Mole Fraction Formula, Definition and Examples

Example Questions based on Mole Fraction Formula

Question 1
Find the mole fraction of Methanol CH₃OH and water in a solution prepared by dissolving 4.5 g of alcohol in 40 g of H₂O.
Molar Mass of H₂O is 18gm/mole and Molar mass of CH₃OH is 32gm/mole
Solution
Moles of CH₃OH = 4.5 / 32 = 0.14 mole
Moles of H₂O = 40 / 18 = 2.2 moles
Therefore, according to the equation
Mole fraction of CH₃OH = 0.14 / 2.2 + 0.14
= 0.061
Mole fraction of H₂O. = 2.2 / 2.2 + 0.14
= 0.940

Question 2
Calculate the mole fraction of HCl and H₂O 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