Potentiometric Determination of Ion-Pair Formation Constants of Crown Ether-Complex Ions with Some Pairing Anions in Water Using Commercial Ion-Selective Electrodes

© 2013 Kudo, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Potentiometric Determination of Ion-Pair Formation Constants of Crown Ether-Complex Ions with Some Pairing Anions in Water Using Commercial Ion-Selective Electrodes


Introduction
Ion-pair formation equilibrium-constants or association ones in water have been determined so far using various methods.As representative methods, one can suppose conductometry, spectrophotometry [1], potentiometry [1], voltammetry [2], calorimetry, electrophoresis [3], and so on.The conductometric measurements generally have high accuracies for their determination for metal salts (MXz at z = 1, 2) and of their metal complex-ions (ML z+ ) with pairing anions (X z  ) in water and in pure organic solvents.According to our knowledge, its experimental operation requires high experimental know-how to handle the measurements.Also, the spectrophotometric measurements require the condition that either species formed in or those consumed in the ion-pair formation are of colored at least.Solvent extraction methods are generally difficult to establish some experimental conditions, such as ionic strength (I ) of both phases and solvent compositions, compared with the above two methods.Strictly speaking, its constants are hard to recognize as thermodynamic ones.
We treat here the ion-pair formation of crown compounds (L), such as 15-crown-5 and 18crown-6 ethers (15C5 and 18C6), with colorless alkali, alkaline-earth metal ions, and so on in water [4][5][6][7][8].The methods described above are difficult to apply for the determination of the constants.For example, conductometry cannot distinguish among the metal ions M z+ , their ML z+ , and X z  in water and ML z+ is unstable in many cases.Also, many M z+ and ML z+ employed here cannot be detected spectrophotometrically. Voltammetric methods cannot apply for the determination, because working electrode suitable for M z+ detection is difficult to get.While, polarography with DME can be effective for the measurements of such systems [2].Unfortunately, it must use mercury and its salts which pollute the environment around us.Thus, in order to overcome these limitations, potentiometry with ISE has been applied for the determination of the ion-pair formation constants (KMLXz 0 ) for MLXz in water at I  0 mol dm  3 , although its applications are limited by kinds of commercial ISE.In the present chapter, its fundamentals and applications for the formation systems of MXz and MLXz in water are described.Here, the determination of KMXz 0 , the ion-pair formation constant of MXz in water at I  0, is always required for that of KMLXz 0 .

Electrochemical cells [4-8]
Constitutions of cells employed for emf measurements of test solutions are described as follows.
Here, the 1 mol dm  3 solution of KNO3 in Cell (B) is a salt bridge, between which and the test solution, Ej estimated from the Henderson equation [2] is in the range of 1 to 3 mV in many cases [9].Standard types for the reference electrodes of Cells (A) and (B) are AgAgCl0.1 mol dm  3 (C2H5)4NCl and AgAgCl0.1 mol dm  3 KCl1 mol dm  3 KNO3, respectively.For Cell (A), the Ej values are corrected by the Henderson equation {see Eq. (1)}, while they are not corrected for Cell (B).

For ion-selective electrodes
Commercial ISEs used here are summarized in Table 1 and some comments for the present emf measurements are described.[2] For emf measurements of the electrochemical cells, the problem of the liquid junction potentials Ej occurred at the interface marked with an asterisk cannot be avoided.Hence, correction procedures of Ej are described in this section.Here, the salt bridges with KNO3 are experimentally used and the Henderson equation [

Corrections of liquid junction potentials
is analytically employed for the correction of Ej.For example, the molar concentration of j in the phase I, cj I , consists of cK I and cCl I , while cj II does of cNa II , cNaL II , and cPic II for the NaPic-L system, where ions involved in a part of the cell are expressed as (see the case 1L).Also, the uNacNa II + uNaLcNaL II term in Eq. ( 1) can be assumed to be uNa(cNa II + cNaL II ) in practice (see Table 2 for the uNa value), because the condition of cNa II >> uNaLcNaL II /uNa holds in many cases with L (low stabilities of ML z+ in water).

Preparation of calibration curves
A representative procedure for preparing a calibration curve is described below.Using a pipette, 55 cm 3 of the aqueous solution of NaCl or KCl is precisely prepared in 100 cm 3  beaker, kept at 25  0.3 or 0.4 C, and then slowly stirred with a Teflon bar containing a magnet.To this solution, the ISE corresponding to Na + or K + and the reference electrode are immersed.A 7 or 10 cm 3 portion of pure water is added by the pipette and, after 5 minutes, emf values at a steady state are read.This operation is repeated, when the amount of the solution is reached to about 100 cm 3 .Consequently, 7 or 5 data are obtained in a unit operation.The thus-obtained calibration curves are shown in Fig. 1.
- A high-purity NaCl (99.98 to 99.99%) is dried about 160 C in an oven [12].The purities of other standards are checked by AgNO3 titration for which the Ag + solution is standardized with the high-purity NaCl.

