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316 ELECTROCHEMISTRY

SAQ 7.12 Write an expression similar to Equation (7.29) for the 2:3
electrolyte Fe 2 (SO 4 ) 3 .

Why is calcium better than table salt at stopping soap
lathering?

Ionic strength I and the Debye–H¨ uckel laws

People whose houses are built on chalky ground find that their kettles and boilers
become lined with a hard ‘scale’. We say that the water in the area is ‘hard’, meaning
that minute amounts of chalk are dissolved in it. The hard layer of ‘scale’ is chalk
that precipitated onto the inside surface of the kettle or boiler during heating.
It is difficult to get a good soapy froth when washing the hands
We look at the actions in ‘hard water’ because the ions from chalk in the water associate
of soaps in Chapter 10. with the long-chain fatty acids in soap, preventing it from ionizing
properly. Conversely, if the water contains table salt – for example,
when washing the dishes after cooking salted meat – there is less of a problem with
forming a good froth. Although the concentrations of sodium and calcium ions may be
similar, the larger charges on the calcium and carbonate ions impart a disproportionate
effect, and strongly inhibit the formation of frothy soap bubbles.
Having discussed ionic screening and its effects on the value
In ‘dynamic’ elec- of γ ± , we now consider the ionic charge z. When assessing the
trochemistry (when influence of z, we first define the extent to which a solute pro-
currents flow) we need motes association, and thus screening. The preferred parameter is
to be careful not to the ‘ionic strength’ I, as defined by
mistake ionic strength
i=i
and current, since both 1
have the symbol I. I = c i z 2 i (7.31)
2
i=1
where z i is the charge on the ion i in units of electronic charge, and c i is its concen-
tration. We will consider three simple examples to demonstrate how ionic strengths
I are calculated.

Worked Example 7.12 Calculate the ionic strength of a simple 1:1 electrolyte, such as
−3
NaCl, that has a concentration of c = 0.01 mol dm .

Inserting values into Equation (7.31) we obtain

+
−
I = 1 { [Na ] × (+1) 2 + [Cl ] × (−1) 2 }
2
terms for the terms for the
sodium ions chloride ions