Elucidation of Abnormal Potential Responses of Cation-selective Electrodes with Solid-state Membranes to Aqueous Solutions of Cucl 2 and Cdi 2

An empirical solution to abnormal potential responses, showing peaks of emf, of commercial Cu 2+-and Cd 2+-selective electrodes with solid-state membranes was proposed for aqueous solutions of CuCl 2 and CdI 2. The two-step processes of M n+ + Y n (s: solid phase) MY(s) and MY(s) + 2X  X 2 MY 2 (s) (n = 1, 2) at a test solution/electrode-interface were considered as a model. Here, M n+ , Y n , and X  refer to a divalent or univalent cation, functional groups of electrode materials, and a halide ion (X  = Cl  , Br  , I ), respectively. By applying electrochemical potentials to these processes at n = 2, we derived an equation. Regression analyses based on the equation reproduced well the plots of emf versus log 2(*[M] t) for the Cd(II) and Cu(II) systems: *[M] t denotes a total concentration of species relevant to M 2+ in a bulk of the aqueous solution. Also, as an apparent selectivity coefficient (K s) we obtained log K s (CdBr 2) = 4.28  0.22, log K s (CdI 2) = 6.98  0.05, log K s (CuCl 2) = 3.96  0.09, and log K s (CuBr 2) = 11.4 at 25˚C. The magnitude in log K s reflected that in the logarithmic solubility product, log {*[M 2+ ](*[X  ]) 2 }, for bulk water, where *[M 2+ ] or *[X  ] denotes a molar concentration of the bulk solution of M 2+ or X  at equilibrium, respectively. Moreover, a mixture of CuSO 4 with NaCl at the molar ratio of 1:1 yielded a plot similar to that of CuCl 2 .


Introduction
Many ion-pair (or complex) formation constants of divalent metal salts (MX 2 ) in water (w) have been determined so far [1][2][3][4].In the course of potentiometric determination of these constants for CdI 2 and CdBr 2 in a bulk w by using a commercial Cd 2+ electrode with a solid-state membrane [4], plots of the emf versus log 2(*[CdX 2 ] t ) gave peaks, where *[CdX 2 ] t (= *[Cd] t ) denotes a total concentration of CdX 2 in the bulk w.Especially, as shown in Figure 1 of the previous paper [4], a slope of the plot for the CdI 2 system was positive in the lower range of log 2(*[CdI 2 ] t ), while it was negative in its higher range.As a result, the Cd 2+ electrode could not be used for the determination of the formation constants.Such plots with the peaks, namely -shaped plots, have been reported in the cases of potential responses of cation-selective electrodes with liquid membranes to some anions, such as F  , SCN  and ClO 4  [5][6][7].Also, similar potential responses were observed in the case of a commercial Cu 2+ electrode with a solid-state membrane, when the ion-pair formation of CuCl 2 in w had been studied for the application to solvent-extraction experiments of some Cu(II) salts by crown compounds into 1,2-dichloroethane.The same application has been reported for Cd(II) salts [8].
However, it is difficult to see some models proposed for elucidating the potential responses of the electrodes with the liquid membranes [5,[7][8][9][10][11][12] and its elucidation seems to be unclear [5,7].The Nicolsky-or Nicolsky-Eisenman-type equation [9,13] does not reproduce the -shaped potential responses.Also, some equations de-rived from the inverted-Nernstian response model based on the complexation of ionophores with primary and/or secondary ions [11,12] can not clearly express the responses.
In the present paper, we tried the reproduction of the above plots by introducing a model with two-step processes around the electrode/solution interface, in addition to ion-pair formation.Applying an electrochemical potential to these processes, we derived an equation and thereby reproduced the -shaped plot of the CdI 2 system.Also, plots similar to that of the CdX 2 system (X = Cl to I) were observed in CuX 2 (Cl, Br) and CaX 2 systems (Cl to I).Furthermore, properties of commercial ISEs, Cd 2+  and Cu 2+ electrodes with solid-state membranes and Ca 2+ one with a liquid membrane, were examined using an apparent selectivity coefficient (K s ) obtained at 25˚C from the analyses of these plots by the derived equation.Additionally, the equation was extended to potential responses of M + -selective electrodes.

