In which of the following pairs of solutions will the values of the van ’t Hoff factor be the same?

0.05 M K_{4} [F e (C N)_{6}]

and

0.10 M F e S O_{4}

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0.15 M K_{4} [F e (C N)_{6}]

and

0.05 M F e S O_{4}

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0.20 M NaCl

and

0.10 M B a C l_{2}

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0.05 M F e S O_{4} . (N H_{4})_{2} S O_{4} .6 H_{2} O

and

0.02 M KCl . M g C l_{2} . 6 H_{2} O

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Solution

The correct option is D $0.05 M F e S O_{4} . (N H_{4})_{2} S O_{4} .6 H_{2} O$ and $0.02 M KCl . M g C l_{2} . 6 H_{2} O$
As both are strong electrolytes, $α = 1$ for them
$K_{4} [F e (C N)_{6}] \to 4 K^{+} + [F e (C N)_{6}]^{4 -}$
n = 5
$F e S O_{4} (N H_{4})_{2} S O_{4} .6 H_{2} O \to F e^{2 +} + 2 N H_{4}^{+} + 2 S O_{4}^{2 -}$
n = 5
As $α = 1$ for both electrolytes and also n = 5 then van 't Hoff factor is the same for them.

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