Question

54% (w/w) water is present in the mixture of ethyl alcohol and water. Calculate the mole fraction of ethyl alcohol and water in the mixture.

Hint:

Always take a 100 g basis for w/w problems. Then convert given masses into moles and divide by total moles to find mole fraction.

Answer 1

Let us consider 100 g of solution.
Mass of water = 54 g, Mass of ethanol = 46 g.

Step 1: Calculate moles of water.
Molar mass of water = 18 g mol$^{-1}$.
Moles of water = $\dfrac{54}{18} = 3.00$ mol.

Step 2: Calculate moles of ethanol.
Molar mass of ethanol = 46 g mol$^{-1}$.
Moles of ethanol = $\dfrac{46}{46} = 1.00$ mol.

Step 3: Total moles.
Total moles = $3.00 + 1.00 = 4.00$ mol.

Step 4: Mole fractions.
Mole fraction of water = $\dfrac{3.00}{4.00} = 0.75$.
Mole fraction of ethanol = $\dfrac{1.00}{4.00} = 0.25$.
\[ \boxed{X_{\text{water}} = 0.75, X_{\text{ethanol}} = 0.25} \]