Solution**
Moles of CH

_{3}OH = 4.5 / 32 = 0.14 mole

Moles of H

_{2}O = 40 / 18 = 2.2 moles

Therefore, according to the equation

Mole fraction of CH

_{3}OH = 0.14 / 2.2 + 0.14

= 0.061

Mole fraction of H

_{2}O. = 2.2 / 2.2 + 0.14

= 0.940

**Question 2**
Calculate the mole fraction of HCl and H

_{2}O in a solution of hydrochloric acid in water, containing 30% HCl by weight.

**Solution**
The solution contains 30 grams of Hydrochloric acid and 70 grams of water. Also,

Molar mass of HCl is 36.5 grams/mole.

Molar mass of water is 18 grams/mole.

Moles of HCl = 30/36.5 = .821 moles of HCl

Moles of water = 70/18 = 3.88 moles of H2O.

Mole fraction of HCl = .821/(.821 + 3.88) = .174

Mole fraction of H2O = 3.88/(.821 + 3.88) = .825

**Question 3**
In a solution , we have 1 mole ofA , 1 mole ofB and 2 mole of C. Find the mole fraction of each of them

**Solution**
This is an extension of two component solution which we discussed above

Mole fraction will be defined as

χ_{A} = n_{A} / (n_{A} + n_{B} + n_{C} ) = 1/(1+1+2) =.25
χ_{B} = n_{B} / (n_{A} + n_{B} + n_{C} ) = 1/(1+1+2) =.25
χ_{C} = n_{C} / (n_{A} + n_{B} + n_{C} ) = 2/(1+1+2) =.5
Also
χ_{A} + χ_{B} + χ_{C} =1