Calculate Molality of H₂SO₄ Solution in Water

What is the molality of a solution containing 583 g of H₂SO₄ dissolved in 1.50 kg of water?

In order to calculate the molality of the solution, we need to determine the moles of solute (H₂SO₄) and the mass of the solvent (water) in kilograms. The molar mass of H₂SO₄ is approximately 98 g/mol, consisting of 2 hydrogen atoms, 1 sulfur atom, and 4 oxygen atoms. Given that there are 583 g of H₂SO₄ in the solution, we can calculate the moles of H₂SO₄ as follows: 583 g / 98 g/mol ≈ 5.95 mol Meanwhile, the mass of the solvent (water) is 1.50 kg. By using the formula for molality: m = n_solute / m_solvent we can then calculate the molality of the solution: m = 5.95 mol / 1.50 kg ≈ 10.26 mol/kg Therefore, the molality of the H₂SO₄ solution in the automobile battery is approximately 10.26 mol/kg.

Explanation:

Calculating Moles of H₂SO₄: H₂SO₄ has a molar mass of 98 g/mol. So by dividing the mass of H₂SO₄ (583 g) by its molar mass, we get: 583 g / 98 g/mol ≈ 5.95 mol Converting Mass of Water to kg: Given that the mass of water in the solution is 1.50 kg, no further conversion is needed. Calculating Molality: Using the formula for molality, we divide the moles of solute by the mass of the solvent in kilograms: m = 5.95 mol / 1.50 kg ≈ 10.26 mol/kg Therefore, the molality of the H₂SO₄ solution in the automobile battery is approximately 10.26 mol/kg.
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