Question

Equimolal solutions of KCl and compound X in ${{H}_{2}}O$ show depressions of freezing points in a 4:1 ratio. Assuming KCl to be ionized completely, the compound X must?
A. Dissociate to extent of 50%
B. Hydrolyse to the extent of 80%
C. Trimerize to extent of 75%
D. Dimerize to extent of 50%

Answer 1

Hint: There is a relationship between depression freezing point and molality of the solution. By using that we can calculate the ionization of compound X.
\[\Delta {{T}_{f}}=i{{K}_{f}}m\]
Where $\text{ }\!\!\Delta\!\!\text{ }{{\text{T}}_{\text{f}}}\text{=Depression in freezing point}$
i = Van't Hoff factor
\[{{\text{K}}_{\text{f}}}\text{=Freezing point constant}\]
m = molality of the solution

Complete step by step answer:
- In the question it is given to find the ionization of the compound X in water.
- For the compound KCl the relation between depression freezing point and molality of the solution and it is as follows.
\[\begin{align}
  & \Delta {{T}_{f}}=i{{K}_{f}}m \\
 & \Delta {{T}_{f}}(KCl)=i{{K}_{f}}m \\
\end{align}\]
- KCl is going to form two ions in water then i = 2 and substitute the value of ‘i' in the above formula.
\[\begin{align}
  & \Delta {{T}_{f}}(KCl)=i{{K}_{f}}m \\
 & \Delta {{T}_{f}}(KCl)=2{{K}_{f}}m \\
\end{align}\]
- For the compound X the relation between depression freezing point and molality of the solution and it is as follows.
\[\begin{align}
  & \Delta {{T}_{f}}=i{{K}_{f}}m \\
 & \Delta {{T}_{f}}(X)=i{{K}_{f}}m \\
 & \Delta {{T}_{f}}(X)=\dfrac{1}{2}(2{{K}_{f}}m) \\
\end{align}\]
- The dissociation constant of compound ‘ X’ can be written as follows.
At Initial: $\begin{align} {\mathop{{}}}\,\underset{1}{\mathop{2X}}\,\to \underset{0}{\mathop{{{X}_{2}}}} \end{align}$
At Sometime: $\begin{align}{\mathop{{}}}\,\underset{1-\alpha }{\mathop{2X}}\,\to \underset{\dfrac{\alpha }{2}}{\mathop{{{X}_{2}}}} \end{align}$
- ‘i' value for the above reaction is as follows.
\[\begin{align}
  & i=1+\alpha +\dfrac{\alpha }{3}=1-\dfrac{2\alpha }{3} \\
 & =\dfrac{1}{2} \\
 & \alpha =\dfrac{3}{4} \\
\end{align}\]
- Means 75% of the compound ‘X’ is going to dissociate in water.
- Therefore the compound ‘X’ is going to trimerize to 75%.

So, the correct option is C.

Note:
Some compounds will dimerize and some compounds trimerize in solution and it is going to depend on the solubility of the compound in water. If the solubility of the compound is less then the compound will dimerize or trimerize in the solution.