Molar mass of H₂SO₄ = 98 g/mol.
Solution 1: 100 g at 98% gives 98 g H₂SO₄ = 1 mol; water = 2 g = 0.111 mol.
Solution 2: 100 g at 49% gives 49 g H₂SO₄ = 0.5 mol; water = 51 g = 2.833 mol.
Mixed solution: Total H₂SO₄ = 1 + 0.5 = 1.5 mol.
Total water = 0.111 + 2.833 = 2.944 mol.
Mole fraction of H₂SO₄ = 1.5/(1.5 + 2.944) = 1.5/4.444 = 0.337.