For the reduction of silver ions with copper metal, the standard cell potential was foound to be `+0.46 V` at `25^(@) C`. The value of standard Gibbs energy, `DeltaG^(@)` will be `(F = 96,500C mol^(-1))`:

Options

A. `-98.00 kJ`
B. `-89.0 kJ`
C. `-89.0 J`
D. `-44.5 kJ`

Answer

B

Explanation

The relationship between `E_("cell")^(@)` for a galvanic cell and `Delta_(r)G^(@)`, the standard Gibbs energy change, for the chemical reaction of the cell is
`Delta_(r)G^(@) = -nFE_("cell")^(@)`
For the cell reaction
`2Ag^(+)(aq.)+Cu(s) rarr Cu^(2+)(aq.)+2Ag(s)`
We have
`n = 2 mol`
`E_("cell")^(@) = +0.46 V` Therefore
`Delta_(r)G^(@) = (-2 mol)(96,500 C mol^(-1))(+0.46 V)`
`= -88780 J = -88.780 kJ`
`= -89.0 kJ`