Question

A solution contains 25% water, 50% ethanoic acid, and 25% ethanol by mass. Compute the mole fraction of each.

Answer 1

Mole fraction of the component is calculated by dividing the mole of the component to the total moles of all the components in the solution. The moles of the component is calculated by dividing the given mass of the component to the molecular mass of it.

Complete answer:
Mole fraction of any component in the solution is equal to the number of moles of that component divided by the total number of moles of all the components. For a solution containing ${{n}_{2}}$ moles of the solute dissolved in ${{n}_{1}}$ moles of the solvent.
Mole fraction of solute = ${{x}_{2}}=\dfrac{{{n}_{2}}}{{{n}_{2}}+{{n}_{1}}}$
Mole fraction of solvent = ${{x}_{1}}=\dfrac{{{n}_{1}}}{{{n}_{2}}+{{n}_{1}}}$
The sum of the mole fraction of the components is equal to 1.
The moles of the component is calculated by dividing the given mass of the component to the molecular mass of it.
$moles=\dfrac{given\text{ }mass}{molecular\text{ }mass}$
So, in the question the solution contains 25% water, 50% ethanoic acid, and 25% ethanol by mass.
25% of water means 25 g of water is present in 100 g of solution.
50% of ethanoic acid means 50 g of ethanoic acid is present in 100 g of solution.
25% of ethanol means 25 g of ethanol is present in 100 g of solution.
The molecular mass of water = $18g/mol$
The molecular mass of ethanoic acid = $60g/mol$
The molecular mass of ethanol = $46g/mol$
Number of moles of water = $\dfrac{25}{18}=1.4$
Number of moles of ethanoic acid = $\dfrac{50}{60}=0.8$
Number of moles of ethanol = $\dfrac{25}{46}=0.54$
So, the total number of moles of all components in the solution = 1.4+0.54+0.8 = 2.74
So, we have the moles of each component and total moles of the solution, therefore,
Mole fraction of water = $\dfrac{1.4}{2.74}=0.51$
Mole fraction of ethanoic acid =$\dfrac{0.8}{2.74}=0.291$
Mole fraction of ethanol = $\dfrac{0.54}{2.74}=0.197$
Hence the mole fraction of water is 0.51, ethanoic acid is 0.291, and ethanol is 0.197.

Note:
Mole fraction is a dimensionless quantity because we are dividing the moles with moles. When the percentage of the components is converted into mass, 100 g of the solution is taken for the easy calculation.