The realtionship between standard `emf(E_("cell")^(@))` of a galvanic cell and standard Gibbs energy change `(Delta_(r)G^(@))` for the chemi-cal reaction of the cell is

Options

A. `Delta_(r)G^(@) = nFE_("cell")^(@)`
B. `Delta_(r)G^(@) = nF//E_("cell")^(@)`
C. `Delta_(r)G^(@) = -nFE_("cell")^(@)`
D. `Delta_(r)G^(@) = -nF//E_("cell")^(@)`

Answer

C

Explanation

Some of the most important results of elecrochemicsty are the realatlionship amonge cell `emf`, Gibbs-energy change and equilibrium constant. The Gibbs enerfy change `DeltaG` (decreases) for a reaction equals the maximum useful work of the reaction
`Delta_(r)G = w_max`
for a voltaic cell, this work is the electrical work, `-nFE_("cell")` (where n is the number of moles of electrons transferred in a reaction), so when the reactants and products are in their standard states, we have
`Delta_(r)G = -nFE_("cell")^(@)`
where `Delta_(r)G^(@)` is measured in joules, `E_("cell")^(@)` is measured in volts, `F` is the faraday, the charge on `1` mole of electrons, `9.65 c 10^(4)C`. With this equation, emf measurement becomes an important source of thermodynamic information. Alternatively, thermodynamic data can be used to calculate cell emfs. Due to negative sign, the direction of spontaneous change gives a negative value for `Delta_(r)G^(@)` but a positive value for `E^(@)`
The two quantitative measures of the driving force of a chemical reaction are: the Gibbs-energy change `DeltaG` (a ther-mochemical quantity) and the cell potential (a thermochemical quantity).