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. 1.0968 V
B. 0.0968 V
C. 1.968 V
D. 2.0968 V

Answer

A

Explanation

`C_(5)H_(12)(g)+ 8O_(2)(g) rarr 5CO_(2)(g) + 6H_(2)O(l)`
`Delta G^(@)= 5(-394.4) + 6(-237.2)- (-8.2) - 8(0)`
`Delta G^(@)= -3387kJ`
The combined reaction can be divided into following two half-cell reactions: `C_(5)H_(12)(g) rarr CO_(2)(g)` (oxidation at anode)
`C_(5)H_(12) + 10H_(2)O rarr 5CO_(2) + 32H^(+) + 32e^(-)` ...(i)
`O_(2)(g) rarr H_(2)O(l)` (reduction at cathode)
`4e^(-) + O_(2)(g) + 4H^(+) rarr 2H_(2)O(l)` ...(ii)
By applying ii) eq.(i) + 8 `xx` eq.( we get:
`C_(5)H_(12) + 8O_(2) rarr 5CO_(2) + 6H_(2)O`, hence `n= 32e^(-) Delta G^(@)= -nF E_("cell")^(@)`
`-3387 xx 10^(3)J= -32 xx 96500 xx E_("cell")^(@)`
`E_("cell")^(@)= 1.0968V`