Emf measurements of test solutions
A representative procedure for the emf measurements of the test solution is described here.Using a pipette, 55 cm 3 of aqueous solution of MXz is precisely prepared in 100 cm 3 beaker, kept at 25  0.3 or 0.4 C, and then stirred with the Teflon bar.To this solution, the ISE and the reference electrode are immersed.A 7 or 10 cm 3 portion of the aqueous solution of L (or pure water for the KMXz determination) is added by a pipette and after 5 minutes, emf values at a steady state are read.This operation is repeated, when the amount of the solution is reached to about 100 cm 3 .Consequently, 7 or 5 data are obtained in a unit operation.Then an example for the plot is shown with that of the corresponding calibration curve of the CdSO4-18C6 system (Fig. 2).

Theoretical treatments and data analysis
3.1.Fundamentals [10,13] In order to determine the ion-pair formation constants at I  0 and 25 C, the ionic activity coefficients (yj ) of ionic species j used for the activity (aj ) calculations are evaluated from the extended Debye-Hückel equation

Ionic activity coefficients
and the Davies one [13] log where a denotes the ion size parameter (see Table 2).In general, it is mentioned that the former equation is employed in the range of less than 0.1 mol dm  3 , while the latter one is done in that of less than about 1 mol dm  3 .Also, the Davies equation can be used for some ions, such as ML z+ and M II X + , or for the yj calculations of species j, of which the ion size parameters (e.g., DDTC  , tfa  ) are not available, because its equation does not involve the parameter a.However, the accuracy of its yj will be less than that of Eq. ( 3).The ion size parameters of some ions in water are listed in Table 2, together with their mobility data [11]  b. cm 2 s  1 V  1 unit.Calculated from ionic conductivity data.See Refs.[2] and [11].c.Calculated from the Brüll formula.See Ref. [10].d.Not be available.
Table 2. Ion size parameters a and mobilities b of some ions in water at 25 C [4,[6][7][8]12] We introduce here three kinds of chemical equilibria for the ion-pair formation of single MX, MX2, and M2X and their mixtures with L, except for chemical ones for the mixture of M2X with L.

Model of ion-pair formation equilibria in water
Case (1).1:1 and 2:2 electrolytes Case (2).2:1 electrolytes Case (1L).1:1 or 2:2 electrolytes with L Ion-pair formation of M + or X 2  for Case (3) is omitted, because an example for the ion-pair formation of ML + with X 2  was not found for the present experiments.First, one determine the formation constants for Case (1) or (2) and next do those for Case (1L) or (2L), using the equilibrium constants determined by analyzing Case (1) or (2), respectively.Therefore, as you know, the experimental errors of the K values obtainable from Cases (1) and ( 2) become influenced those in the K determination of Cases (1L) and (2L), respectively (see Table 5).

Theoretical treatments and data analysis for Case (1) [4]
Analytical equations are derived from the models represented in the section 3.1.2.Using these equations, analytical procedures are described for the cases of the metal salts MX, M2X, MX2, and their mixtures with L, except for those of M2X with L. Here, M z+ and X z  at z = 1 and 2 denote a metal ion and a pairing (or counter) anion, respectively.

Mass and charge balances and the theoretical treatments
To solve the above equilibria, mass-and charge-balance equations are shown.As an example, Case (1) is described as follows [4].
[MX]t = [M + ] + [MX] + bs for the species with M + (10) and For Case (1), its ion-pair formation constant (KMX) in molar concentration unit is defined as Considering an apparent total concentration to be [MX]t  bs, one can express [MX] and [X  ] as functions of [M + ].Thus, taking logarithms of the both sides of Eq. ( 13) and rearranging its equation, the following one is obtained.(14) with y  =   y y  and When the [M + ] value is determined with ISE, then Eq. (14-2) is easily obtained at a given I.

Data analysis [4]
Hence, one can plot log (KMX/y  2 ) against aM 2 and immediately obtain the KMX 0 and bs values (mol dm  3 unit) from analyzing its plot by a non-linear regression.Figure 3 shows the plot for the NaPic system at 25 C [4].Table 3 lists the analytical equations for the other cases, together with equations expressing I which are derived from the charge-balance equations.Also, details for calculation of the parameters listed in Equations and plots for the equilibrium analyses and I expressions corresponding to them [4,6,8,12] Case Molar concentrations of respective species at equilibrium Remarks Ref. [12] (1L) where and by a successive approximation.See Ref. [8] for its details.

2:2 electrolytes [6]
Table 3 lists the equation [6] for the equilibrium analysis and the parameters for its analytical plot corresponding to Case (1) at z = 2. Similarly, the equations for the calculation of the parameters and equilibrium constants are summarized in Table 4.

