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NEET CHEMISTRYMedium

The density of a 2 M2 \text{ M} aqueous solution of NaOHNaOH is 1.28 g/cm31.28 \text{ g/cm}^3. The molality of the solution is: [molecular mass of NaOH=40 g mol−1NaOH = 40 \text{ g mol}^{-1}]

A

1.20 m1.20 \text{ m}

B

1.56 m1.56 \text{ m}

C

1.67 m1.67 \text{ m}

D

1.32 m1.32 \text{ m}

Step-by-Step Solution

  1. Understand Molarity: A 2 M2 \text{ M} solution contains 2 moles of solute (NaOHNaOH) in 1 Litre (1000 mL1000 \text{ mL}) of solution .
  2. Calculate Mass of Solution: Mass=Density×Volume\text{Mass} = \text{Density} \times \text{Volume} Mass of solution=1.28 g/mL×1000 mL=1280 g\text{Mass of solution} = 1.28 \text{ g/mL} \times 1000 \text{ mL} = 1280 \text{ g}
  3. Calculate Mass of Solute (NaOHNaOH): Mass=Moles×Molar Mass\text{Mass} = \text{Moles} \times \text{Molar Mass} Mass of NaOH=2 mol×40 g/mol=80 g\text{Mass of } NaOH = 2 \text{ mol} \times 40 \text{ g/mol} = 80 \text{ g}
  4. Calculate Mass of Solvent (Water): Mass of Solvent=Mass of Solution−Mass of Solute\text{Mass of Solvent} = \text{Mass of Solution} - \text{Mass of Solute} Mass of Solvent=1280 g−80 g=1200 g=1.2 kg\text{Mass of Solvent} = 1280 \text{ g} - 80 \text{ g} = 1200 \text{ g} = 1.2 \text{ kg}
  5. Calculate Molality (mm): Molality is defined as moles of solute per kilogram of solvent . m=Moles of SoluteMass of Solvent (kg)m = \frac{\text{Moles of Solute}}{\text{Mass of Solvent (kg)}} m=21.2≈1.666... mm = \frac{2}{1.2} \approx 1.666... \text{ m} Rounding to two decimal places, the molality is 1.67 m1.67 \text{ m}.
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