Before You Begin

Question #44784

Difficulty: 8/10 | 🟢 Free

The Question

For a standard $H_2-O_2$ fuel cell operating at $1\text{ bar}$ , the standard molar entropies of $H_2(g)$ , $O_2(g)$ , and $H_2O(l)$ are $130.6$ , $205.0$ , and $69.9\text{ J K}^{-1}\text{ mol}^{-1}$ respectively. The standard enthalpy of formation of $H_2O(l)$ is $-285.8\text{ kJ mol}^{-1}$ . Assuming $\Delta H^\circ$ and $\Delta S^\circ$ are independent of temperature, which of the following represents the temperature coefficient of the cell $\left(\frac{\partial E^\circ}{\partial T}\right)_P$ and the theoretical maximum electrical work obtainable from $1\text{ mole}$ of $H_2(g)$ at $398\text{ K}$ ? (Given: $F = 96500\text{ C mol}^{-1}$ )

Options

A.
$-8.46 \times 10^{-4}\text{ V K}^{-1}$ and $220.8\text{ kJ}$
B.
$-1.38 \times 10^{-3}\text{ V K}^{-1}$ and $180.1\text{ kJ}$
C.
$+8.46 \times 10^{-4}\text{ V K}^{-1}$ and $350.7\text{ kJ}$
D.
$-1.69 \times 10^{-3}\text{ V K}^{-1}$ and $220.8\text{ kJ}$

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

Electrode Potential Dependencies|Fuel Cell Efficiency|Temperature Coefficient (Q10)

Why This Question Is Tricky

Common Mistakes

The problem tests the thermodynamic dependency of fuel cell potential on temperature.

Students often assume that higher temperatures increase the efficiency or work output of a cell due to increased kinetic energy.

However, for a hydrogen-oxygen fuel cell, the reaction is exothermic and involves a decrease in gaseous moles, leading to a negative $\Delta S^\circ$ .

Consequently, the temperature coefficient $\left(\frac{\partial E^\circ}{\partial T}\right)_P$ is negative, meaning the cell potential and maximum electrical work ( $-\Delta G^\circ$ ) actually decrease at higher temperatures.

The trap options exploit errors in stoichiometry (forgetting the $1/2$ coefficient for $O_2$ ), misidentifying $n=1$ , or assuming a positive entropy change.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Electrochemistry - Class 12
Concept	Electrode Potential Dependencies
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free