V. Rapid Approaches for Quantity/Intensity Determinations
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V. P. EVANGELOU E T A .
tinuous monitoring capabilities, and ( 5 ) in situ determinations of ions. Clearly,
these unique advantages of ISE can lead to a new way of characterizing the
various forms and reactions of K in soils and minerals.
A. ISE THEORY
AND ITSAPPLICATIONS
An ISE has been defined by the Commission on Analytical Nomenclature of
the International Union of Pure and Applied Chemistry (1976) as an electrochemical sensor, the potential of which is linearly dependent on the logarithm of
the activity of a given ion in solution. The response of an ISE to its primary ion
in the presence of interfering ions can be described by the extended Nicolsky
equation (Bailey, 1976):
where E is the electrode potential and
is the standard potential of the electrode; R, T, and 9 are the gas constant, absolute temperature, and Faraday constant, respectively; Z, and a,, and Z, and a, are the valence and activity of the
primary ion i and interfering ions j, respectively; and kr' is the potentiometric
selectivity coefficient, which defines the ability of an ISE to distinguish between
the primary and interfering ions in the same solution (Bailey, 1976). For a situation where a, >> k ~ ' ( ~ , ) ~ the
~ ' ' Nicolsky
~,
equation is reduced to the classical
Nernst equation,
E
=
EP
RT
+ z,
In a,
9
which, for a system with a monovalent cation in a solution at a temperature of
295.2"K predicts a 58.6mV potential response for each 10fold change in ai.
Apparently, the successful measurement of an ion in a mixed system, e.g., soil
solution, is very much dependent on the effectiveness of the selectivity of the
ISE for that particular ion. For the K + ISE (KISE), major improvement in its
selectivity came about when the highly K+selective neutral macrocycle valinomycin was discovered (Moore and Pressman, 1964) and incorporated into polyvinyl chloride (PVC) (Fielder and Ruzicka, 1973) to make the electrode membrane. Such an electrode has been reported to yield selectivity ratios of 10,000:1,
1000: 1, and 100: 1 for K + over Na+, H + , and NH4+, respectively (Bailey,
1976).
In the past 40 years, there has been a great deal of literature on the application
of the KISE in characterizing soil K. Mortland (1961) first used a cationic glass
SOIL POTASSIUM QUANTITY/INTENSITY RELATIONSHIPS 2 1 1
electrode (CGE) to determine Mgexchangeable K+ in soil suspensions. Since
then, CGEs have been used to determine K+ activities in aqueous soil suspensions and pastes (Krupskiy et d., 1974a,b), the rate of K+ exchange on clay
minerals (Malcolm and Kennedy, 1969), and the K status at the soilroot interface (Xu and Liu, 1982). As the new generation of valinomycinbased Kselective electrodes (VKEs) have become commercially available, the widespread use of KISEs in soils research has been reported. Banin and Shaked
(197 1) studied K + activityconcentration relations in soil water extracts, Farrell
and Scott (1987) determined the concentration of soluble and exchangeable K in
soil extracts, and others measured K + diffusion coefficients (Wang and Yu,
1989) and intraparticle diffusion kinetic constants (Ogwada and Sparks, 1986).
Finally, KISEs alone (Para and Torrent, 1983) or in combination with other ISEs
(Wang, 1986, 1990; Wang et al., 1988, 1990; Yu et al., 1989) have been used
to expedite potassium Q/I and activity ratio (ARK) determinations.
B. Q I I MEASUREMENTS
In the ISEsimplified Q/I procedure described by Parra and Torrent (1983), a
single KISE in an electrochemical cell with liquid junction was used to measure
the concentration of potassium (C,) in soil suspensions based on a successiveaddition procedure, whereas values of ARK were estimated from the empirical
expression
+
ARK = (11.5  0 . 3 b ) C ~ 22
X
(83)
where ARKis the activity ratio in (mol liter’)”*, CKis the potassium concentration in mol liter) of equilibrated soil solutions, and b is the CEC (cmol) based
on the weight of soil samples used. This method is significantly quicker than the
conventional procedure employing spectrophotometry, especially because equilibration time is cut down to 10 minutes in comparison to the traditional 1024
hours. Although this approach yielded Q/I results that were comparable to those
based on analyses of soil extracts by atomic absorption spectrophotometry
(AAS), the universal applicability of this method in estimating ARK values is
apparently under question due to the large variation in soil properties of the
various soils (Wang, 1986; Wang er al., 1990).
