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Draw a neat labelled diagram of ${H_2} - {O_2}$ fuel cell. Write the reactions that occur at the cathode of the cell.

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Hint: In a fuel cell, electrical energy gets converted from chemical potential energy (energy stored in molecular bonds). A Proton Exchange Membrane (PEM) cell uses hydrogen gas (\[{H_2}\]) and oxygen gas (\[{O_2}\]) as fuel. The products of the reaction are water, heat, and electricity.

Complete step by step answer:
The diagram of ${H_2} - {O_2}$ fuel cell is shown below:
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The reaction occurs at cathode of the cell is given below:
The Reducing process at cathode: Oxygen gas water molecules are reduced to Hydroxide ions:
\[{O_2}(g) + 2{H_2}_O(l) + 4{e^ - } \to 4O{H^ - }(aq)\].
Fuel cells are galvanic cells in which the energy of combustion of fuels is directly converted into the electrical energy. This Fuel Cell is also known as ${H_2} - {O_2}$ cell. In this cell the commonly used fuels are methanol, hydrogen etc.
The cell reactions in ${H_2} - {O_2}$ cell takes place at both the electrodes that are at cathodes and anodes. At Cathodes the reduction process takes place while on an Anode the Oxidation process takes place. The reaction at the both the terminals is explained below:
At Anode: The reaction (Oxidation) which takes place at anode is given below:
\[2{H_2}(g) + 4O{H^ - }(aq) \to 4{H_{2}}O(l) + 4{e^ - }2{H_2}(g) + 4O{H^ - }(aq) \to 4{H_2}O(l) + 4{e^ - }\]
In this reaction Hydrogen Gas and hydroxide ions are oxidized to form water. The valency of all the components are taken care of.
At cathode: Reduction process takes place –
\[{O_2}(g) + 2{H_2}O(l) + 4{e^ - } \to 4O{H^ - }(aq)\]
In this reaction Oxygen gas and Water molecules are reduced to Hydroxide ions. The valency of all the elements have been taken care of and fulfilled.

Note: 1) Both Oxidation and Reduction processes take place in the cell reaction.
2) Fuel cells can attain 80% of the energy efficiency.
3) Fuel cells are significantly lighter and more compact.
4) Hydrogen is expensive to produce and not widely available.
5) High cost in manufacturing due to the cost of catalyst (platinum).
6) The ${H_2} - {O_2}$ fuel cell is used as fuel in Space crafts and the end products of the cell reaction are eco friendly.