Theoretical treatments and data analysis for Case (2) [12]
From the mass-and charge-balance equations [12] of Case (2), the following equations are derived. or The concentrations of other species are and On the basis of the above equations, one can immediately calculate KMX ] for a given I.For the other cases, see Tables 3 and 4. As an example, the plot of the Na2CrO4 system is shown in Fig. 4. Also, Table 5 lists the KMX 0 and K2 0 values determined in the section 3.2 and the present one [4][5][6][7][8]12,14].

HSAB principle [15,16]
According to Pearson, the HSAB classifications of some species are as follows.
As soft bases: R2S, RSH, RS  , I  , SCN  , CN  etc. with R = aryl or alkyl group These species are best classified by using the following criteria.Class

For Cases (1L) and (2L) [4,8]
As similar to the section 3.2, Table 3 summarizes the analytical equations and their plot types.Examples of the plots for Cases (1L) and (2L) are shown in Figs. 5 and 6, respectively.The plot in Fig. 5 is similar to that in Fig. 3.A fitting curve of log (KMLX/y  2 ) versus aMLaX is depicted with a solid line in Fig. 5, where aML = yML([X  ]  [M + ]) [4].The former parameter obviously corresponds to log (KMX/y  2 ) in Case ( 1) and the latter one to aM 2 {see the section 3.2.1.

Effect of sizes of anions
Effect of sizes of anions X z  on the KMLX 0 values is described and thereby its cause is examined.Effective ionic radii or sizes estimated from the Van der Waals (vdw) volumes are on the order X z  = Cl  < Br  < tfa  (estimated from vdw vol.)  I  < MnO4  < ReO4  < DDTC  (from vdw vol.) < (SO4 2  <) Pic  < BPh4  [8].The KMLX 0 values in Table 5 are on the orders and The two orders, (O1) and (O2), suggest hydrophobic interactions between BPh4  and Na(15C5) + or Na(B15C5) + and those between Pic  and Na(B15C5) + .That is, the former two cases reflect the interaction between the large ions, while the latter case does that between a benzene ring in Pic  and a benzo group in Na(B15C5) + .Other KMLX 0 orders seem to have the characteristics that DDTC  << BPh4  (is due to the hydrophobic interaction), Pic  < MnO4  , and ReO4   tfa  (are due to the electrostatic one).

Effect of a benzo group added to L skeleton
Effect of a benzo group of L on the KMLX 0 values is described and thereby its cause is discussed.Table 5  Considering the electrostatic interaction between ML + and X  and water molecules hydrated to M + to be basic interactions, these relations of Inequalities (R5) to (R8) may be changed into the following expression: Na + (15C5)- (B15C5)Na + -X  and wAg + (15C5)- (B15C5)Ag + -Pic  for Inequality (R5); (15C5)K + w-> wK + (B15C5)-X  for (R6) and wNa + (18C6)-< (B18C6)Na + -X  and K + (18C6)-< (B18C6)K + -Pic  for (R7); (18C6)K + - K + (B18C6)-MnO4  and (18C6)M + w- M + (B18C6)-X  for (R8).Here, w denotes the water molecules which hydrate to M + and act as Lewis base.Also, we simply define the following sequence as a measure for the strength of the interaction between ML z+ and X z  at z = 1.In other words, the standard order (SO9) can be interpreted as L-separated ion pair with water molecule(s) < L-separated one < w-shared one < contact one.When a cavity size of L is smaller than a size of M + , we will assume an opposite relation of LM + w-X  < M + L-X  ; namely, M + L-X  approaches to LM + -X  .The relations, (R5) and (R7), seem to reflect the hydrophobic properties of ML + .The others can reflect simply effects of the sizes of the L skeletons with benzo groups.
In (O12), the inverse between K(15C5) + and Na(15C5) + is due to the fact that K(15C5) + satisfies the condition that the cavity size of 15C5 < the size of K + (see 4.1.2);that between Na(15C5) + and Ag(15C5) + suggests that a fraction of (15C5)Ag + w-Pic  is dominant.Further, the Na(B15C5) + < Ag(B15C5) + relation in (O13) suggests that Na + in the former complex ion is more shielded by B15C5 than Ag + in the latter ion.The same can be true of the relation of Na(18C6) + < Ag(18C6) + in (O14).
In the present section 4.1, the orders in magnitude among the KMLX 0 values are interpreted by supposing the shapes of the MLX ion pairs based on Inequality (SO9).Of course, validity of such interpretations has to be clarified experimentally.

