At T K xg of a non-volatile solid (molar mass 78 g mol - 1 ) when added to 0 . 5 kg water, lowered its…

At TKxg of a non-volatile solid (molar mass 78 g mol-1 ) when added to 0.5 kg water, lowered its freezing point by 1.0°C. What is x (in g) (Kf of water at T(K)=1.86 KKgmol-1)
  1. 10.48
  2. 20.96
  3. 41.92
  4. 5.24

Solution

\(\begin{aligned} &\begin{aligned} \Delta T_f & =k_f{}^* \text { molality } \\ \text {Weight } & =x g \\ \text {Mwt } & =78 \text { g } \\ \text {Molality } & =\text { moles present in 1kg solvent } \\ & =(x / 78) / 0.5 \\ & =\frac{x}{39} \end{aligned}\\ &\begin{aligned} \Delta T_f & =k_f{ }^* \text { molality } \\ 1 & =1.86 \times \frac{x}{39} \\ x & =\frac{39}{1.86} \\ x & =20.96 \mathrm{~g} . \end{aligned} \end{aligned}\) *

Asked in: JEE-TOPICTESTS-CHEMISTRY

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