Instruments
As the commercial ISEs, the Cu 2+ electrode (Horiba, type 8006-10C) with the solid-state membrane and the Ca 2+ electrode (Horiba, type 8203-10C) with the liquid membrane were employed.The emf values were measured with a Horiba pH/ion meter F23 equipped with the ISE and a reference electrode (Horiba, type 2565A-10T) [4,15].

Emf Measurements
Emf values were measured at 25  0.3˚C in the following cell: AgAgCl0.1 molL 1 KCl or NaCl 1 molL 1 KNO 3 test solutionISE [4].As the test solutions, aqueous solutions of CuCl 2 , CuBr 2 , CaBr 2 , CaI 2 , NaCl, and mixtures of CuSO 4 with NaCl were used.As a result of computation by the Henderson equation, the liquid junction potentials (< 3 mV) at the 1 molL −1 KNO 3 test solution-interface were neglected [4]: this shows that the aqueous solution of 1 molL −1 KNO 3 adequately functions as a salt bridge.The mixtures were prepared by mixing 0.5006 molL −1 of CuSO 4 with 0.5007 molL 1 of NaCl at given volume-ratios.

Log *[X] t -Dependence of Emf
Figure 1 shows the dependence of the experimental emfvalues on the log *[X] t ones for (a) the CuX 2 (X = Cl, Br), (b) CdX 2 , and CaX 2 (Br, I) systems.Here, *[X] t denotes a total concentration of species relevant to X  in the bulk w and equals 2(*[MX 2 ] t ).Therefore, this relation indicates that the plots of emf versus log *[X] t are actually equivalent with those versus log {2(*[MX 2 ] t )} in Figures 1 and 2 {see Equations ( 10) & (10a)} and accordingly the plots become showed the log (*[MX 2 ] t )dependence of emf with a constant deviation of log 2. Except for the CuBr 2 system, these plots had positive slopes of 26 to 37 mV/decade in the lower log *[X] t ranges, showing the Nernstian responses of the electrodes, and then became the lower or negative slopes in the higher ranges.Only the negative slope was observed for the CuBr 2 system (open diamond in Figure 1(a)) under the present experimental conditions.Its value shows that the Cu 2+ electrode used can act as a selective electrode for Br  , as suggested on its instruction manual.Also, the fact means that, even in the lower log *[X] t range, its solid-state membrane more-preferentially interacts with Br  than does with Cu 2+ .
Peaks in emf seemed to shift into the higher values of log *[X] t in the order X = I < Br < Cl for the MX 2 systems employed (Figure 1).In going from X = Br to I, their peaks were well-defined for the Cd(II) system (Figure 1(b)), while, in going from Cl to Br, those was less-defined for the Cu(II) system (Figure 1(a)).

Contribution of Ion-Pair Formation to the Plots of Emf versus Log *[X] t
Only the Nernstian slopes of about 30 mV/decade have been observed in calibration curves for the aqueous solutions of Cd(NO 3 ) 2 with 0.1 molL −1 KNO 3 (as an adjuster of ionic strength, I ), CuSO 4 with 0.1 molL 1 KNO 3 , and CaCl 2 with 0.1 molL 1 KCl, as shown in the figures of their instruction manuals.These facts indicate that the ion-pair (or complex) formation for these salts at I = 0.1 molL 1 with KX (X  = NO 3  , Cl  ) does not practically Copyright © 2011 SciRes.AJAC  ion-pair formation is less effective for the b (slope) value of the calibration curve, while it is somewhat effective for the a (intercept) value.Also, it is predicted that its effects on the Cd(NO 3 ) 2 and CaCl 2 (K CaCl  41 molL 1 at 25˚C [4,15]) solutions are lower than that on the CuSO 4 solution.In comparison with the KCuSO 4 value(s) [16], the above condition should hold for the CdI 2 system with The above results may be similar to that clarified by Kakiuchi: when the volume ratio of the membrane to the test solution approaches zero, the potential generated at its interface does not affected by the ion-pair formation in the membrane [17].

