Page 159 - Analytical Electrochemistry 2d Ed - Jospeh Wang

144 POTENTIOMETRY

z =z ˆ 1. In practice, the contribution of all interfering ions present in the sample
j
i
P z i
matrix k a =z † should be included in the Nikolskii±Eisenman equation. For
j
ij j
example, for a sodium electrode immersed in a mixture of sodium, potassium, and
lithium, the response is given by
2:303RT
a ‡ k
E ˆ K ‡ log a Na ‡ k Na;K K Na;Li Li 5-7†
a †
F
Accordingly, an ISE displays a selective response when the activity of the primary
ion is much larger than the summation term of the interferents; that is, when
P z i =z j
a k a . Under this condition, the effect of interfering ions is negligible, and
i ij j
changes in the measured potential can be related with con®dence to variations in the
activity of the target ion. The selectivity coef®cients thus serve as guidelines of how
far a given ISE should be applicable for a particular analytical problem. Nonselective
ISEs are rarely useful for real-life applications (with the exception of their
combination with the operation of ISE arrays; see Section 6-4). In reality, equations
with more than two components are rarely used. Deviations from the Nikolski±
Eisenman equation have been reported for various situations (particularly for
mixtures of ions of different charge, in the case of non-Nernstian behavior of
interfering ions, and due to the concentration dependence of k ).
ij
It is important for the analytical chemist to realize the selectivity coef®cient of a
particular electrode. Various methods have been suggested for determining the
selectivity coef®cient, including the ®xed-interference method, separate-solution
method, and the ®xed primary-ion method (10,11). The most popular ®xed-
interference method involves two solutions, one containing a constant concentration
of the interfering ion and the second containing a zero concentration. Also popular is
the separate-solution method, which involves the preparation of calibration curves
for each ion. As selectivity is a complex function of the membrane composition and
the experimental design, the values of selectivity coef®cients should be regarded as
operationally de®ned (i.e., valid for the particular set of conditions used for their
determination).
Usually the analytical chemist needs to determine the concentration of the ion of
interest rather than its activity. The obvious approach for converting potentiometric
measurements from activity to concentration is to make use of an empirical
calibration curve, such as the one shown in Figure 5-3. Electrode potentials of
standard solutions are thus measured and plotted (on semilog paper) versus the
concentration. Since the ionic strength of the sample is usually unknown, it is often
useful to add a high concentration of an electrolyte to the standards and the sample
to maintain about the same ionic strength (i.e., the same activity coef®cient). The
ionic-strength adjuster is usually a buffer (since pH control is also desired for most
ISEs). The empirical calibration plot thus yields results in terms of concentration.
Theoretically, such a plot should yield a straight line with a slope of approximately
59=z mV (Nernstian slope). Detection by means of ion-selective electrodes may be
i
performed over an exceedingly broad concentration range, which, for certain
electrodes, may embrace ®ve orders of magnitude. In practice, the usable range