Try to understand the ion-pair formation based on the HSAB principle [8]
According to the HSAB classification, Pic  , MnO4  , ReO4  , tfa  , and BPh4  were reported to be hard bases [8].Also, DDTC  has been classified as a soft base [19].Then the KMLX 0 values are on the orders Here, only DDTC  has S donor atoms in it, while the other X  does O donor atoms in them.
The sequence of donor atoms in X  obviously show S  O < O < O < O (or F) for (O3) and S < O < O (or F) < O < O for (O4), except for X  = BPh4  .Comparing the orders with those described in 3.4, they indicate at least that Na(18C6) + and Na(B18C6) + have the higher affinities for the O donor atoms in their X  than the S donor ones in DDTC  .This fact suggests that both the NaL + are classified as hard acids [8].
Similarly, from the following orders, readers can see that the same is true of the KCdLX 0 values for the CdX + -L systems with X  = Cl  , Br  , and I  .
X  = I  < Br  < Cl  ( Pic  ) for Cd(18C6)X + and Cd(B18C6)X + (O18) That is, it is suggested that both the complex ions are hard acids [8], although Cd 2+ is classified as a soft acid (see 3.4); KCdX2 0 is on the order X  = Cl   (Pic  ) Br  < I  (see Table 5).
As can be seen from the section 3.4 and the above, the facts that Cl  and Pic

Application to solvent extraction [20]
Using the thus-determined formation constants for M I X and M Here, the subscript "o" denotes an organic phase.The reactions (19-1) to  correspond to the extraction into low polar diluents (or organic solvents) and the reaction (19-6) will be added to the cases of the extraction into high polar diluents.In general, the equilibrium constants of the process (19-1) and the reaction (19-3) can be determined by separate experiments.Then, the overall extraction equilibria are characterized on the basis of their component ones, either  to  or to .One can clearly see that, for the above extraction model, the ion-pair formation, (19-2) and , is important.The NaMnO4 extraction by B15C5 into 1,2-dichloroethane (DCE) and nitrobenzene (NB) are analyzed as the results in Table 6.There are remarked differences in KD,NaLX, KD,X, and KNaLX org between DCE and NB.According to the relation Kex = KMLKMLXKD,MLX/KD,L [21], a difference in Kex between NB and DCE mainly comes from that between KD,MLX.Similarly, that between Kex  does from the difference between KMLX org in addition to KD,MLX, because Kex  = Kex/KMLX org .

Development into study of the abnormal potential responses of ISEs [9]
Abnormal potential responses, -shaped potential ones [9,12] of emf-versus-log [CdX2]t plots (X = I, Br), of the commercial Cd 2+ -selective electrode listed in Table 1 have been observed and then an answer is described using a model for the potential response with interactions of the electrode surface with counter X  , in addition to that with Cd 2+ .Its processes are Cd 2+ + Y 2  s   CdYs (subscript "s": solid phase) ( CdYs + 2X    X2CdYs (20-2) Cd 2+ + X    CdX + ,  where Y 2  s is a functional group of the electrode material and X  denotes halide ions.Applying electrochemical potentials [2] for the electrode processes (20-1) and (20-2) and introducing mass-balance equations in the overall process, we obtain the following equation as an expression of emf.
Here, A, [Cd]t, B, C, and Ks refer to a constant (V versus AgAgCl electrode), the total concentration of CdX2 in the test solution, values (V) corresponding to 2.3RT/2F, and value (mol  3 dm 9 unit) being inversely proportional to the solubility product of CdX2, respectively.One can immediately obtain these values, analyzing the plot of emf versus log [Cd]t by nonlinear regression: Ks(CdCl2) (not be determined) < Ks(CdBr2) (= 10 4.2 mol  3 dm 9 ) < Ks(CdI2) (= 10 6.98 ) [8].It is obvious that the larger Ks is, the more easy CdX2 interacts with the electrode and accordingly the larger the interference of X  against the electrode response becomes.Similar tendencies have been obtained in a commercial Cu 2+ -selective electrode with a solid membrane and a Ca 2+ -selective one with a liquid membrane.

a
(a) acids (hard ones) form more stable complexes with ligands having the Y donor atoms in the order Y = N >> P > As > Sb; O >> S > Se > Te; F > Cl > Br > I[15].On the other hand, Class (b) acids (soft ones) form in the order N << P > As > Sb; O << S < Se  Te; F < Cl < Br < I[15].So, what criteria do ML z+ classify?What criteria do L classify?For some ions and crown ethers, these HSAB classifications are going to be examined below (see 4.2) on the basis of the KMXz 0 and KMLXz 0 values at z = 1 and 2. Na /mol dm-3

Table 1 .
Commercial ISEs used here a a.The above ISEs are used with a AgAgCl reference electrodes, Horiba, types 2660A-10T (single junction type) and 2565A-10T (double junction one).
Table 5 lists the KMLX 0 (and 2 0 ) values thus determined at 25 C.From this table, one can easily see that the KMLX 0 values are larger than the KMX 0 ones, except for several cases.
These results indicate that M z+ dehydrates in the complex formation with L in water and thereby increases its hydrophobic property.