Page 355 - Physical chemistry understanding our chemical world

322 ELECTROCHEMISTRY

The protons on the left-hand side come from the water. Being spontaneous, the value
of G r for Equation (7.25) is negative. The value of G r comprises two components:

−
+
(1) G for the oxidation reaction Na −−→ Na + e ; and
1
−
(2) G for the reduction reaction H + 2e −−→ H 2 .
+
2
Since these two equations represent redox reactions, we have effectively separated a
cell into its constituent half-cells, each of which is a single redox couple.
By contrast, copper metal does not react with water to liberate hydrogen in a
reaction like Equation (7.35); on the contrary, black copper(II) oxide reacts with
hydrogen gas to form copper metal:

+
CuO (s) + H 2(g) −−→ Cu (s) + 2H + O 2− (7.36)
The protons and oxide ions combine to form water. Again, the value of G r for
Equation (7.36) is negative, because the reaction is spontaneous. G would be pos-
itive if we wrote Equation (7.36) in reverse. The change in sign follows because the
Gibbs function is a function of state (see p. 83).
The reaction in Equation (7.36) can be split into its two constituent half-cells:

(1) G for the reaction Cu 2+ + 2e −−→ Cu; and
−
+
−
(2) G for the reaction H 2 −−→ 2H + 2e .
Let us look at Equation (7.36) more closely. The value of G r comprises two
components, according to Equation (7.36):

G r = ( G Cu →Cu ) + ( G H 2 →2H ) (7.37)
2+
+
If we wished to be wholly consistent, we could write both reac-
This change of sign tions as reduction processes. Reversing the direction of reaction
follows from the (2) means that we need to change the sign of its contribution toward
change in direction of the overall value of G r ,so
the second reaction.
G r = ( G Cu →Cu ) − ( G 2H →H 2 ) (7.38)
2+
+
We remember from Equation (7.15) how G (cell) =−nF × emf . We will now
invent a similar equation, Equation (7.39), which relates G for a half-cell and
its respective electrode potential E O,R , saying:

(7.39)
G O,R =−nFE O,R
Substituting for G O,R in Equation (7.38) with the invented expression in Equation
(7.39) gives
G r = (−nFE Cu ,Cu ) − (−nFE H ,H 2 ) (7.40)
2+
+