Solutions and Colligative Properties - Result Question 12-1
12. For $1$ molal aqueous solution of the following compounds, which one will show the highest freezing point?
(2018 Main)
(a) $\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_3$
(b) $\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{Cl}\right] \mathrm{Cl}_2 \cdot \mathrm{H}_2 \mathrm{O}$
(c) $\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{Cl}_2\right] \mathrm{Cl} \cdot 2 \mathrm{H}_2 \mathrm{O}$
(d) $\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_3 \mathrm{Cl}_3\right] \cdot 3 \mathrm{H}_2 \mathrm{O}$
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Answer:
Correct Answer: 12. (d)
Solution:
Key idea: “Addition of solute particles to a pure solvent results to depression in its freezing point.”
All the compounds given in question are ionic in nature so, consider their van’t Hoff factor $(i)$ to reach at final conclusion.
The solution with maximum freezing point must have minimum number of solute particles. This generalisation can be done with the help of van’t Hoff factor (i) i.e.
Number of solute particles $\propto$ van’t Hoff factor $(i)$
Thus, we can say directly
Solution with maximum freezing point will be the one in which solute with minimum van’t Hoff factor is present
Now, for $\left.\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_3 \rightleftharpoons\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}+3 \mathrm{Cl}^{-}$
van’t Hoff factor $(i)$ is $4$ . Similarly for,
$ \begin{gathered} {\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{Cl}\right] \mathrm{Cl}_2 \cdot \mathrm{H}_2 \mathrm{O} \rightleftharpoons\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{Cl}^{2+}+2 \mathrm{Cl}^{-} \cdot i \text { ’ is } 3\right.} \\ {\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{Cl}_2\right] \mathrm{Cl} \cdot 2 \mathrm{H}_2 \mathrm{O} \rightleftharpoons\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{Cl}_2\right]^{+}+\mathrm{Cl}^{-} \text {’ } i \text { ’ is } 2} \end{gathered} $
and for $\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_3 \mathrm{Cl}_3\right] \cdot 3 \mathrm{H}_2 \mathrm{O}$, ’ $i$ ’ is $1$ as it does not show ionisation. Hence, $\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_3 \mathrm{Cl}_3\right] \cdot 3 \mathrm{H}_2 \mathrm{O}$ have minimum number of particles in the solution.
So, freezing point of its solution will be maximum.
BETA
