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320 ELECTROCHEMISTRY

√
From Equation (7.28), we expect a plot of log γ ± (as ‘y’) against I (as ‘x’)
10
to be linear. It generally is linear, although it deviates appreciably at higher ionic
strengths.

Worked Example 7.15 What is the activity coefficient of copper in a solution of copper
−3
sulphate of concentration 10 −4 mol dm ?

Copper sulphate is a 2:2 electrolyte so, from Table 7.5, the ionic
Note how we ignore −4
strength I is four times its concentration. We say I = 4 × 10
the sign of the negative −3
charge here. mol dm .
Inserting values into Equation (7.33):
−4 1/2
log γ ± =−0.509 |+ 2 ×−2|(4 × 10 )
10
−2
log γ ± =−2.04 × (2 × 10 )
When calculating with 10
Equation (7.33), be log 10 γ ± =−4.07 × 10 −2
sure to use ‘log’ (in
base 10) rather than Taking the anti-log:
‘ln’ (log in base e). −0.0407
γ ± = 10
γ ± = 0.911

We calculate that the perceived concentration is 91 percent of the real
At extremely low ionic
concentration.
strengths, the simpli-
fied law becomes the For solutions that are more concentrated (i.e. for ionic strengths
−1
limiting law. This fol- in the range 10 −3 <I < 10 ), we need the Debye–H¨ uckel sim-
lows since the denomi- plified law:
√ √
nator ‘I + b I’tends to A|z z | I
+ −
one as ionic strength log γ ±=− √ (7.34)
10
I tends to zero, caus- 1 + b I
ing the numerator to where all other terms have the same meaning as above, and b
become one.
is a constant having an approximate value of one. We include b
because its units are mol −1/2 dm 3/2 . It is usual practice to say b =
1mol −1/2 dm 3/2 , thereby making the denominator dimensionless.

SAQ 7.14 Prove that the simplified law becomes the limiting law at very
low I.

Worked Example 7.16 What is the activity coefficient of a solution of CuSO 4 of con-
−3
centration 10 −2 mol dm ?
−3
Again, we start by saying that I = 4 × c,so I = 4 × 10 −2 mol dm . Inserting values
into Equation (7.34):
√
0.509 |2 ×−2| 4 × 10 −2
log γ ± =− √
10 −2
1 + 4 × 10