It has been recommended that short equilibration periods (10 to 30 minutes)
be used to minimize the effects of microbial activity and release of nonlabile K+
during the determination of Q/I relationships (Moss and Beckett, 1971), and of
the CRK [concentration ratio: CK/(CCa+Mg)l/*]term instead of ARK (Evangelou et
al., 1986; Wang, 1986). Therefore, Wang et al. (1988) later modified the successiveaddition procedure of Para and Torrent (1983) to keep the equilibration
2 12
V. P. EVANGELOU E T A .
period short and characterize the Q/I relationships by introducing direct measurements of CRK values with Ca and KISEs in an electrochemical cell with or
without liquid junction. The cells with and without liquid junction, referred to
as singleISE [ISE(S)] and dualISE [ISE(D)] methods, consist of electrochemical cell arrangements of the type
DJRE(Li0Ac) I( CaCl,
(0.01 M ) ,
KCl (05 mM) 1 MISE
(A)
and
CaISE I CaCI, (0.01 M ) ,
KCI (05 mM) I KISE
(B)
respectively, where M is K+ or Ca2+. The electromotive force (emf) values
of these cells were measured and the related concentrations [CM] and ratios
[ C,/( Cca)”z]were calculated from
E,(M) = EO,’(M) + 58.6 LOg[(CM YJ”Zu]

E,
(84)
and
EB = E!’
+ 58.6 ~ o g [ ( C , / C 6 ) ( r K / r ~ ~ ) ]
(85)
in which P ‘ ( M ) includes the standard electrode potential of the MISE and the
potentials of the internal reference element and inner liquid junction of the
DJRE(Li0Ac) assembly; EE’ = EX’(K)  ER’(Ca); 58.6 is the slope (Nernst)
factor at 295.2”K; yM and ZMdenote the activity coefficient and valence of the
cations, respectively; and E, is the outer liquidjunction potential between the
LiOAc salt bridge and the CaCI,KCI test solution. The CaCI,KCl solutions
specified for cells A and B were used to characterize the ISEs, but were replaced
by suspensions of the soils in the same salt solutions for the Q/I measurements.
In the above application of the DJRE(SB) assembly, the inner liquidjunction
potential between the internal reference element and the salt bridge was considered constant (Hefter, 1982); thus, EX’(M) and Eg’ are constant terms in Eqs.
(84)and (85). In addition, the effects of Ej were minimized by using a concentrated solution of nearly equitransferent LiOAc (10 M ) for the salt bridge (Farrell, 1985) and by dominating the ionic environment of the test solutions and soil
suspensions with CaCI, . On the other hand, in the ISE(D) method C, was estimated from CR, based on the assumption of a constant Ccain the equilibrated
suspension. Although these two methods demonstrate good agreement with the
traditional (spectrophotometric) methods (Wang er af., 1988), some uncertainties associated with the E, effect and C, calculations that are inherent in the
ISE(S) and ISE(D) methods, respectively, have been reported (Wang et af.,
1990). To eliminate these uncertainties, Wang er af. (1990) introduced a new
electrochemical cell ternary arrangement referred to as ISE(T). In this method,
K, Ca, and C1ISEs were combined:
ClISE I CaCl,
(0.01 M),
KNO,
(05 mM) 1 MISE
(C)
SOIL POTASSIUM QUANTITY/INTENSITY RELATIONSHIPS 2 13
1.6 *

 AAS
0
0
ISE(S)
ISE(D)
A lSE(f1
r
01
0.4
0
i
I
t
0.01
0.02
003
CR, (mol
0.04
L’
Figure I5 Q/I relationships determined with the ISE(S), ISE(D), and ISE(T) methods in soil
suspension; the AAS method in filtrate; and the successiveaddition procedure. After Wang et al.
(1988, 1990).
