Page 141 - Basic physical chemistry for the atmospheric sciences

Oxidation-reduction reactions 1 2 7

or,

2 . 30R*T
Ecen = � en - l ogQ (6.25)
nF
This last relationship is called the Nernst equation. Substituting the
va u es of R* and F i nto Eq. (6.2 ) , and taking = 298K,
l
T
5
0.0591
Ecell = � ell - -- logQ (6.26)
n
Exercise 6 . 9 . Calculate the initial electric potential difference gener­
ated in an electrochemical cell at 298K by the redox reaction
2Cr(s) + 6H + (aq)� 2Cr3 + (aq) + 3H 2(g)
3
if [Cr(s)] = 0.5 M, [H + ( aq)] = 1 M , [Cr + (aq)] = 2 M , and [ H z(g)] =
I M .
Solution. In Exercise 6.8 we calculated that the electric potential
difference generated by this reaction under standard conditions (i . e . ,
�en) was 0.74 V ; we also saw that n = 6. We can use the Nernst
equation to derive the electric potential difference generated by the
reaction under the nonstandard concentrations specified in the present
exercise if we know the value of Q. Applying Eq. ( l . 1 0) to the reaction
(remembering that the concentrations of liquids and solids are equated
to unity in this expression), we get
2 3 2
[Cr 3 + (aq)] [Hz(g)] (2) ( 1) 3
Q 6 = 4
[H + (aq)] (1T
Therefore, from Eq. (6.26)

5
0.0 9 1
4 - - 6- log4
Ecen = 0 .7
or,
�en = 0.74 - 0 .006 = 0.73 V

We saw in Exercise 6.8 that when all the species in the specified
reaction were present in concentrations of I M, the cell potential was
0.74 V and the reaction was spontaneous from left to right. Exercise