Q68 / 180 · AIIMS 2018 (26 May) · Chemistry

When $45 \mathrm{~g}$ of solute is dissolved in $600 \mathrm{~g}$ water, freezing point gets lowered by $2.2 \mathrm{~K}$, calculate molar mass of solute. $\left(K_f=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$

  • Correct answer
    A
    $63.4 \mathrm{~g} \mathrm{~mol}^{-1}$
  • B
    $80 \mathrm{~g} \mathrm{~mol}^{-1}$
  • C
    $90 \mathrm{~g} \mathrm{~mol}^{-1}$
  • D
    $21 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} & \text { } w_1=600 \mathrm{~g}, \quad \Delta T_f=2.2 \mathrm{~K} \\ & w_2=45 \mathrm{~g}, \quad K_f=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \\ & M=\frac{K_f \times w_2}{\Delta T_f \times w_1}=\frac{1.86 \times 45 \times 1000}{2.2 \times 600}=63.4 \mathrm{~g} \mathrm{~mol}^{-1}\end{aligned}$

Hence, the correct answer is option: 'A'.

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