For the fuel cell reaction `2H_(2)(g) +O_(2)(g) rarr 2H_(2)O(l), Deta_(f)H_(298)^(@) (H_(2)O,l) =- 285.5 kJ//mol` What is `Delta_(298)^(@)` for the given fuel cell reaction?
Given: `O_(2)(g) +4H^(+)(aQ) +4e^(-) rarr 2H_(2)O(l) E^(@) = 1.23 V`

Options

A. `-0.322 J//K`
B. `-0.635 kJ//K`
C. `3.51 kJ//K`
D. `-0.322 kJ//K`

Answer

D

Explanation

`{:(2H_(2) +O_(2) rarr H_(2)O ,DeltaH = 2X - 285.5 kJ),(O_(2)+4H^(+) +4e^(-) rarr 2H_(2)O, E^(@) = 1.23),(2H_(2) rarr 4H^(+) +4e^(-),E^(@) = 0),("for reaction":,),(O_(2) +2H_(2) rarr 2H_(2)O, E^(@) = 1.23):}`
`DeltaG^(@) = -nFE^(@) =- 4 xx 96500 xx 1.23 =- 474780`
`DeltaG^(@) = DeltaH^(@) - T DeltaS^(@) - 474780 =- 571000 - 298 DeltaS^(@)`
`DeltaS^(@) =- 322.8 J//K`