This eliminates the liquidjunction potential and yields emf values (Ec) that are
related to the cation concentrations by the equation
Ec = Egr
58.6 b g ( c M ‘ f~)’”~(Cc1
’ Ycl)
(86)
The components of cell C and Eq. (86) are defined by the same terms as those
used with the other ISE methods, but reflect the inclusion of a CIISE as the
reference electrode. By assuming that the C1 activity in the solutions and soil
, Eo’ terms of Eq.(86) are also assumed
suspensions is constant, the C,, * T ~and
to be constants, and the CMvalues can be estimated from the measured emf
values. Rapid, sequential determinations of E,(K) and Ec(Ca) were carried out
and the measured emf values were combined to obtain CRK values from the
equation
Ec(K)  Ec(Ca) = &’(K)  EOf‘(Ca) + 58.6 l o g ~ c ~ / c ~ ~ ) ( ~ (87)
K/Y~~)
Figure 15 shows the comparison of potassium Q/I relationships for Iowa
Clarion soil determined with the above three ISE methods of characterizing soil
suspensions along with atomic abso~tions~ctrophotometric(AAS) determinations of soil filtrates based on the successiveadditionprocedure. Whereas the
overall agreement between the Q/I curves is excellent when CRK values are
K0.02 (mol literl)l’z, the Q/I curve tends to diverge at higher CRK values for
the ISE(S) method. This difference can also be seen in Table IV, which shows
the results of regression analyses comparing the A[ExK] and CRK values obtained with the various ISE and AAS methods. A[ExK] and CR, values obtained
with the ISE(S) method demonstrate largest deviation from a I :I relationship
among the comparisons. Clearly the ISE(S) method is subject to a source of error
2 14
V. P. EVANGELOU ET AL.
Table IV
Results of Linear LeastSquares Regression Analysis Comparing the ISE Methods of
CharacterizingSuspensions and the AAS Method of Characterizing Filtrates for Iowa Clarion
Soila
Linear regression
Variable
Comparison’
Slope
A[ExK] (cmol kg’)
ISE(S) vs. AAS
ISE(D) vs. AAS
ISE(T) vs. AAS
ISE(S) vs. AAS
ISE(D) vs. AAS
ISE(T) vs. AAS
0.933
1.039
CRK (mol liter’)”’
1.040
1.055
0.993
0.993
Intercept
1
6
3
3
I
I
x 102
X
x 103
x
x
x 105
r
0.998
0.999
0.999
0.999
0.999
0.999
‘After Wang er al. (1990).
*ISE, Ionselective electrode; S, D, and T, single, dual, and ternary; AAS, atomic absorption
spectrophotometry.
that is not encountered with either the ISE(T) or ISE(D) method. Such error has
been attributed to the physical blockage of the liquid junction that exists in the
electrochemical cell for the ISE(S) measurements (i.e., cell A), rather than E,
effects (Wang et al., 1990). On the other hand, although the ISE(D) method
demonstrates no essential difference in measuring Q/I curves as compared with
AAS (Fig. 15 and Table IV), caution must be taken when this method is used.
This is because in the ISE(D) method the K concentration and thus A[ExK] is
calculated based on the assumption that added Ca concentration in the equilibrated soil solutions is not changed (Wang er al., 1988). However, such an assumption was later shown to be invalid for general application (Wang et al.,
1990). In contrast, the assumption of constant added CI concentration in the
ISE(T) method was found to hold for most temperate soils, in which the permanent negativecharged clay particles are dominant. It is for this reason that the
ISE(T) method has been recommended for rapid determination of potassium Q/
I relationships with soil suspensions (Wang et al., 1990).
The Q/I parameters based on leastsquares regression quadratic equations using only the data obtained with the CRK values <0.01 (mol liter’)’’* (Wang er
al., 1988) were compared in Table V. It is clear that agreement between the ISE
and AAS results was excellent, especially in the CQ and P B Q results (no significant differences between all methods). In addition, the ISE methods were
generally found more reproducible than the traditional spectrophotometric approach method in terms of low coefficients of variation for the Q/I parameters
(Wang et al., 1990). However, only ISE(T) demonstrates overall excellent agreement with the AAS method (Fig. 15; Tables IV and V).
