Standard free energies of formation (I `kJ //`mol ) at `298 K` are ` -237 .2 , - 394 .4` and `- 8.2 ` for `H_2 O(1), CO_2 (g)` and pentange (g) , respectively . The value of `E_(cell)^@` for the pentane-oxygen fuel cell is .

Options

A. `1.968 V`
B. `2.0968 V`
C. `1.0968 V`
D. `0.1968 V`

Answer

C

Explanation

( c) `DeltaG ` of `H_(2)O(l) =-237.2 kJ//mol`
`DeltaG " of " CO_(2)(g) =-394.4 kJ//mol`
`Delta G ` of pentane (g) `=-8.2kJ//mol`
In pentane-oxygen fuel cell following reaction takes place
`{:(C_(5)H_(12)+10H_(2)O(l) to 5CO_(2)+32H^(+)+32e^(-)),(underline(8O_(2)+32H^(+)+32e^(-) to 16H_(2)O(l)" ")),(C_(5)H_(12)+8O_(2) to 5CO_(2)+6H_(2)O(l)","E^(@)=?):}`
`DeltaG_("reaction")=sumDeltaG_("product")-sumDeltaG_("reactant")`
`=5xxDeltaG_((CO_(2)))+6 DeltaG_((H_(2)O))-[DeltaG_((C_(6)H_(12)))+8xxDeltaG_(O_(2))]`
`=5xx(-394.4)+6xx(-237.2)-(-(8.2+0)`
`=-3387 kJ//mol`
`=-3387xx10^(3) J//mol`
`DeltaG=-nFE_(cell)^(@)`
`-3387xx10^(3)=-32xx96500xxE_(cell)^(@)`
`E_(cell)^(@)=(-3387xx10^(3))/(-32xx96500)=1.0968 V`