Thermodynamics of Mineral Resources - Thanatia: The Destiny of the Earth's Mineral Resources - page 270

moves an electric current of q Coulombs until equilibrium is reached.

W = qE = G (9.18)

Faraday's constant relates the electric charge of 96,485 C for each mole of elec-
trons and accordingly G becomes:

G = qFE (9.19)

or at standard conditions (T = 298K)
G 0 = qFE 0 (9.20)

The negative sign in Eq. (9.20) is placed in the equation to make the overall
solution positive, since the Gibbs free energy variation in a spontaneous reaction is
negative whilst the potential E is positive.
Furthermore, thermodynamic analysis provides the relationship between G
and the concentration of reactant species [Ox] and [Red] through Eq. (9.21), with
Q = [Red]=[Ox]. When equilibrium is reached, Q becomes the equilibrium constant
of the reaction (K p ) and G and subsequently E vanish. Therefore, Eq. (9.21)
becomes Eq. (9.22) and Eq. (9.23).
G = G 0 RTlnQ (9.21)

E = E 0 RT

nF lnQ = E 0 2:303RT

log 10 Q (9.22)

nF

or

E = E 0 0:0592
n

lnQ when T 0 =298K

(9.23)

The latter two equations bear the name of their discoverer Walther Nernst. They
link the concentration and electric gradients in a redox reaction. They also deter-
mine the relative electrode potential of any chemical species at any concentration
and temperature. In fact, if the assigned standard hydrogen electrode potential
E 0 is 0:0000V , then it is possible to measure and tabulate any other standard
redox potential.
This standard hydrogen electrode is based on the reaction 2H + (aq) + 2e ! H 2
and consists of a semi-cell in which bubbling hydrogen passes through an acid
electrolyte at a H + concentration of 1 mol/l at 1 bar and 298K.
Thus a sample cell of Zinc=Hydrogen (represented in Eq. (9.24)), oxidises
Zn(s) ! Zn 2+ + 2e and reduces 2H + (aq) + 2e ! H 2 , with a cell potential
of E 0 = 0.76 V, thus assigning a standard redox potential of E 0 = 0.76 V to
Zn=Zn 2+ oxidation.
Zn(s) j Zn 2+ ( aq, 1 M) jj H + ( aq, 1 M) j H 2 (1 atm)(g) (9.24)

The standard redox potentials are tabulated in Table D.1 in the Appendix. The
difference between two such potentials permits the calculation of the cell potential