Calculate the molar mass of solute when 1.5 gram nonvolatile solute dissolved in $100 \mathrm{~mL}$ solvent…

Calculate the molar mass of solute when 1.5 gram nonvolatile solute dissolved in $100 \mathrm{~mL}$ solvent having density $0.8 \mathrm{~g} \mathrm{~mL}^{-1}$ lowers its freezing point by $0.75 \mathrm{~K}$. (Freezing point depression constant for solvent is $5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ )
  1. $125 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $110 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $100 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $75 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} & \Delta T_f=k_f \cdot \frac{W_B}{M_B} \times \frac{1000}{W_A} \\ & 0.75=5 \times \frac{1.5}{M_B} \times \frac{1000}{80} \\ & M_B=125 \mathrm{~g} / \mathrm{mol}\end{aligned}$

Asked in: MHT CET 2022 (06 Aug Shift 2)

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