MX is a sparingly soluble salt that follows the given solubility equilibrium at 298 K. The standard reduction potential for the metal/metal insoluble salt electrode is
Q. MX is a sparingly soluble salt that follows the given solubility equilibrium at 298 K.

MX(s) ⇌ M+(aq) + X(aq);   Ksp = 10−10

If the standard reduction potential for M+(aq) + e → M(s) is (EΘM+/M) = 0.79 V, then the value of the standard reduction potential for the metal/metal insoluble salt electrode EΘX/MX(s)/M is ______ mV. (nearest integer)

[Given: \( \dfrac{2.303RT}{F} = 0.059 \, \text{V} \)]
Correct Answer: 200

Explanation (Complete Conceptual Solution)

For the metal/metal insoluble salt electrode, the reduction half reaction is:

\[ MX(s) + e^- \rightarrow M(s) + X^-(aq) \]

This reaction can be obtained by combining:

\[ M^+ + e^- \rightarrow M(s) \quad E^\Theta = 0.79 \, V \]

and the solubility equilibrium:

\[ MX(s) \rightleftharpoons M^+ + X^- \]

From the equilibrium expression:

\[ K_{sp} = [M^+][X^-] \]

For standard electrode potential of the insoluble salt electrode:

\[ E^\Theta = E^\Theta_{M^+/M} + \frac{0.059}{1} \log K_{sp} \]

Substituting the given values:

\[ E^\Theta = 0.79 + 0.059 \log (10^{-10}) \]

\[ \log (10^{-10}) = -10 \]

\[ E^\Theta = 0.79 + 0.059(-10) \]

\[ E^\Theta = 0.79 - 0.59 \]

\[ E^\Theta = 0.20 \, V \]

Convert into mV:

\[ 0.20 \, V = 200 \, mV \]

Final Answer = 200

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