Calculate the molar mass of a non-volatile solute when $1 \ g$ of it is dissolved in $100 \ g$ of solvent,which decreases its freezing point by $0.2 \ K$. Given: $K_{f} = 1.2 \ K \ kg \ mol^{-1}$.

  • A
    $55 \ g \ mol^{-1}$
  • B
    $60 \ g \ mol^{-1}$
  • C
    $65 \ g \ mol^{-1}$
  • D
    $70 \ g \ mol^{-1}$

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Column-$I$ (Various solutions) Column-$II$ (Freezing point)
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Given: Freezing point of $0.1 \, M$ sucrose solution $= 272 \, K$ and freezing point of water $= 273 \, K$.
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Statement $(I) :$ Molal depression constant $K_{f}$ is given by $\frac{M_1 R T_f^2}{1000 \Delta H_{\text {fus }}}$,where symbols have their usual meaning. (Note: The provided formula in the prompt was corrected to the standard thermodynamic expression $K_f = \frac{M_1 R T_f^2}{\Delta H_{\text {fus }}}$).
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Calculate the mass of ascorbic acid (Vitamin $C$,$C_{6}H_{8}O_{6}$) to be dissolved in $75 \ g$ of acetic acid to lower its melting point by $1.5 \ ^{\circ}C$. $K_{f} = 3.9 \ K \ kg \ mol^{-1}$.

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