Q61 / 180 · JIPMER 2018 · Chemistry

Which one of the following electrolytes has the same value of van't Hoff factor (i) as that of $\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]$ ?

  • Correct answer
    A
    $\mathrm{Al}_2\left(\mathrm{SO}_4\right)_3$
  • B
    $\mathrm{K}_2 \mathrm{SO}_4$
  • C
    $\mathrm{K}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right]$
  • D
    $\mathrm{Al}\left(\mathrm{NO}_3\right)_3$

Solution

The value of van't Hoff factor of the given molecule is as follows : $\begin{aligned} \mathrm{Al}_2\left(\mathrm{SO}_4\right)_3 & \rightleftharpoons 2 \mathrm{Al}^{3+}+3 \mathrm{SO}_4^{2-}, \mathrm{i}=5 \\ \mathrm{~K}_2 \mathrm{SO}_4 & \rightleftharpoons 2 \mathrm{~K}^{+}+\mathrm{SO}_4^{2-}, \mathrm{i}=3 \\ \mathrm{~K}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right] & \rightleftharpoons 3 \mathrm{~K}^{+}+\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3+}, \mathrm{i}=4 \\ \mathrm{Al}\left(\mathrm{NO}_3\right)_3 & \rightleftharpoons \mathrm{Al}^{3+}+3 \mathrm{NO}_3^{-}, \mathrm{i}=4\end{aligned}$ The van't Hoff factor for $\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]$ is $\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right] \rightleftharpoons 4 \mathrm{~K}^{+}+\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{4-}, \mathrm{i}=5$ $\therefore \mathrm{Al}_2\left(\mathrm{SO}_4\right)_3$ has the same value of van't Hoff factor as that of $\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]$.

Hence, the correct answer is option: 'A'.

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