Consider the reaction fo extraction of gold from its ore
`Au +2CN^(-) (aq)+(1)/(4)O_(2) (g)+(1)/(2)H_(2)O rarr Au(CN)_(2)^(-) +OH^(-)`
Use the following data to calculate `DeltaG^(@)` for the reaction
`K_(f) [Au(CN)_(2)^(-)] = X`
`{:(O_(2)+2H_(2)O +4e^(-)rarr4OH^(-),:,E^(@) =+0.41 "volt"),(Au^(3+)+3e^(-)rarr Au,:,E^(@) = +1.5 "volt"),(Au^(3+)+2e^(-)rarr Au^(+),:,E^(@) =+1.4 "volt"):}`

Options

A. `-RT ln X+1.29 F`
B. `-RT ln X-2.11 F`
C. `-RT ln. (1)/(X)+2.11F`
D. `-RT ln X-1.29 F`

Answer

A

Explanation

`Delta G=Delta G^(@)+RT ln K`
`Delta G^(@)=Delta G_(1)^(@)+Delta G_(2)^(@)+Delta G_(3)^(@)`
`=-n_(1)F E_(1)^(@)-n_(2)F E_(2)^(@)-n_(3)F E_(3)^(@)`