Question

Molal depression constant for a solvent is \[4.0Kkgmo{l^{ - 1}}\]. The depression in the freezing point of the solvent for \[0.03molk{g^{ - 1}}\] solution of \[{K_2}S{O_4}\] is: (Assume complete dissociation of the electrolyte).
A. \[0.12K\]
B. \[0.36K\]
C. \[0.18K\]
D. \[0.24K\]

Answer 1

Hint: Depression in freezing point is a colligative property observed in solutions that results from the introduction of solute molecules to a solvent. The freezing points of solutions are all lower than that of the pure solvent and is directly proportional to molality of the solute.

Complete step by step answer:
To proceed for the solution. First, use the basics of the molal depression constant that is denoted by $\left( {{K_f}} \right)$. It is defined as the depression in the freezing point when solute is dissolved in a particular amount of the solvent. Now, start the numerical.
Given that,
Molal depression constant $\left( {{K_f}} \right)$\[ = 4K\,kg\,mo{l^{ - 1}}\]
Molality\[\left( m \right)\]of\[{K_2}S{O_4}\]solution \[ = 0.03K\,kg\,mo{l^{ - 1}}\]
To find \[van't\]hoff factor \[\left( i \right)\]
\[van't\]hoff factor \[\left( i \right)\] \[ = \]\[\dfrac{{number{\text{ of moles of solute particles after dissociation}}}}{{Initial{\text{ moles of solute}}}}\]
\[\therefore \,1{K_2}S{O_4}\xrightarrow{{{H_2}O}}2{K^ + } + 1SO_4^{2 - }\]
\[Then\,\,i\,\, = \dfrac{3}{1} = 3\]
By using the formula,
\[\Delta {T_f} = i\,{K_f}m\]
Where\[\Delta {T_f} = \]Depression in freezing point
\[i = van't\,{\text{ }}hoff\,factor\]
Kf\[ = \]molal depression constant
\[m{\text{ }} = \] molality of a solution
By putting the value of molal depression constant$\left( {{K_f}} \right)$, van’t hoff factor$\left( i \right)$and molality of a solution$\left( m \right)$, we get
\[\therefore \]\[\Delta {T_f} = 3 \times 4 \times 0.03\]
\[ = 0.36K\]
Thus, depression in freezing point \[(\Delta {T_f}) = 0.36K\]
Depression in freezing point behaves as a colligative property because it depends upon molality of the solution.

Hence the correct option is (B).

Note:
Colligative property is the property of the solution depending only upon the number of solute particles per unit volume. They are relative lowering of vapour pressure, elevation in boiling points, depression in freezing point and Osmotic pressure. These properties are valid and applicable only for dilute solutions in which the solute is a non – volatile solid. Depression in freezing point is the property of decrease in freezing point when non – volatile solute is dissolved. Freezing point is the temperature at which liquid and solid forms of the solvent are in equilibrium.