A 1 molal (1 m) aqueous solution of sodium chloride has a density of 1.21 g mL−1. What is the molarity of this solution? (Molar mass of NaCl = 58.5 g mol−1)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1.143 M
Molality is moles of solute per kilogram of solvent; molarity is moles of solute per litre of solution. A 1 m solution has 1 mol of NaCl in 1000 g of water; the density turns the mass of this solution into its volume.
Mass of NaCl: 1 mol × 58.5 g mol−1 = 58.5 g.
Mass of solution: 1000 g + 58.5 g = 1058.5 g.
Volume of solution: \( \displaystyle V=\frac{1058.5\,\mathrm{g}}{1.21\,\mathrm{g\,mL^{-1}}}=874.8\,\mathrm{mL}=0.8748\,\mathrm{L} \)
\( \displaystyle \text{Molarity}=\frac{\text{Moles of solute}}{\text{Volume of solution in litre}} \)
\( \displaystyle \text{Molarity}=\frac{1\,\mathrm{mol}}{0.8748\,\mathrm{L}} \)
\( \displaystyle \text{Molarity}=1.143\,\mathrm{mol\,L^{-1}}=1.143\,\mathrm{M} \)