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# What is the approximate value of $\Delta S{}^\circ$ for the fuel cell reaction at $25{}^\circ$? A.$-0.1624\text{ }J{{K}^{-1}}$B.$-162.4\text{ }J{{K}^{-1}}$C.$+162.4\text{ }J{{K}^{-1}}$D.$+0.1624\text{ }J{{K}^{-1}}$ Verified
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Hint: We know that we know that a device that converts chemical potential energy into electrical energy is called a fuel cell. Water, electricity, and heat are the products of this cell. We must remember that the standard emf of the hydrogen-oxygen cell, the positive value of the emf value indicates that the cell reaction is spontaneous under standard conditions.

A hydrogen-oxygen fuel cell contains an electrolyte solution like potassium hydroxide solution and two inert carbon electrodes. The gases of hydrogen and oxygen are bubbled through the anode and cathode compartments in which the following reactions take place. We must remember that the standard emf of the hydrogen-oxygen cell is the positive value of the emf value indicates that the cell reaction is spontaneous under standard conditions.
Here we have fuel cell; $\Delta H=-285.6\text{ }J/K\text{ };\text{ }\Delta G=-237.4\text{ }J/K\text{ }and\text{ }T=25+273=298K.$
According to Law of Thermodynamics; $\Delta G=\Delta H-T\Delta S$
where, $\Delta G=$ Gibbs Energy; $\Delta H=$ Enthalpy Change; $T=$ Temperature and $\Delta S=$ Entropy Change.
On substituting the values we get;
$-237.4=-285.6-298\left( \Delta S \right)$
On further solving we get;
$\Delta S=-162.4\text{ }J{{K}^{-1}}$
Therefore,the correct answer is option B.

Note:
Remember that the porous carbon electrodes in the cell serve as electrical conductors and also provide the necessary surfaces for the initial decomposition of the molecules into atomic species. The porous carbon electrodes in the cell serve as electrical conductors and also provide the necessary surfaces for the initial decomposition of the molecules into atomic species.