The density of 'x' M solution ('x' molar) of NaOH is 1.12 g mL⁻¹, while in molality, the concentration of the solution is 3 m ( 3 molal). Then x is
(Given : Molar mass of NaOH is 40 g / mol)

Solution

Chemistry ma’am · 4 steps

Take 1000 g of water, add 3 mol of NaOH, and find out how many litres that solution fills.

1. Read the molality. 3 molal means 3 mol of NaOH dissolved in 1000 g of water. That is 3 × 40 = 120 g of NaOH.
2. Mass of solution. Solution mass is solute plus solvent: 1000 + 120 = 1120 g.

   V = mass/density = (1120 g)/(1.12 g mL⁻¹) = 1000 mL = 1 L

3. Molarity. Molarity is moles of solute per litre of solution: x = (3 mol)/(1 L) = 3 M.
4. So. x = 3.0, option (b). Here molarity and molality happen to be equal because the solution's volume works out to exactly 1 L.

The idea to keep. To switch between molality and molarity, fix 1000 g of solvent, add the solute's mass, and use density to turn that total mass into solution volume. Or use M = (1000 m d)/(1000 + m Mₛₒₗᵤₜₑ).

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