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HALF-CELLS AND THE NERNST EQUATION 321

Table 7.6 Typical activity coefficients γ ± for ionic electrolytes as a function of concentration c
in water
Electrolyte/ γ ±
−2
−3
−1
mol dm −3 c = 10 /mol dm −3 c = 10 /mol dm −3 c = 10 /mol dm −3 c = 1.0/mol dm −3
HCl (1:1) 0.996 0.904 0.796 0.809
KOH (1:1) – 0.90 0.80 0.76
CaCl 2 (1:2) – 0.903 0.741 0.608
CuSO 4 (2:2) 0.74 0.41 0.16 0.047
In 2 (SO 4 ) 3 (2:3) – 0.142 0.035 –

0.4072
log γ ± =−
10
1 + 0.2
log γ ± =−0.3393
10
γ ± = 10 −0.3383

so
γ ± = 0.458

Table 7.6 cites a few sample values of γ ± as a function of concentration. Note how
multi-valent anions and cations cause γ ± to vary more greatly than do mono-valent
ions. The implications are vast: if an indium electrode were to be immersed in a
−3
solution of In 2 (SO 4 ) 3 of concentration 0.1 mol dm , for example, then a value of
γ ± = 0.035 means that the activity (the perceived concentration) would be about 30
times smaller!

SAQ 7.15 From Worked Example 7.15, the mean ionic activity coefficient
γ ± is 0.911 for CuSO 4 at a concentration of 10 −4 mol dm −3 . Show that
adding MgSO (of concentration 0.5mol dm −3 )causes γ ± of the CuSO 4 to
4
drop to 0.06. [Hint: first calculate the ionic strength. [MgSO ]ishigh, so
4
ignore the CuSO 4 when calculating the ionic strength I.]

7.4 Half-cells and the Nernst equation

Why does sodium react with water yet copper doesn’t?

Standard electrode potentials and the E scale
O
Sodium reacts with in water almost explosively to effect the reaction

+ + 1
Na (s) + H (aq) −−→ Na (aq) + H 2(g) (7.35)
2