Page 140 - Basic physical chemistry for the atmospheric sciences

1 2 6 Basic physical chemistry

can use Eq. (6. 20) to derive the value of �ell for a reaction from the
)
6.G0 value, where 6.G0 for molar quantities is given by Eq . (2. 3 4 . We
can also relate the standard cell potential for a reaction that is in
chemical equilibrium to the equilibrium constant Kc for the reaction.
Combining Eqs. (2.46) and (6.20), we get

*
- n F �ell = - R T i n Kc
or,

2 . 3 0 R * T
.
�ell = n F logK c (6 2 1 )
8 = 298K,
or, substituting R* = . 3 1 4 J deg - • mo1 - 1 and T
0.0591
logK c (6.22)
n
�ell = --
l
where, as usua , �ell is in volts.

6. 7 The Nernst equation
So far we have considered only standard cell potentials , that is, the
electric potential difference developed by a chemical reaction that is
at equilibrium in an electrochemical cell at normal atmospheric pres­
sure and a temperature of 25°C, and when the chemical species are
s
present in standard concentration . We can derive an expression for
the electric potential difference generated under nonequilibrium and
nonstandard conditions (Ecell) as follow s . If we write Eq. (2. 4 1 ) in
terms of concentrations and remove the requirement of molar concen­
trations , we get

(6. 2 3)

and [G] , [H] are the concentrations of the reactants
where [A] , [B] . . .
and products in the general chemical reaction given by Eq. ( 1 .3),
which may or may not be in equilibriu m . Combining Eq . (6.23) and
s
( 1 . 1 0 )

6.G - M1° + R * T l nQ (6.24)
where Q is the reaction quotient. From Eq. (6.20), 6.G = - n F Eccll
°
and 6.G = - n F �ell· Therefore, Eq . (6.24) becomes