Lead storage battery contains 38 % by weight solution of H₂ SO₄. The van't Hoff factor is 2.67 at this concentration. The temperature in Kelvin at which the solution in the battery will freeze is ________. (Nearest integer).
Given K_f=1.8 K kg mol⁻¹

Solution

Chemistry ma’am · 4 steps

38% by weight means 38 g acid in 62 g water, and that 62 g of water is your solvent for molality.

1. Take 100 g. Take 100 g of solution. It holds 38 g of H₂SO₄ and 100 - 38 = 62 g of water. Molality needs the mass of the solvent only, so use 0.062 kg.
2. Find the molality. Moles of H₂SO₄ = 38/98 = 0.3878 mol. So m = 0.3878/0.062 = 6.254 mol kg⁻¹.

   Δ T_f = i K_f m = 2.67 × 1.8 × 6.254 = 30.06 K

3. Lower the freezing point. Water freezes at 273.15 K. The solution freezes at 273.15 - 30.06 = 243.09 K.
4. So. The battery solution freezes at about 243 K.

The common slip: 262. Leaving out the van't Hoff factor gives Δ T_f = 11.26 K and a freezing point of 262 K. Here i = 2.67 because H₂SO₄ ionises, so it must multiply K_f m.

The idea to keep. For a percent-by-weight solution, take a 100 g sample and subtract the solute to get the solvent mass. Molality always divides by kilograms of solvent, never of solution.

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