Semi-Theoretical Treatment for Potential
Response of M 2+ -Selective Electrodes to X  We considered here the following three processes around the test solution/ISE-interface for the electrode response, neglecting the formation of MX 2 .
  Here, taking the easy formation of four-coordinated Cu(II) and Cd(II) complexes with X  into account, we neglected the formation of XMY  species in Equation (2).
For the overall process of the electrode processes ( 1) and ( 2), therefore, the corresponding equilibrium-constant was defined as and those for the process (1) to (3) were and where [j] and *[j] refer to molar concentrations of species j (= M 2+ , MX + , X  ) around the electrode interface and j in a bulk of the test solution, respectively.The subscript (or superscript) "s" means the solid phase of the electrode and can be replaced by "o", which means an organic phase, for the liquid membrane ISE.We used here the molar concentrations instead of the activities, because they render the theoretical treatment complicated and also the experimental calibration curves keep linearity in the ranges of 10 −5 (or 10 −6 ) to 10 −1 molL −1 for Cu 2+ in w, 10 −6 to 10 −1 molL −1 for Cd 2+ , and 2.5  10 −5 to 0.25 (or 1) molL −1 for Ca 2+ , as shown in the specifications [18-20] of a Website.The above electrode processes (1) and ( 2) at the interface were also expressed by electrochemical potentials (  ) as follows.
Arranging Equations (1b) and (2b) by the properties of  [21], we have easily Here,  j , 0 j j    , and 0 j  denote an inner potential for the species j (= M 2+ , Y 2 , X 2 MY 2 ) in each phase, a standard electrode potential, and a standard chemical potential corresponding to j, respectively.R, T and F have the usual meanings.By the sum of Equations (5a) and (6a), we could express the emf value in question as Also, the following relations were derived from mass balance equations around the test solution/electrodeinterface.
by assuming that 1 >> K 2 [X  ] 2 and then with )} and then introducing Equation (9) into Equation ( 7), we have easily Here, the D M and D X values like distribution ratios at the test solution/electrode-interface were assumed to be much smaller than unity and the term 2 }, we can immediately analyze the plots of emf versus log *[X] t by a non-linear regression: the alphabet A to C mean A = Δ 0 Y/M + Δ 0 X2MY/X + (RT /2F )ln (K m /2), B = 2.303RT/2F for log *[X] t , and C = 2.303RT/2F in Equation (10).Considering asymmetry of the plots (see Figures 1(b) and 2), we distinguished here B from C and computed their values together with estimating whether they are positive or negative.In Equation (10), K s will act as the potentiometric selectivity coefficient (k pot ), usually-described for a glass electrode [21], of the anion X  against M 2+ .Namely, like k pot , the larger the K s value is, the larger the interference of X  to the potential response of the electrode becomes.
An equation similar to Equation (10) was obtained for the M + X  system: with A Δ 0 Y/M + Δ 0 X2MY/X + (RT /2F )ln (K m D M ), B = 2.303RT/F, and C = 2.303RT/F,and Here, taking account of the processes, M + + Y  (s) MY(s) and M + + X  MX 0 instead of Equations ( 1) and (3), we modified the Δ 0 Y/M , D M , and g terms.

