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Question #44770

Difficulty: 8/10 | 🟢 Free

The Question

A regenerative $\ce{H2-O2}$ fuel cell system operates at $298\text{ K}$ . The cell consists of two compartments separated by a bipolar ion-selective membrane that maintains a strict pH gradient. The anode compartment is buffered at $\text{pH} = 10$ and the cathode compartment is buffered at $\text{pH} = 4$ . Gases $\ce{H2}$ and $\ce{O2}$ are continuously supplied and maintained at $1\text{ bar}$ pressure.

During the discharge phase, the fuel cell delivers electrical work with a total overpotential loss (activation + ohmic) of $0.39\text{ V}$ . During the regeneration phase, the product water is electrolyzed back into $\ce{H2}$ and $\ce{O2}$ at $1\text{ bar}$ in their respective compartments, requiring an overpotential of $0.41\text{ V}$ .

Given: Standard reversible potential for the $\ce{H2-O2}$ fuel cell is $E^\circ = 1.23\text{ V}$ . Use $\frac{2.303 RT}{F} = 0.06\text{ V}$ .

Calculate the round-trip electrical energy efficiency of this regenerative system.

Options

A.
$60.0\%$
B.
$51.2\%$
C.
$37.5\%$
D.
$56.0\%$

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

Fuel Cell Efficiency|Faraday's First and Second Laws|Electrolysis Product Prediction

Why This Question Is Tricky

Common Mistakes

This problem tests the integration of thermodynamics (concentration cells) with real-world electrochemical kinetics (overpotential).

The primary trap is ignoring the Nernstian shift caused by the pH gradient.

Students who blindly use the standard potential ( $E^\circ = 1.23\text{ V}$ ) will calculate $V_{dis} = 0.84\text{ V}$ and $V_{reg} = 1.64\text{ V}$ , leading to the incorrect efficiency of $51.2\%$ .

The problem requires recognizing that an acid-base fuel cell generates a higher thermodynamic potential because the reaction is driven forward by producing protons in a basic medium and consuming them in an acidic medium.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Electrochemistry - Class 12
Concept	Fuel Cell Efficiency
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free