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Comprehension
A fuel cell is the device to convert the energy of a fuel into electrical energy without the use of heat engine, where the fuel is burnt directly. Such conversions are possible because the combustion reactions are essentially redox reactions and highly exothermic as well as highly exergonic. Electrical energy can be obtained indefinitely from a fuel cell as along as the outside supply of fuel is maintained. In hydrogen-oxygen fuel cell, the following reactions take place:
Anode reaction: \( \quad 2 \mathrm{H}_{2}(\mathrm{~g})+4 \mathrm{OH}^{-}(\mathrm{aq}) \rightarrow 4 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+4 \mathrm{e}^{-} \)
Cathode reaction: \( \quad \mathrm{O}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+4 \mathrm{e}^{-} \rightarrow 4 \mathrm{OH}^{-}(\mathrm{aq}) \)
Overall reaction: \( \quad 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \)
The overall reaction has a value of \( \Delta H^{\circ}=-285.8 \mathrm{~kJ} \) and \( \Delta G^{\circ}=-237.39 \mathrm{~kJ} \) at \( 25^{\circ} \mathrm{C} \) per mole of \( \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \).
What volume of gaseous \( \mathrm{H}_{2} \) (at STP), when
(a) \( 2.27 \mathrm{~L} \)
(b) \( 4.54 \mathrm{~L} \) combined with excess \( \mathrm{O}_{2} \) in the fuel cell, is needed to produce \( 23.739 \mathrm{~kJ} \) of useful work under
(c) \( 1.13 \mathrm{~L} \)
(d) \( 2.24 \mathrm{~L} \) standard conditions?
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