A fuel cell is a cell that is continuously supplied with an oxidant and a reductant so that it can deliver a current indefinitely. Fuel cell offer the possibility of achieving high thermodynamic efficiency in the conversion of Gibbs energy into mechanical work. Internal combustion engines at best convert only the fraction `(T_(2)-T_(1))T_(2)` of heat of combustion into mechanical work. While the thermodynamic efficiency of the fuel cell is give by, `eta=(|DeltaG|)/(|DeltaH|)`, where `DeltaG` is the Gibbs energy change for the cell reaction and `DeltaH` is the enthalpy change of the cell reaction. This efficiency can be upto 80%-90% also in contrast to normal heat engine efficiency which are generally about 40%

Fuel cells may be classified according to the temperature range in wich they operate low temperature (25 to `100^(@)C`), medium temperature (100 to `500^(@)C)`), high temperature `(500 "to" 1000^(@)C)` and very high temperature is that catalyst for the various steps in the process are not so necessary. Polarization of a fuel cell reduces the current. Polarization is the result of slow reactions or processes such as diffusion in the cell. The figure indicates the construction of hydrogen-oxygen fuel cell with a solid electrolyte, which is an ion exchange membrane. The membrane is impermeable to the reactant gases, but is permeable to hydrogen ions, which carry the current between the electrodes. To facillitate the operation finely divided platinum that function as a catalyst. Water is drained out of the cell during operation. Fuel cells of this general type have been used successfully in the space program and are quite efficient. their disadvantages for large-scale commercial application are that hydrogen presetns storage problems, and platinum is an expensive catalyst. Cheaper catalysts have been found for higher temperature operatureof hydrogen-oxygen fuel cells. Fuel cells taht use hydrocarbons and air have been developed, but their power per unit weight is too low to make them practical in ordinary automobiles. Better catalysts are needed. A hydrogen-oxygen fuel cell may hae an acidic or alkaline electrolyte. The half-cell reactions are:
`(1)/(2)O_(2)(g)+2H^(+)+2e^(-)rarrH_(2)O(l) E^(@)=1.2288V`
`2H^(+)+2e^(-)rarrH_(2)(g)E^(@)=0`
`H_(2)(g)+(1)/(2)O_(2)(g)rarrH_(2)O(l) E^(@)=1.2288V`
or `(1)/(2)O_(2)(g)+H_(2)O(g)+2e^(-)rarr2OH^(-) E^(@)=0.4009V`
`2H_(2)O(l)+2e^(-)rarrH_(2)(g)+2OH^(-)E^(@)=-0.8279V`
`H_(2)(g)+(1)/(2)O_(2)(g)rarrH_(2)O(l) E^(@)=1.2288V`
To maximize the power per unit mass of an electrochemical cell, the electronic and electrolytic resistances of the cell must be minimized. than aqueous solutions, high-temperature electrochemical cells are of special interest for practical applications. High temperature also allow the use of liquid metal electrode, which makes possibel high current densities than solid electrodes.
For a hydrogen-oxygen fuel cell if `DeltaH_(f)^(2)(H_(2)O,l)=-285kJ//""mole""`, then what will be its thermodynamic efficiency under standard conditions (use data given in the passage if required)?

Options

A. 0.91
B. 0.41
C. 0.63
D. 0.83

Answer

D