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Question #44336

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The Question

A metal $M$ forms two sparingly soluble salts, $MX$ and $MY$ , with anions $X^-$ and $Y^-$ . The standard reduction potential of the $M^+(aq) / M(s)$ electrode is $+0.75\text{ V}$ at $298\text{ K}$ . The anions $X^-$ and $Y^-$ have identical ionic radii and hydration enthalpies. However, due to the higher polarizability of $Y^-$ , the standard Gibbs free energy of lattice formation ( $\Delta G^\circ_{\text{lattice}}$ ) for $MY(s)$ is $34.23\text{ kJ/mol}$ more negative than that of $MX(s)$ due to covalent stabilization (Fajans' rule).

If the solubility product $K_{sp}$ of $MX$ is $10^{-10}$ at $298\text{ K}$ , what is the standard reduction potential of the $MY(s) / M(s), Y^-(aq)$ electrode?

(Given: $\frac{2.303 RT}{F} = 0.059\text{ V}$ , $1\text{ F} = 96500\text{ C/mol}$ , $2.303 RT = 5.705\text{ kJ/mol}$ )

Options

A.
$-0.194\text{ V}$
B.
$+0.160\text{ V}$
C.
$+1.694\text{ V}$
D.
$+0.514\text{ V}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Numerical_Precision

Improve calculation stamina and avoid rounding errors in high-stakes competitive examinations.

Concepts Behind This Question

Fajans' Rule Polarization Power|Electrode Potential Dependencies|Gibbs Energy and Spontaneity

Why This Question Is Tricky

Common Mistakes

This question tests the intersection of Fajans' rule (polarization) and electrochemistry.

Students often memorize standard reduction potentials or Nernst equations without understanding the thermodynamic cycles behind them.

The 'Hidden Variable' here is how the covalent character in a solid lattice (polarization) stabilizes the solid state, thereby decreasing its solubility product ( $K_{sp}$ ).

This stabilization directly alters the Gibbs free energy of the half-reaction, shifting the reduction potential to a more negative value.

Failing to account for the thermodynamic stabilization of the lattice leads to incorrect $E^\circ$ values.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Bonding and Molecular Structure - Class 11 Part 1
Concept	Fajans' Rule Polarization Power
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free