SOIL POTASSIUM QUANTITY/INTENSITYRELATIONSHIPS 2 15
Table V
Parameters of the Q/I Relationships Determined with
ISE Suspension and AAS Filtrate Methods and a
Successive Addition Procedure for Iowa Clarion Soil”
Q/I parameterb,‘
Q/ I
method
CRKO
PBCKod
KLd
ISE(S)
ISE(D)
ISE(T)
AAS
0.0030a
0.0031a
0.0031a
0.0030a
75.5a
73.5a
72.3a
73.8a
0.279ab
0.294a
0.274ab
0.257b
“After Wang et al. (1990).
’CRKo = (mol liter’)’’*, PBCKO = cmol kg’/(mol
liter1)’’2, and KL = cmol kgI.
‘Within columns, means followed by the same letter are
not significantly different at the 5% probability level by
Duncan’s multiple range test.
d P B C Kis~ defined as d(AExK)/d(CRK) at CRKO(Wang
et al., 1988); and K L is the sum of ExK, and ExK,
(Beckett, 1964b; see Fig. 2).
VI.EXPERIMENTAL OBSERVATIONS AND FUTURE
QUANTITY/IN”ENSITY APPLICATIONS
A. EXPERIMENTAL
OBSERVATIONS
The use of Q/I relationships to describe potassium status in soils is based on
Woodruff’s observation that K availability to plants can be characterized by the
free energy of KCa exchange with respect to solidsolution reactions. Beckett
(1972) later listed a number of assumptions that need to be met in order for
Woodruff‘s observation to be valid. The reader is referred to Beckett’s (1972)
article for a detailed description of all the assumptions. One of these assumptions
is that the rate of uptake of K by the plant root must be regulated by “the difference in the equivalent free energies of K and Ca as offered to the uptake sites.”
Evidence that this assumption could be met under certain conditions is demonstrated from ion uptake data of excised maize roots obtained by Maas (1969).
These data are presented in Fig. 16 and show uptake of K by excised maize roots
from solutions with various concentrations of KCl and in the presence of 10
mmol, liter’ CaCI,. Figure 16 demonstrates that the uptake of Ca2+in the presence of K+ is a competitive process. The data also show the rate of uptake of K
maximized in the AG range predicted by Woodruff (1955b). Such experimental
evidence of K uptake by excised maize roots provides additional support to the
216
V. P. EVANGELOU ET AL.

70
,

Woodruff's predicled range of A G for
optimum K a v o l l o b i l i t y to p l a n t s
a 70
0
50
?
2
0)
0
'im
+
(u
0
u
10

1
w"
1
I
I
I
'0
0
1
2
4
6
8
10
J*iiI
I
K;C mmol C'
1
9.37 7.61
11.13
11.84
12.84
14.56

I
I
6.57
5.77
L
5.19
AG, kJ/Equivalent
Figure 16 The effect of increasing K + concentration on the uptake of K in 24 hours. The
concentration of Ca2+was 10 mmol, liter' and the pH was 6. Modified from Mass (1969).
validity of Woodruff's observation that K availability could be described by the
free energy of KCa exchange as long as all other plant growth soil factors are
not limiting and are held constant (Beckett, 1972).
The use of Q/I in predicting K availability to plants in soils has been extensively tested in the past (Beckett, 1972; Bertsch and Thomas, 1985, and references therein). However, it has been shown that the Q/I relationship does not
enjoy universal application, because a single relationship for all soils between K
uptake by a given crop and ARK does not exist, perhaps due to the nature of the
soil components regulating ARK. Recall that the term ExK is related to
KG(CEC)(ARK) [Eq. (48)].By rearranging Eq.(48)and substituting the relationship AG =  RT In K G we can show that
RT ln[ARK] = RT In ExK
+ RT ln(l/KG) + RT ln(l/CEC)
(88)
Equation (88) reveals that when ExK represents an insignificant portion of the
CEC of a soil (Evangelou and Karathanasis, 1986), RT In[ARK]is determined
by three terms, namely, quantity of exchangeable K+, magnitude of K G , and
magnitude of CEC. The latter two components represent the PBCK of the soil.
Experimental evidence on the role of PBCK on K availability to plants was summarized by Khasawneh (1971). He pointed out that in the case of two soils with
the same K G and the same quantity of exchangeable K + ,but with one soil having
a CEC lower than the other, the ARK would be higher in the soil with the lower
CEC. Consequently, the soil with the lower CEC would allow greater K uptake