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$3.24 g$ of $Hg {({NO}_{3})}_{2}$ (molar mass = 324) dissolved in 1000 g of water constitutes a solution having a freezing point of $- {0.0558}^{\circ} C$ while 21.68 g of ${HgCl}_{2}$ (molar mass = 271) in 2000 g of water constitutes a solution with a freezing point of $- {0.0744}^{\circ} C$ The $K_{f}$ for water is $1.86 \frac{K - K g}{Mol}$ About the state of ionization of these two solids in water it can be inferred that:

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$Hg {({NO}_{3})}_{2}$ and ${HgCl}_{2}$ both are completely ionized

$Hg {({NO}_{3})}_{2}$ is fully ionized but ${HgCl}_{2}$ is fully unionized

$Hg {({NO}_{3})}_{2}$ and ${HgCl}_{2}$ both are completely unionized

$Hg {({NO}_{3})}_{2}$ a is fully unionized but ${HgCl}_{2}$ is fully ionized.

answer is B.

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Detailed Solution

For ${Hg}_{g} {({NO}_{3})}_{2} :$

$0.0558 = i \times 1.86 \times \frac{\frac{3.24}{324}}{1} \Rightarrow i = 3 ∴ α = 100 %$

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