Reproduction of Plots of Emf versus Log *[X] t
A curve in Figure 2 shows the semi-theoretical curve for the CuCl 2 system obtained from the above treatment.Thus, the plot was reproduced well.The same analyses also yielded results similar to those for other plots.These A, B, C, and log K s values are summarized in Table 1.
The curve (Figure 2) was resolved into emf M and emf X , where emf = emf M + emf X , indicating emf Cu = A + B log *[Cl] t and emf Cl = C log {1 + K s (*[Cl] t ) 2 } with M = Cu and X = Cl, from Equation (10).Their emf values are listed in Table 2 with some experimental emf values (emf found ).One can see easily the sum of the two emf values, emf Cu and emf Cl , well reproduces the emf found values within error of about 2mV.Additionally, Ta- ble 2 shows that the emf Cl values depress the Nernstian response of the Cu 2+ electrode in the log *[Cl] t range more than 2.Other experimental plots of the emf versus log *[X] t were resolved similarly, except for the CuBr 2 system.As Figure 1(a) shows, the Nernstian response for Cu 2+ in the presence of Br  in w was not observed at all.Hence, its plot was analyzed by using the following linear equation: emf 2 in Equation (10).
The same regression analyses were performed by using Equation (10) for the potential response of the Ca 2+ electrode with the liquid membrane.The thus-obtained results are listed in Table 1.The values obtained seem to be comparable with those for the solid-state electrodes.electrode.In addition to the fact, the peak seems to shift into the lower log *[CuSO 4 ] t values in going from *[NaCl] t /*[CuSO 4 ] t = 1 to 3.These facts also support the validity of the semi-theoretical treatment described above.Moreover, the Cu 2+ electrode did not respond clearly aqueous solutions of NaCl (see the plot at the open triangles in Figure 3): the C' value analyzed by emf Cl was less than 8 mV/decade at R = 0.948.This fact indicates that the presence of only the Cl  ion is not adequate for the potential response of the Cu 2+ -selective electrode to Cl  , namely, the response of the electrode to Cl  needs the presence of Cu 2+ in the test solutions.This result is not inconsistent with the presence of the [Cl 2 = Cu-Y] 2 unit in the electrode process (2).Since a washing of the electrode with w resets the electrode potential into an initial condition, it can be supposed that an interaction of M 2+ (or X 2 M) with Y 2 (s) is weaker than or comparable with that of M 2+ with H 2 O.The same can be true of the Cd(II) system.Using Equation (10a), we analyzed the plot at *[NaCl] t / *[CuSO 4 ] t = 1 in the same manner.The A, B, C and log K s values at R = 0.994 were 247  5 mV, 24  1 mV/decade, 21  1 mV/decade, and 4.10  0.09, respectively (see the curve in Figure 3).The log K s value was the same as that for CuCl 2 within the experimental errors (see Table 1).Also, a difference in A between the mixture at *[NaCl] t /*[CuSO 4 ] t = 1 and the aqueous solution of CuCl 2 was + 30 mV (= A CuCl2  A 1:1 ).That is, the difference between the log K m (CuCl 2 ) and log K m (1:1) values was 1.

Addition of NaCl into Aqueous
, where the (Δ 0 Y/Cu + Δ 0 Cl2CuY/Cl ) term was assumed to be constant between the two systems.These facts suggest that the K m value is dependent on the *[Cl] t value, while the K s value is independent of the present * [Cl]   2 = K s {see the above K s definition at Equa-tions (10) and (10a)}.

Application of the Present Model to Other Liquid Membrane ISEs
In the same manner as that (see 3.4) for the potential responses measured by the commercial Ca 2+ electrode, we analyzed data [5]  and then this equation is easily arranged into A + B log a H+ + C log {K ex (a H+ ) 2 + 1}, being equivalent to Equation (11).Here, a j ( j = H + , F  ), tot Am C , and tot R C denote an activity of j in the test solution, total concentrations of amine (Am) and a lipophilic univalent anion R  included in a liquid membrane, respectively.The term K ex is an extraction constant (mol 2 L 2 ) of H + F  by Am into the liquid membrane and so corresponds to the K s value in unit.At least, the results for the two Ca 2+ electrodes suggest essential similarity in model between the solid-state membrane ISE and the liquid membrane ISE [7,9].Also, a model suggesting the formation of X 2 MY 2 in a liquid membrane has been proposed [12], where Y 2 means a basic ionophore.However, its detailed description was not found [12].Furthermore, another model with the formation of XM I Y  (s) in Equation ( 2) could reproduce the -shaped plot at R = 0.983 for the above H + electrode.This R value was smaller than that (0.991) of the model with X 2 M I Y 2 (s), showing the advantage of the X 2 MY 2 (s) formation.

