Of the following $0.1 M$ aqueous solutions, which one will exhibit the largest freezing point depression?

(AIMPT 2015)

C_{6} H_{12} O_{6}

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K_{2} S O_{4}

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K C l

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A l_{2} (S O_{4})_{3}

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Solution

The correct option is D $A l_{2} (S O_{4})_{3}$
Depression in freezing point is given by,
$Δ T_{f} = i \times K_{f} \times m$

where,

$Δ T_{f}$ is the depression in freezing point.

$K_{f}$ is molal depression constant.

$m$ is molality of solution.

$i$ is van't Hoff factor

Molality of all given solutions are same,
hence,
$Depression in freeziong point \propto i$

$K_{2} S O_{4} \to 2 K^{+} (a q) + S O_{4}^{2 -} (a q)$
$i = 3$

$K C l \to K^{+} + C l^{-}$
$i = 2$

$A l_{2} (S O_{4})_{3} \to 2 A l^{3 +} + 3 S O_{4}^{2 -}$
$i = 5$

$i$ for $C_{6} H_{12} O_{6}$ is $1$

Hence, option (c) is correct.

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