Before You Begin

Question #44734

Difficulty: 8/10 | 🟢 Free

The Question

A galvanic cell is constructed as follows: $\ce{Ag(s) | Ag+(aq, 1 M) || Cl-(aq) | Cl2(g, 1 bar) | Pt(s)}$ .

The chloride ions in the cathode compartment are continuously consumed by a pseudo-first-order chemical reaction. During the kinetic study, the cell potential $E_{cell}$ is observed to increase linearly with time $t$ .

Let $S$ be the constant rate of increase of the cell potential ( $S = \frac{dE_{cell}}{dt}$ ). The experiment is conducted at two different temperatures, $T_1$ and $T_2$ ( $T_2 > T_1$ ), yielding rates $S_1$ and $S_2$ , respectively.

Assuming the pre-exponential factor of the consumption reaction is independent of temperature, which of the following expressions correctly represents the activation energy ( $E_a$ ) of the chloride consumption reaction?

Options

A.
$E_a = \frac{R T_1 T_2}{T_2 - T_1} \ln \left( \frac{S_2 T_1}{S_1 T_2} \right)$
B.
$E_a = \frac{R T_1 T_2}{T_2 - T_1} \ln \left( \frac{S_2}{S_1} \right)$
C.
$E_a = \frac{R T_1 T_2}{T_2 - T_1} \ln \left( \frac{S_2 T_2}{S_1 T_1} \right)$
D.
$E_a = \frac{R T_1 T_2}{T_2 - T_1} \ln \left( \frac{S_1 T_2}{S_2 T_1} \right)$

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|Graphical Slopes Analysis|Instantaneous vs. Average Rate

Why This Question Is Tricky

Common Mistakes

The core trap lies in the assumption that the slope of the $E_{cell}$ vs $t$ graph is directly proportional ONLY to the rate constant $k$ .

Students frequently forget that the Nernst equation itself contains a temperature-dependent term ( $\frac{RT}{nF}$ ).

Consequently, they equate the ratio of rate constants $\frac{k_2}{k_1}$ directly to the ratio of slopes $\frac{S_2}{S_1}$ , leading to the incorrect Arrhenius expression (Option B).

This problem elegantly bridges Electrochemistry, Chemical Kinetics, and Thermodynamics, penalizing superficial formula memorization.

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