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Question #44731

Difficulty: 8/10 | 🟢 Free

The Question

Consider the following electrochemical cell at $298 \text{ K}$ :

$Pt(s) | H_2(g, 1 \text{ bar}) | HA(aq, 0.1 \text{ M}) || Cu^{2+}(aq, 0.01 \text{ M}) | Cu(s)$

Given: Acid dissociation constant of the weak acid $HA$ , $K_a = 1.0 \times 10^{-5}$ Standard reduction potential, $E^\circ_{Cu^{2+}/Cu} = +0.34 \text{ V}$ $\frac{2.303 RT}{F} = 0.059 \text{ V}$ Faraday's constant, $F = 96500 \text{ C mol}^{-1}$

Calculate the Gibbs free energy change ( $\Delta G$ ) for the cell reaction.

Options

A.
-88.39 \text{ kJ mol}^{-1}
B.
-65.62 \text{ kJ mol}^{-1}
C.
-71.31 \text{ kJ mol}^{-1}
D.
-122.55 \text{ kJ mol}^{-1}

Check Your Answer

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

Nernst Equation Concentration Dependence|Degree of Dissociation (Alpha)|Gibbs Energy and Spontaneity

Why This Question Is Tricky

Common Mistakes

The core trap tests the distinction between stoichiometric concentration and active ion concentration in weak electrolytes.

Students often blindly substitute the given molarity ( $0.1 \text{ M}$ ) into the Nernst equation, ignoring the degree of dissociation ( $\alpha$ ) dictated by $K_a$ .

This leads to an incorrect reaction quotient ( $Q=1$ instead of $10^{-4}$ ) and a severely underestimated cell potential and Gibbs free energy (Option B).

Furthermore, the stoichiometry of the hydrogen half-cell requires squaring the $[H^+]$ term in $Q$ , acting as a secondary trap for those who forget to balance the electron transfer properly (Option C).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Electrochemistry - Class 12
Concept	Nernst Equation Concentration Dependence
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free