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Question: Molal depression constant of water is \[1.86Kgmo{l^{ - 1}}\].0.02 mole of urea dissolved in 100g of ...

Molal depression constant of water is 1.86Kgmol−11.86Kgmo{l^{ - 1}}.0.02 mole of urea dissolved in 100g of water will freeze at:
A. 0.186∘C^\circ C
B. -0.372∘C^\circ C
C. 1.86∘C^\circ C
D. 3.72∘C^\circ C

Explanation

Solution

This question is of depression in freezing point where we have molal depression constant and molality given so we can calculate freezing point with the help of formula that depression of freezing point is proportional to molality of the solution.

Complete step by step solution:
First let us discuss depression in freezing point before solving the question.
The lowering of vapour pressure of a solution causes a lowering of the freezing point compared to that of the pure solvent .We know that at the freezing point of a substance, the solid phase is in dynamic equilibrium with the liquid phase. Thus, freezing point of a substance may be defined as the temperature at which the vapour pressure of the substance in its liquid phase is equal to its vapour pressure in the solid phase.
According to Raoult’s law, when a non-volatile solid is added to the solvent its vapour pressure decreases and now it would become equal to that of solid solvent at lower temperature. Thus, the freezing point of the solvent decreases.
Let Tf∘{T_f}^\circ be the freezing point of pure solvent and Tf{T_f} be its freezing point when non-volatile solute is dissolved in it. The decrease in freezing point
ΔTf=Tf∘−Tf\Delta {T_f} = {T_f}^\circ - {T_f} is known as depression in freezing point.
ΔTf∝m\Delta {T_f} \propto m,
Now we apply given data to our formula.
ΔTf=Kfm ⇒Tf∘−Tf=KfnV  \Delta {T_f} = {K_f}m \\\ \Rightarrow {T_f}^\circ - {T_f} = {K_f}\dfrac{n}{V} \\\
Where n-number of moles of solute, V-volume of solvent

⇒ΔTf=1.86×0.02100×10−3\Rightarrow \Delta {T_f} = 1.86 \times \dfrac{{0.02}}{{100 \times {{10}^{ - 3}}}}
⇒ΔTf=−0.372∘C\Rightarrow \Delta {T_f} = - 0.372^\circ C

Hence our correct option is B.

Note: Remember the formula carefully sometime students learn molarity instead of molality and solve incorrectly. Molal depression constant is also known as cryoscopic constant or freezing point depression constant.