Mole Fraction Formula with Solved Examples

Mole Fraction Formula

Mole fraction is used to calculate the sum of mole fraction of all the components in a solution. We will learn the mole fraction formula with conceptual clarity.

What Is Mole Fraction?

Mole fraction refers to the ratio of the number of moles of the specific component and the total number of moles of all the components comprising the given mixture. Mole fraction signifies the relative amount of solute and solvent in a solution. It is denoted by X. It is the sum of the mole fractions of all the components which equals 1. Mole fraction is a dimensionless and unitless quantity.  

Applying Mole Fraction Formula

To calculate mole fraction, knowing the density of the component is not required. For the gas mixture, the mole fraction of a specific component is the ratio of partial pressure of a specific component to the total partial pressure of all the components comprising the solution. To calculate the mole fraction, consider a mixture consisting of two components A and B then the mole fraction of one component A = number of moles of A/ sum of total moles of A and B components comprising the mixture. 

Mole fraction of A component —>XA=nA /nA+nB

Mole fraction of B component —> XB=nB / nA+nB

Total mole fraction of A and B = XA + XB = 1

Solved Examples

1. Calculate the mole fraction of MgCl2 and H2O, if 2 moles of MgCl2 are dissolved in 1000 grams of water.

The molecular weight of H2O = 18 grams per mole

Number of moles of H2O = Given weight/ Molecular weight  = 55.6 moles

Mole fraction of MgCl2 = number of moles of MgCl2/ total moles = 2/ 57.5

Mole fraction of MgCl2= 0.034

Mole fraction of H2O = 55.6/ 57.6 = 0.96

2. Calculate the mole fraction of Ethanol and water, if 3 moles of ethanol are dissolved in 1000 grams of water.

The molecular weight of H2O = 18 grams per mole

Number of moles of H2O = Given weight/ Molecular weight  = 55.6 moles

Mole fraction of Ethanol = number of moles of ethanol/ total moles = 3/ 58.5

Mole fraction of Ethanol = 0.05128

Mole fraction of H2O = 55.6/ 58.5 = 0.95