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Solutions — Chemistry STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceChemistrySolutions4 Marks
Question
Obtain the relationship between freezing point depression of a solution containing nonvolatile nonelectrolyte and its molar mass.
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Answer

The freezing point depression, $\Delta T_f$ of a solution is directly proportional to molality (m) of the solution.
$ \therefore \Delta T _f \propto m$
$\therefore \Delta T _{ f }= K _{ f } m $
where $Kf$ is a molal depression constant.
The molality of a solution is given by,
$m=\frac{\text { Number of moles of the solute }}{\text { Weight of the solvent in } kg }$
If $W_1$ grams of a solvent contain $W_2$ grams of a solute of the molar mass $M_2$, then the molality $m$ of the solution is given by,
$ \text { g } g mol ^{-1} kg \quad kg mol ^{-1}$
$\therefore \Delta T_{ f }=K_{ f } \times \frac{W_2 \times 1000}{W_1 M_2 \text { }}$
If the weights are expressed in $kg$ then,
$\Delta T _{ f }= K _{ f } \times \frac{W_2}{W_1 M_2}$
The unit of $K _{ f }$ is $K kg mol ^{-1}$
Hence, from the measurement of the depression in the freezing point of the solution, the molar mass of the substance can be determined.

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