Page 356 - Physical chemistry understanding our chemical world

HALF-CELLS AND THE NERNST EQUATION 323

This expression does not relate to a true cell because the two electrode potentials
are not measured with electrodes, nor can we relate G r to the emf , because elec-
trons do not flow from one half-cell via an external circuit to the other. Nevertheless,
Equation (7.40) is a kind of proof that the overall value of G r relates to the con-
stituent half-cells.
If we write a similar expression to that in Equation (7.40) for the reaction between
sodium metal and water in Equation (7.35), then we would have to write the term
for the hydrogen couple first rather than second, because the direction of change
within the couple is reversed. In fact, any couple that caused hydrogen gas to form
protons would be written with the hydrogen couple first, and any couple that formed
hydrogen gas from protons (the reverse reaction) would be written with the hydrogen
term second.
This observation led the pioneers of electrochemical thermodynamics to construct
+
a series of cells, each with the H |H 2 couple as one half-cell. The emf of each
was measured. Unfortunately, there were always more couples than measurements,
so they could never determine values for either E Cu ,Cu or E H ,H 2
+
2+
(nor, indeed, for any electrode potential), so they commented on
their relative magnitudes, and compiled a form of ranking order. The ‘standard electrode
should potential’ E O is the
+
These scientists then suggested that the value of E H ,H 2 O,R
value of E O,R obtained
be defined, saying that at a temperature of 298 K, pumping the
hydrogen gas at a pressure of hydrogen of 1 atm through a solution at standard conditions.
that is always
+
of protons at unit activity generates a value of E H ,H 2
zero. They called the half-cell ‘H 2(g) (p = 1atm)|H (a = 1)’the
+
standard hydrogen electrode (SHE), and gave it the symbol E O + . A pressure of p = 1atm
H ,H 2 is not the same as
O
The ‘ ’ symbol indicates standard conditions.
O
p , but its use is a
Then, knowing E O , it was relatively easy to determine values
+
H ,H 2 permissible deviation
of electrode potentials for any other couple. With this methodology, within the SI scheme.
they devised the ‘standard electrode potentials’ E O scale (often
called the ‘E nought scale’, or the ‘hydrogen scale’).
O
Table 7.7 contains a few such values of E , each of which was
Negative values of
determined with the same standard conditions as for the hydrogen E O indicate that the
O,R
couple, i.e. at T = 298 K, all activities being unity and p = 1atm reduced form of the
O
(the pressure is not, therefore, p ). couple will react with
Negative values of E O (such as E O =−2.71 V) indicate protons to form hydro-
Na ,Na
+
that the reduced form of the couple will react with protons to form gen gas.
hydrogen gas, as in Equation (7.35). The more negative the value
O
of E , the more potent the reducing power of the redox state, so
E O for the magnesium couple is −2.36 V, and E O =−2.93.
O
K ,K Positive values of E O,R
+
Zinc is a less powerful reducing agent, so E O =−0.76 V, indicate that the oxi-
Zn ,Zn
2+
and a feeble reducing agent like iron yields a value of E O of dized form of the redox
Fe ,Fe couple will oxidize
2+
only −0.44 V.
hydrogen gas to form
And positive values of E O indicate that the oxidized form of protons.
the redox couple will oxidize hydrogen gas to form protons, again