The density of a 3M3 M (molar) solution of NaClNaCl is 1.25 g mL11.25 \text{ g mL}^{-1}. The molality (mm) of the solution is:

Model Answer & Options

Source: Extra Practice

2.79 m

3.25 m

1.50 m

3.00 m

Explanation

Molality (mm) = (moles of solute) / (mass of solvent in kg). Molarity (MM) = 3 mol/L. Mass of 1 L (1000 mL) of solution = density ×\times volume = 1.25 g/mL×1000 mL=1250 g1.25 \text{ g/mL} \times 1000 \text{ mL} = 1250 \text{ g}. Mass of NaClNaCl (solute) in 1 L = moles ×\times molar mass = 3 mol×58.5 g/mol=175.5 g3 \text{ mol} \times 58.5 \text{ g/mol} = 175.5 \text{ g}. Mass of solvent (water) = mass of solution - mass of solute = 1250 g175.5 g=1074.5 g=1.0745 kg1250 \text{ g} - 175.5 \text{ g} = 1074.5 \text{ g} = 1.0745 \text{ kg}. Molality (mm) = 3 mol/1.0745 kg2.79 mol/kg3 \text{ mol} / 1.0745 \text{ kg} \approx 2.79 \text{ mol/kg} or 2.79 m2.79 \text{ m}. Option 2 and 3 are incorrect due to calculation errors, and Option 4 incorrectly assumes molarity equals molality when density is not 1 g/mL1 \text{ g/mL}.

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