# What is Mole Fraction?

There are several ways to indicate the concentration of the solution and mole fraction is one of them. Mole fraction is a unit of concentration. In the solution, the relative amount of solute and solvents are measured by the mole fraction and it is represented by “X.”

 The mole fraction is the number of moles of a specific component in the solution divided by the total number of moles in the given solution.

## Formula related to the mole fraction

Consider a solution consists of two substances A and B, then the mole fraction of each substance is,

$Mole fraction of solute=\frac{Moles of solute}{Total number of moles of all the solvent}$ $X_{A}= \frac{mol A}{mol A + mol B}$

And

$X_{B}= \frac{mol B}{mol A + mol B}$

Note:

1. In the given mixture, sum of all the mole fractions is equal to one.

XA + XB = 1

2. The multiplication of the mole fraction by 100 gives the mole percentage.

3. Mole fraction is a unitless and dimensionless expression.

• Mole fraction is not dependent on the temperature.
• The information about the density of the phase is not necessary to calculate the mole fraction.
• In the case of an ideal gas mixture, the mole fraction is represented by the ratio of partial pressure to total pressure of the mixture.

### Solved examples

1. Calculate the mole fraction of NaCl and H2O, if 0.010 moles of NaCl is dissolved in 100 grams of pure water.

Answer: Mole fraction of NaCl is 0.018 and the mole fraction of water is 0.982

Solution:

The molecular weight of water = 18.0153 grams per mole

Number of moles of water = $\frac{100 grams}{18.0153 grams}$

= 5.56 moles

Mole fraction of NaCl = $\frac{0.100 moles}{5.56 moles + 0.100 moles}$

= $\frac{0.100 moles}{5.66 moles}$

Mole fraction of NaCl = 0.018

Mole fraction of H2O = $\frac{5.56 moles}{5.66 moles}$

Mole fraction of H2O = 0.982

2. Calculate the mole fraction of acetone in the solution containing 1 mole of benzene, 2 moles carbon tetrachloride and 7 moles acetone.

Answer: Mole fraction of acetone is 0.7

Solution:

Number of moles of acetone = 7 moles

Total number of moles in the solution = Number of moles of benzene + number of moles of

carbon tetrachloride + number of moles of acetone

= 1 mole + 2 moles + 7 moles

= 10 moles

Mole fraction of acetone = $\frac{number of moles of acetone}{Total number of moles in the solution}$

=$\frac{7moles}{10 moles}$

Mole fraction of acetone = 0.7

Mole fraction of benzene = $\frac{1 mole}{10 moles}$

= 0.1

Mole fraction of carbon tetrachloride = $\frac{2 moles}{10 moles}$

Mole fraction of carbon tetrachloride = 0.2

3. 25.7 grams of formaldehyde (CH2O) is dissolved in 3.25 moles of carbon tetrachloride (CCl4), calculate the mole fractions of formaldehyde.

Answer: Mole fraction of formaldehyde is 0.208

Solution:

The molecular weight of formaldehyde = 30.03 grams

The number of moles of formaldehyde = $\frac{25.7 grams}{30.03 grams}$

= 0.856 moles

Total number of moles in the solution = 0.856 moles + 3.25 moles

= 4.106 moles

Mole fraction of formaldehyde = $\frac{0.856 moles}{4.106 moles}$

= 0.208 moles

4. The solution is prepared by mixing 25.0 grams of ethanol and 25.0 grams of water. Determine the mole fractions of each component.

Ans: Mole fraction of water is 0.71 and the mole fraction of ethanol is 0.29.

Solutions:

The molecular weight of ethanol = 46.07 g/mol

The number of moles of ethanol = $\frac{25.0 g}{46.07 g/mol}$

= 0.543 moles

The molecular weight of water = 18.0 g/mol

The number of moles of water = $\frac{25.0 g}{18.0 g/mol}$

= 1.34 moles

Total number of moles in the solution = 0.543 mol + 1.34 mol

= 1.883 moles

Mole fraction of ethanol = $\frac{0.543 moles}{1.886 moles}$

= 0.29

Mole fraction of water = $\frac{1.34 moles}{1.886 moles }$

= 0.71