Mole fraction is another way of expressing solution concentration. Mole fraction is the ratio of moles of solute to the total number of moles of solute and solvent.

The symbol, ** X** with a subscript is normally used to denote the mole fraction of solute or solvent. That is X

_{A}is the mole fraction of solute A, and X

_{B }is the mole fraction of solvent B.

For instance, if an aqueous solution consists of solute A and solvent B. We can express the mole fraction of solute A as:

And the mole fraction of solvent B as:

Where **n _{A }**is the moles of solute A and

**n**

_{B}_{ }moles of solvent B.

Since each component in solution contributes a fraction of the total moles, the sum of all component’s mole fraction must equal to 1.

The mole percent is the mole fraction expressed as a percentage.

That is Mole percent (mol %) = mole fraction x 100

Mole fraction gives the actual proportion of solute or solvent particles in the solution.

**Question**

Calculate the mole fraction of NaCl in an aqueous solution that contains 20.0% NaCl by mass.

**Solution**

**Assume 100 g of solution and convert mass in percent to mass in grams**

Since solution is aqueous, it means the solution consists of only NaCl and water. And since concentration of NaCl in solution is in mass percent, we must assume 100 g of solution, and then convert the 20.0% NaCl to 20.0 g NaCl. Once we do, we will then subtract the mass of NaCl from the 100 g of solution to get mass of water in g. That is

mass of solvent (H_{2}O) in grams = 100 g solution – 20.0 g NaCl = 80.0 g H_{2}O.

**Convert mass of each component to moles**

*For molar mass NaCl, will calculate as*:

{(1 mol x 22.99 g/mol) + (1 mol x 35.45 g/mol)} = 58.44 g/mol

*For moles of NaCl, will calculate as: *

20.0 g x 1 mol/58.44 g = 0.342 mol NaCl

*For molar mass H _{2}O, will calculate as: *

{(2 mol x 1.01 g/mol) + (1 mol x 16.00 g/mol) =18.02 g/mol

*For moles of H _{2}O, will calculate as:*

80.0 g x 1 mol/18.02 g = 4.44 mol

Total moles of solute (NaCl) and solvent (H_{2}O) = 0.342 mol + 4.44 mol = 4.78 mol

Mole fraction of NaCl (X_{NaCl}) = mol of NaCl/ moles of (solute and solvent)

Mole fraction of NaCl (X_{NaCl}) = 0.342mol/4.78mol = 0.0715

To learn how to calculate solution concentration in Molarity, click here and in mass percent, click here.