JEE MAIN - Chemistry (2021 - 22th July Evening Shift - No. 14)
Explanation
To determine which solution has the lowest freezing point, you should consider the van 't Hoff factor $i$, which represents the number of particles the solute dissociates into when dissolved. The freezing point depression is given by:
$$ \Delta T_f = i \cdot K_f \cdot m $$
where:
$\Delta T_f$ is the change in freezing point,
$K_f$ is the freezing point depression constant,
$m$ is the molality of the solution,
$i$ is the van 't Hoff factor, which depends on the dissociation of the solute.
For each solute, the van 't Hoff factor $i$ can be determined as follows:
Option A: $\text{Al}_2(\text{SO}_4)_3$
Dissociates into 2 Al$^{3+}$ ions and 3 SO$_4^{2-}$ ions.
$i = 2 + 3 = 5$
Option B: $\text{C}_6\text{H}_{12}\text{O}_6$ (glucose)
Does not dissociate in solution (non-electrolyte).
$i = 1$
Option C: $\text{KI}$
Dissociates into K$^+$ and I$^-$ ions.
$i = 1 + 1 = 2$
Option D: $\text{K}_2\text{SO}_4$
Dissociates into 2 K$^+$ ions and 1 SO$_4^{2-}$ ion.
$i = 2 + 1 = 3$
Comparing the van 't Hoff factors, the solution of $\text{Al}_2(\text{SO}_4)_3$ will have the highest factor ($i = 5$), leading to the greatest freezing point depression. Thus, the $\text{Al}_2(\text{SO}_4)_3$ solution will have the lowest freezing point since the extent of freezing point depression is directly proportional to $i$.
Therefore, the solution of $\text{Al}_2(\text{SO}_4)_3$ has the lowest freezing point.
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