Question

100 g 98% by weight \( \mathrm{H_2SO_4} \) is mixed with 100 g 49% by weight \( \mathrm{H_2SO_4} \). Mole fraction of \( \mathrm{H_2SO_4} \) in the solution is:

• A. \(0.9\)
• B. \(0.1\)
• C. \(0.67\)
• D. \(0.33\)

Hint:

When solutions are mixed:
Always compute masses of solute and solvent separately
Convert masses into moles before finding mole fraction

Answer 1

The Correct Option is D

Concept: Mole fraction of a component is given by: \[ \text{Mole fraction} = \frac{\text{Number of moles of the component}}{\text{Total number of moles of all components}} \] We calculate moles from given mass percentages.
Step 1: Calculate mass of \( \mathrm{H_2SO_4} \) and water. From 100 g of 98% solution: \[ \mathrm{H_2SO_4} = 98 \text{ g}, \quad \mathrm{H_2O} = 2 \text{ g} \] From 100 g of 49% solution: \[ \mathrm{H_2SO_4} = 49 \text{ g}, \quad \mathrm{H_2O} = 51 \text{ g} \] Total masses: \[ \mathrm{H_2SO_4} = 147 \text{ g}, \quad \mathrm{H_2O} = 53 \text{ g} \]
Step 2: Convert mass into moles. Molar masses: \[ \mathrm{H_2SO_4} = 98 \text{ g mol}^{-1}, \quad \mathrm{H_2O} = 18 \text{ g mol}^{-1} \] \[ \text{Moles of } \mathrm{H_2SO_4} = \frac{147}{98} = 1.5 \] \[ \text{Moles of } \mathrm{H_2O} = \frac{53}{18} \approx 2.94 \]
Step 3: Calculate mole fraction of \( \mathrm{H_2SO_4} \). \[ X_{\mathrm{H_2SO_4}} = \frac{1.5}{1.5 + 2.94} \] \[ = \frac{1.5}{4.44} \approx 0.33 \] \[ \boxed{X_{\mathrm{H_2SO_4}} = 0.33} \]