Explanation

Molar mass of H₂SO₄ is:

\[ 2(1) + 32 + 4(16) = 98\ \text{g mol}^{-1} \]

From 100 g of 98% (w/w) H₂SO₄ solution:

Mass of H₂SO₄ = 98 g
Mass of water = 2 g

Moles of H₂SO₄ = \( \frac{98}{98} = 1 \) mol
Moles of water = \( \frac{2}{18} = 0.111 \) mol

From 100 g of 49% (w/w) H₂SO₄ solution:

Mass of H₂SO₄ = 49 g
Mass of water = 51 g

Moles of H₂SO₄ = \( \frac{49}{98} = 0.5 \) mol
Moles of water = \( \frac{51}{18} = 2.833 \) mol

Total moles of H₂SO₄ = \(1 + 0.5 = 1.5\) mol

Total moles of water = \(0.111 + 2.833 = 2.944\) mol

Total moles in solution = \(1.5 + 2.944 = 4.444\) mol

Mole fraction of H₂SO₄ is:

\[ X_{\text{H}_2\text{SO}_4} = \frac{1.5}{4.444} \approx 0.337 \]

Hence, the mole fraction of H₂SO₄ in the resultant solution is 0.337.

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