Anal. Chem. 1990, 62, 1004-1010
1004
Ionization and Dissociation of Weak Electrolytes. An Initial Approach to Ki and K, Evaluation Giancarlo Franchini, Andrea Marchetti, Lorenzo Tassi, and Giuseppe Tosi* Department of Chemistry, University of Modena, via G. Campi 183, 41100 Modena, Italy
The experimental dissociation constant K of weak electrolytes may be consldered as derlved from dlfferent contributions due to the Ionization, K,,and dlssociation, Kd,equlllbrla, respectively. A simple method for K ,and K d evaluatlon is herein proposed, startlng from experimental K data, obtained by the conductometric method, for plcrlc acld in a set of binary solvent system mixtures at temperatures ranging from -10 to +80 O C . The correlatlons between K,and Tand between K, and Tare moreover suggested on the basis of a general expression derlved from the Integrated Van’t Hoff equation.
INTRODUCTION
solutesolid== solutesolvated + ionization dissociation homoconjugation and, in addition, heteroconjugation when other species are eventually present. Each equilibrium will be characterized by a proper thermodynamic constant and a complete description of such a complex system should start from the evaluation of all these constants. By applying a series of simplifying hypotheses, such as complete solubility and dilute solutions, we are able to eliminate some of the above mentioned equilibria and to reduce the above sequence to the ionization and dissociation steps only solv(A+B-) Kd‘solvA+
system
A
B C D E F G
H I L M a
It is well-known that the solutions of weak electrolytes represent quite complex systems owing to the physicalchemical equilibria that take place therein. We may consider, for instance, the sequence of the equilibria
solv(AB)
Table I. Coefficientsn of Relation In K with T (Equation 3)
+ solvB-
XCliet
1.oooo 0.9272 0.8499 0.7676 0.6799 0.5861 0.4856 0.3776 0.2614 0.1359
0.0000
a
b
c
d
-279.43 -56.161 167.79 229.18 922.37 1048.5 1619.1 901.73 -580.54 -2788.4 -4693.8
-0.122 19 -0.063 86 -0.006 16 0.002 16 0.213 15 0.251 58 0.419 36 0.22405 -0.184 65 -0.853 96 -1.467 2
4310.9 -1999.7 -8379.6 -10269 -27979 -31020 -45825 -26035 14644 72254 119211
51.839 13.311 -25.280 -35.441 -157.77 -180.18 -280.44 -156.06 101.44 489.94 828.60
From ref 4.
an empirical study to describe the trend of K as a function of both independent variable quantities, absolute temperature (2”) and composition of various solvent systems (4-6). The conductometric method (3, utilized for K evaluation, although very versatile and particularly suitable to our purposes, is not able to determine separately the constants of the two equilibria (eq 1). Moreover, it provides K values on the basis of strongly averaged properties of all the species involved in the ionization and dissociation equilibria.
DISCUSSION The symbol K of our previous papers (2-4), that we will use always in the present work, has the same meaning of Kexp used by Lichtin and Bartlett (8);according to these authors we may consider the K value as a combination of Ki and Kd values of the type
K=-
(1)
where AB is the molecular species of a binary electrolyte solute and solv represents a certain number of molecules of the solvent species which constitute the solvation shell. Ki is a thermodynamic constant of the true ionization process where the molecule of the AB solute (ionogen) separates into ions that, however, are strongly interacting because of electrostatic attraction and, according to Winstein and co-workers ( I ) , reveals itself as a “tight ion pair”, even if a nonzero probability of the presence of an equilibrium with “loose” or solvent separated ion pair could exist. Kd represents the constant of the dissociation process on the basis of which the solvated ion pairs are finally separated into solvated ionic species by action of solvent molecules that, insinuating themselves with their oriented dipoles between charged particles, decrease the electostatic interaction until the progressive and reciprocal removal and breaking of the ion pairs take place. In our previous papers (2-4) we have reported the experimental dissociation constant of picric acid in two pure solvents, 1,2-ethanediol (Gliet) and 2-methoxyethanol (Gliem), and in a set of their binary mixtures expressed by xGLet varying in [O,l] range composition and with the temperature ranging from -10 to +80 “C. Moreover, we have recently performed
KiKd
1
+ Ki
The experimental K values of picric acid (HPi) in the Gliet/Gliem solvent system ( 4 ) are reported in Table 1 (available as supplementary material); the best-fitting equations for these data are of the type In K = a
+ b T + c / T + d In T
(3)
which represents the commonly used integrated Van’t Hoff equation for the thermodynamic K = K ( 7‘) function. The a, b, c, and d coefficients for each binary system, expressed in terms of mole fraction of Gliet, are presented in Table I. One of the principal features of the curves is the considerable difference on passing from system A to system M (Figure 1). Many studies of other authors (4-I2), carried out on several solutes in different pure solvents, have demonstrated that the function K = K ( T )may be represented in the T { K , T }plane, for each proper system, by a suitable concave or convex curve. Now, introducing eq 2 into eq 3, it is possible to write
and hypothesizing that the four adjustable parameters a, b,
0003-2700/90/0362-1004$02.50/0 0 1990 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 62, NO. 10, MAY 15, 1990
K
x lo3
2 .o
1.5
1.0 D E
F
0.5
G
Ii
4
0.0
- 10
50
20
80
t Figure 1. Plot of Kvs t ("C) for picric acid in the GlietIGliem solvent system and isodielectric trend (dotted line) for t = 20, 25,30, 35, 40 from bottom to top. c , and d can be split into two ionization and dissociation
contributions as follows par = pard
+ pari
par = a, b, c, d
where we can write In
Kd
= ad
+ bdT + C d / T + d d In T
(4)
and In
Ki = ai+ biT + c i / T + di In T 1 + Ki
(5)
where the terms relative to the dissociation and ionization steps, respectively, are separated. It is noteworthy that, while all the variable quantities and the adjustable parameters of eq 3 are known, those of eqs 2,4, and 5 are all unknown, except T and K . At first, one might think that the only actual way to resolve the set of eqs 2, 4, and 5 is to separate the Ki and Kd contributions by applying any artifice. Because of the little cognitions about eqs 4 and 5 in particular, we may only intuitively suppose that Kiquantity may be a function depending on T and t , while Kd contribution may be expressed as a function of t only. In fact, to this purpose, it is enough to think of the role of temperature and dielectric constant on the ionization and dissociation reactions of a molecular ionogen solute AB in a given solvent system. Generally, ionization reactions are endothermal processes; therefore an increase of the temperature certainly promotes the ionization of the AB species as it induces progressively the molecule to higher vibrational energetic levels, up to the breaking point of the covalent bond and the consequent formation of the ion pair (A+B-). However, we may think that the possibility of the solute ionization also depends on the dielectric properties of the medium. In fact, the solvent plays, t y e t h e r with the temperature, a significant role in the deformation of the electronic shell of the solute molecule AB; this deformation is induced by electrostatic interactions of the dipole moments of solvent molecules that constitute the solvation sphere. As a consequence, it is probable that small or very small variations of the charge separation induced into the ionizable bond A-B can lead to very large differences of potential energy of the covalent bond itself (13).
