A solution of H₂ SO₄ is 31.4 % H₂ SO₄ by mass and has a density of 1.25 g / mL. The molarity of the H₂ SO₄ solution is _________ M (nearest integer)
[Given molar mass of H₂ SO₄=98 g mol⁻¹]

Solution

Chemistry ma’am · 4 steps

Take 100 g of solution, then use the density to turn that mass into a volume.

1. Pick a sample. Take 100 g of solution. At 31.4% by mass, it holds 31.4 g of H₂SO₄.
2. Moles of acid. n = 31.4/98 = 0.3204 mol of H₂SO₄.
3. Volume of solution. Molarity needs litres of solution, so use the density. V = (100 g)/(1.25 g mL⁻¹) = 80 mL = 0.080 L.

   M = (0.3204 mol)/(0.080 L) = 4.005 mol L⁻¹

4. So. The molarity is about 4.0 M, which rounds to 4.

The common slip: 3. Taking the volume of 100 g of solution as 100 mL ignores the density and gives about 3.2 M, which rounds to 3.

The idea to keep. For mass percent and density to molarity, use M = (% by mass × 10 × d)/(molar mass), with d in g/mL. It is just the 100 g sample method in one line.

Answer from the NTA final answer key. Solution by PrepWiser.