An aqueous KCl solution of density 1.20 g mL⁻¹ has a molality of 3.30 mol kg⁻¹. The molarity of the solution in mol L⁻¹ is ____________ (Nearest integer) [Molar mass of KCl = 74.5]

Solution

Chemistry ma’am · 3 steps

Take 1 kg of water, add the KCl to get the solution's mass, then use density to find its volume.

1. Pick a basis. Molality 3.30 mol kg⁻¹ means 3.30 mol of KCl dissolved in 1000 g of water. The mass of KCl is 3.30 × 74.5 = 245.85 g.
2. Mass and volume. The solution's mass is 1000 + 245.85 = 1245.85 g. Its volume is 1245.85/1.20 = 1038.2 mL, which is 1.0382 L.

   M = (3.30 mol)/(1.0382 L) = 3.18 mol L⁻¹

3. So. The molarity is 3.18 mol L⁻¹, which rounds to 3.

The common slip: 4. Taking the solution's mass as just 1000 g, without adding the 245.85 g of KCl, gives a volume of 833 mL and a molarity of 3.96, which rounds to 4.

The idea to keep. To go from molality to molarity, start with 1 kg of solvent. Add the solute's mass to get the solution's mass, and divide by density to get its volume. Molarity always uses the solution's volume.

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