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Question #44805

Difficulty: 8/10 | 🟢 Free

The Question

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

$\ce{Ag(s) | AgNO3 (aq, C_2) || AgNO3 (aq, C_1) | Ag(s)}$

Initially, the concentrations in both half-cells are $C_1 = C_2 = 0.10 \text{ M}$ . The anodic compartment ( $C_2$ ) is subjected to a controlled photochemical process that causes the zero-order reduction of $\ce{Ag+}$ to $\ce{Ag(s)}$ with a rate constant $k = 1.0 \times 10^{-3} \text{ mol L}^{-1} \text{ s}^{-1}$ .

Given that the transport number of the nitrate ion is $t_- = 0.60$ and assuming ideal behavior, calculate the rate of change of the cell potential, $\frac{dE_{\text{cell}}}{dt}$ , at $t = 50 \text{ s}$ .

[Use $\frac{RT}{F} = 25 \text{ mV}$ ]

Options

A.
$0.60 \text{ mV s}^{-1}$
B.
$0.50 \text{ mV s}^{-1}$
C.
$0.40 \text{ mV s}^{-1}$
D.
$0.30 \text{ mV s}^{-1}$

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

Zero Order Rate Integration|Liquid Junction Potential|Nernst Equation Concentration Dependence

Why This Question Is Tricky

Common Mistakes

This problem tests the synthesis of chemical kinetics and advanced electrochemical thermodynamics.

The primary trap is twofold: First, students often conflate linear concentration decay (zero-order kinetics) with linear voltage decay, failing to apply the nested chain rule to the logarithmic Nernst equation.

Second, the 'Hidden Variable' is the Liquid Junction Potential ( $E_{\text{lj}}$ ).

In a concentration cell with transference, the measured potential is not just the Nernst potential; it is scaled by a factor of $2t_-$ due to the unequal mobilities of the ions across the junction.

Ignoring $E_{\text{lj}}$ leads to Option B, while misapplying the transport numbers leads to Option C.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Kinetics - Class 12
Concept	Zero Order Rate Integration
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free