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CONCENTRATION CELLS 337

between the inner chloride solution and the outer, unknown acid. Empirically, we find
the best response when the glass is extremely thin: the optimum seems to be 50 µmor
so (50 µm = 0.05 mm = 50 × 10 −6 m). Unfortunately, such thin glass is particularly
fragile. The glass is not so thin that it is porous, so we do not need to worry about
junction potentials E j (see Section 7.6). The non-porous nature of the glass does
imply, however, that the cell resistance is extremely large, so the circuitry of a pH
meter has to operate with minute currents.
The magnitude of the potential developing across the glass de-
pends on the difference between the concentration of acid inside A pH meter is essen-
the bulb (which we know) and the concentration of the acid outside tially a precalibrated
the bulb (the analyte, whose pH is to be determined). In fact, the voltmeter.
emf generated across the glass depends in a linear fashion on the
pH of the analyte solution provided that the internal pH does not alter, which is why
we buffer it. This pH dependence shows why a pH meter is really just a pre-calibrated
voltmeter, which converts the measured emf into a pH. It uses the following formula:

2.303RT
emf = K + pH (7.49)
F
SAQ 7.19 An emf of 0.2532 V was obtained by immersing a glass elec-
◦
trode in a solution of pH 4 at 25 C. Taking E (SCE) = 0.242 V, calculate the
‘electrode constant’ K.
SAQ 7.20 Following from SAQ 7.19, the same electrode In practice, we do not
was then immersed in a solution of anilinium hydrochloride know the electrode
of pH = 2.3. What will be the new emf? constant of a pH elec-
trode.

Electrode ‘slope’

We can readily calculate from Equation (7.49) that the emf of a pH electrode should
change by 59 mV per pH unit. It is common to see this stated as ‘the electrode
has a slope of 59 mV per decade’. A moment’s pause shows how this is a simple
+
statement of the obvious: a graph of emf (as ‘y’) against [H ](as ‘x’) will have
a gradient of 59 mV (hence ‘slope’). The words ‘per decade’ point to the way that
each pH unit represents a concentration change of 10 times, so a pH of 3 means
−3
+
+
that [H ] = 10 −3 mol dm , a pH of 4 means [H ] = 10 −4 mol dm −3 and a pH of
−3
+
5 means [H ] = 10 −5 mol dm , and so on. If the glass electrode does have a slope
of 59 mV, its response is said to be Nernstian, i.e. it obeys the Nernst equation. The
discussion of pH in Chapter 6 makes this same point in terms of Figure 6.1.
Table 7.11 lists the principle advantages and disadvantages encountered with the
pH electrode.
SAQ 7.21 Effectively, it says above: ‘From this equation, it can be readily
calculated that the emf changes by 59 mV per pH unit’. Starting with the
Nernst equation (Equation (7.41)), show this statement to be true.