In a face centred cubic array of the ions of a metal, all the tetrahedral voids are occupied by chloride ions. The reduction potential of a chlorine electrode measured at 1 bar in contact with a satur

Question

In a face centred cubic array of the ions of a metal, all the tetrahedral voids are occupied by chloride ions. The reduction potential of a chlorine electrode measured at 1 bar in contact with a saturated solution of this metal chloride is 1.72 V at $2 5^{\circ} C$ . If the $K_{sp}$ of the salt is $x \times 1 0^{- 19}$ , what is the value ' $x$ '?

TestHub · Accepted Answer

The formula of the metal chloride must be $MCl_{2}$ as all tetrahedral voids are occupied.

$MCl_{2} (s) ⟶ M^{2 +} (aq) + 2 Cl^{-} (aq)$

Let S be the solubility.

$Cl_{2} + 2 e^{-} ⟶ 2 Cl^{-} 1.72 = 1.36 - \frac{0.06}{2} lo g \frac{[ Cl ^{-} ] ^{2}}{p _{Cl_{2}}} \Rightarrow [Cl^{-}] = 1 0^{- 6} M 2 S = 1 0^{- 6} \Rightarrow S = \frac{1}{2} \times 1 0^{- 6} K_{sp} = 4 S^{3} = 4 \times (\frac{1}{2} \times 1 0^{- 6})^{3} = 5 \times 1 0^{- 19}$

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JEE Advanced (2028)