Mole fraction is defined as the ratio of moles of one components to the total no. of moles of all the components present in solution. It is a unit/Dimension less quantity.
If a substance A of n_{A} moles is dissolves in solution of B having n_{B } ,then mole fraction is expressed as denoted by (chi)
For two components

where, n = moles
$moles = \frac {Weight }{Molar Mass}$

Solved Examples

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 of A , 1 mole of B 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