X  Concentration at Peak Potential
The concentration (*[X] t peak ) at the peak potential was estimated from the derivative of Equation ( 10) under the condition of ) for Equation (10a)}.The *[X] t peak values were 2.6  10 −4 and 0.010 mol L −1 for the CdI 2 and CuCl 2 systems, respectively.These values are in good agreement with those of the peaks shown in Figures 1 and 2. The same result was also obtained for the Ca(SCN) 2 system with the experimental log *[Ca] t peak of about 2.5 [5].Similarly, the log *[HF] t peak value (= 2.0) was in good agreement with the experimental upper limit of the proton response [7].These results indicate well the reproducibility of the plots based on Equations (10) and (11).

For Properties of the M 2+ Electrodes Employed
The K s values were calculated to be {K s (CdCl 2 ) <} K s (CdBr 2 ) < K s (CdI 2 ).This fact indicates that the selectivity of the Cd 2+ electrode (Horiba, type 8007-10C with a solid-state membrane) against X  is in the order X  = I  < Br  < Cl  .The same is partly true of the Cu 2+ electrode (type 8006-10C): K s (CuCl 2 ) << K s (CuBr 2 ) (Table 1).Predicting [j] s (j = Y 2 , X 2 MY 2 ) to be unity in Equation ( 4), then the log K s value can be proportional to the logarithmic solubility product, log From solubility (S) data [22] at 25˚C in w, the estimated values were in the orders CdI 2 {log (K sp /mol 3 L 3 ) = log 4S where it was assumed that 100 g of aqueous solutions equals 0.10 0 L and then the S data in a %(w/w) unit was converted to that in a mol L −1 one.This order suggests that the smaller the log K sp (MX 2 ) value is, the more easy MX 2 interacts with the electrode, and then the larger the interference of X  against the electrode becomes.The same discussion can hold for the CaX 2 system with the liquid membrane, as follows.[22].The log K sp order for X = Cl, Br and I was in good agreement with the log K s one, although the log K s (CaCl 2 ) value could not be determined.A deviation of the Ca(SCN) 2 system from the order suggests that an incorporation of Ca 2+ in complex formation with the neutral carrier (L) around the test solution/liquid membrane-interface strongly contributes an increase in K s , namely a transfer of CaL 2+ , XCaL + , X 2 CaL and so on [8] into the o phase.

Conclusion
It was demonstrated that the present model based on the balances among the electrochemical potentials reproduce well the potential responses of the commercial Cd 2+ and Cu 2+ electrodes with the solid-state membranes in the presence of only the counter halide ions.Also, one could see that the phenomena for the Ca 2+ and H + electrodes with the liquid membranes are similarly treated.These facts suggest that the present model contains essential processes being important for the potential responses of electrodes with liquid membranes at least.Further studies will be required for this agreement in potential response between the electrodes with the solid-state membranes and those with the liquid membranes, because the latter electrodes respond under the more-complicated experimental conditions.Not taking account of so-called interfering ions in the test solutions, Equations ( 10) and (10a) do not reach the general equations derived before.However, Equations ( 10) and (10a) could directly estimate the parameters, K s and A (with K m ).By these equations, one can relate properties of the M 2+ and M + electrodes with K sp , although their applications are limited to the solid-state membrane ISEs showing the -shaped potential responses.

Figure 2 .
Figure 2. Plots of emf versus log *[Cl] t for the CuCl 2 system.

Solution of CuSO 4 Figure 3 Figure 3 .
Figure 3 shows a variation of the emf values for mixtures of aqueous solutions of CuSO 4 with those of NaCl at *[NaCl] t /*[CuSO 4 ] t = 1.00 (open circles) and 3.00 (open squares).Obviously, the emf-versus-log *[CuSO 4 ] t plots were spread out a range of negative slopes with an increase in amount of NaCl.This shows any interferences of Cl  against the potential response of the Cu 2+

Table 1 . Some electrochemical parameters obtained from the plots of emf versus log 2(*[MX 2 ] t ) at 25˚C.
Determined by using emf = A' + C' log *[X] t .b The Nernstian response was not observed.c Estimated from the condition of K s  1/(*[Br] t ) 2 at the experimental minimum *[Br] t . a

Table 2 . Comparison of calculated emf values a with the experimental values for the CuCl 2 system at 25˚C.
a Calculated from the data of CuCl 2 in Table1.b Emf vs. Ag/AgCl electrode.