Page 158 - Analytical Electrochemistry 2d Ed - Jospeh Wang

5-1 PRINCIPLES OF POTENTIOMETRIC MEASUREMENTS 143

corresponds to 4% and 8% changes in the activity of monovalent and divalent ions,
respectively. The term ``Nernstian'' behavior is used to characterize such behavior. In
contrast, when the slope of the electrode response is signi®cantly smaller than
59.1=z , the electrode is characterized by a sub-Nernstian behavior.
i
It should be noted again that ISEs sense the activity, rather than the concentration
of ions in solution. The term ``activity'' is used to denote the effective (active)
concentration of the ion. The difference between concentration and activity arises
because of ionic interactions (with oppositely charged ions) that reduce the effective
concentration of the ion. The activity of an ion i in solution is related to its
concentration, c ,by
i
a ˆ f c 5-4†
i i i
where f is the activity coef®cient. The activity coef®cient depends on the types of
i
ions present and on the total ionic strength of the solution. The activity coef®cient is
given by the Debye±HuÈckel equation:

0:51z 2 i p m


log f ˆ p  at 25 C† 5-5†
i
1 ‡ m
where m is the ionic strength. The activity coef®cient thus approaches unity (i.e.,
a  c ) in very dilute solutions. The departure from unity increases as the charge of
i
i
the ion increases.
Equation (5-3) has been written on the assumption that the electrode responds
only to the ion of interest, i. In practice, no electrode responds exclusively to the ion
speci®ed. The actual response of the electrode in a binary mixture of the primary and
interfering ions (i and j, respectively) is given by the Nikolskii±Eisenman equation
(9):

E ˆ K ‡ 2:303RT=z F† log a ‡ k a z i =z j † 5-6†
ij j
i
i
where k is the selectivity coef®cient, a quantitative measure of the electrode ability
ij
to discriminate against the interfering ion (i.e., a measure of the relative af®nity of
ions i and j toward the ion-selective membrane). For example, if an electrode is 50
times more responsive to i than to j, k has a value of 0.02. A k of 1.0 corresponds
ij
ij
to a similar response for both ions. When k 1, then the ISE responds better to the
ij
interfering ion j than to the target ion i. Usually, k is smaller than 1, which means
ij
that the ISE responds more selectively to the target ion. The lower the value of k ,
ij
the more selective is the electrode. Selectivity coef®cients lower than 10 5 have
been achieved for several electrodes. For an ideally selective electrode, k would
ij
equal zero (i.e., no interference). Obviously, the error in the activity a due to the
i
interference of j would also depend upon their relative levels. The term z =z corrects
j
i
for a possible charge difference between the target and interfering ions. Normally,
the most serious interferences have the same charge as the primary ion, so that