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Question #44218

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The Question

Consider a hydrogen-oxygen fuel cell operating reversibly and isothermally at $298 \text{ K}$ and $1 \text{ bar}$ . The overall cell reaction is: $\ce{H2(g) + 1/2O2(g) -> H2O(l)}$ Given the standard thermodynamic data at $298 \text{ K}$ : $\Delta_f H^\circ(\ce{H2O, l}) = -285.8 \text{ kJ mol}^{-1}$ $\Delta_f S^\circ(\ce{H2O, l}) = -163.3 \text{ J K}^{-1} \text{ mol}^{-1}$ $R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}$ Assume ideal gas behavior and negligible volume for liquid water. Which of the following represents the correct values of heat exchanged ( $q$ ) and the change in internal energy ( $\Delta U$ ) for the consumption of $1 \text{ mole}$ of $\ce{H2(g)}$ ?

Options

A.
$q = -48.66 \text{ kJ mol}^{-1}$ , $\Delta U = -282.08 \text{ kJ mol}^{-1}$
B.
$q = -285.80 \text{ kJ mol}^{-1}$ , $\Delta U = -282.08 \text{ kJ mol}^{-1}$
C.
$q = -48.66 \text{ kJ mol}^{-1}$ , $\Delta U = 0 \text{ kJ mol}^{-1}$
D.
$q = -237.14 \text{ kJ mol}^{-1}$ , $\Delta U = -285.80 \text{ kJ mol}^{-1}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

Don't get tricked by the process! Learn the mechanical traps used in competitive exam questions.

Concepts Behind This Question

First Law Consistency|Fuel Cell Efficiency|Electrode Potential Sign Conventions

Why This Question Is Tricky

Common Mistakes

The problem tests the application of the First Law of Thermodynamics to electrochemical systems involving non-PV work.

Students often fall into two traps: (1) Assuming $\Delta U = 0$ because the process is isothermal, confusing ideal gas expansion with a chemical reaction. (2) Assuming $q = \Delta H$ at constant pressure, forgetting that this relation only holds when non-PV work (like electrical work in a fuel cell) is zero.

By forcing the calculation of $q$ in a reversible fuel cell, students must recognize that $q_{rev} = T\Delta S$ and $\Delta U$ depends on $\Delta H$ and $\Delta n_g RT$ .

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Thermodynamics - Class 11 Part 1
Concept	First Law Consistency
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free