1005
On the other hand, the same theory and the spherical cavity model in any of the proposed forms (14), where the solute molecule is symbolized a t the center of the sphere and this one is immersed in the continuum medium constituted by the bulk solvent molecules, do not explain enough the ionization processes phenomenology in solution. As regards the dissociation step, we could think that temperature and thermokinetic effects are negligible factors in order to promove the separation of the ions in solution, while the preminent role for this process may be ascribable to the solvent molecules. These, owing to their dielectric properties, are able to separate the ions and to depress the ion-pair formation. The temperature is a very important factor on ionic mobilities and on any other dynamic property that may be correlated with transport phenomena in solution, but it is not significant in order to separate the ions. In fact, the ions in general present strong long-range interactions due to the overlap of their electrostatic fields which are practically independent on the temperature of the system. Therefore, only the short-range forces, due to the oriented dipoles of solvation sphere molecules, are active on ions dissociation. These interactions, if strong enough, may neutralize the electrostatic attractive effects between opposite charges and, as a consequence, may produce free solvated ions in solution. On the other hand, if these interactions are quite weak, as in the case of low t solvents, the ions should preferably form ion pairs; in fact in these conditions the active dipole forces of the solvent molecules could not overcome the ones due to the electrostatic attraction between opposite charges. If this hypothesis is true, for a given ionogen or ionophore solute solubilized into any solvent system, the Kd isodielectric values should be at least nearly constant for all similar solvents (15,16). Actually, this hypothesis could appear 'hazardous', but too few investigations have been made about this problem to establish its reliability, and for the aim of this paper we may consider it acceptable as an approximated attempt, probably susceptible of refinements, to describe the dissociation processes in solution. Now, on the basis of these considerations, we may write eq 2 in the form
(2.1) and generalizing
K(T,4 = f(T,t). d e )
(2.2)
where Ki(T,t) and Kd(t) are still implicit functions of the variable quantities T and/or t. In any case, all the above suggested hypotheses should be accepted if the solutesolvent systems were considered ideal; probably, the idea becomes faulty for particular real systems in which strong interactions between different species take place, as in the case of the formation of solute-solvent and charge-transfer complexes. This fact occurs and has been demonstrated for solvents as liquid NH, and SO2and for any solvent having marked electron-donor or electron-acceptor properties. In fact, for these systems, the model of the spheres-in-continuum medium is too simplified and appears inadequate to represent them. In the case of our solvent systems the solute-solvent interactions and the solvation processes are achieved by hydrogen bonds involving either solv(HPi) or solv(H+Pi-)species; in addition, with the remote possibility of charge-transfer complex formation, we could approximate, with moderate straining, the real systems under study to the ideal ones. It is noteworthy that the increase of T also induces a lowering of solvent structure because the consequently increased vibrational and kinetic energy of the molecules always in-
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 10, MAY 15, 1990
Table 11. Experimental Dielectric Constant Values for 1,2-Ethanediol/2-MethoxyethanolSolvent System at Different Temperatures t , "C
-10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 a
system A" system B" system C" 49.23 47.80 46.65 45.41 44.49 43.17 42.15 40.97 39.95 38.84 37.99 36.98 36.07 35.14 34.30 33.44 32.68 31.84 31.00
45.99 44.97 43.77 42.62 41.65 40.49 39.47 38.44 37.41 36.60 35.57 34.80 33.76 32.99 32.14 31.34 30.58 29.90 28.99
43.15 42.08 41.06 39.99 39.05 37.98 37.11 36.08 35.11 34.28 33.36 32.57 31.65 30.93 30.16 29.41 28.65 27.98 27.21
system D 40.46 39.39 38.35 37.39 36.41 35.43 34.50 33.70 32.68 31.99 31.09 30.31 29.41 28.78 27.92 27.30 26.47 25.89 25.09
system E" system F system G" 37.55 36.60 35.58 34.70 33.91 32.90 32.11 31.18 30.43 29.59 28.81 28.01 27.34 26.64 25.99 25.34 24.50 24.08 23.30
34.62 33.74 32.80 32.00 31.17 30.28 29.50 28.87 28.00 27.35 26.60 25.95 25.20 24.51 23.89 23.32 22.67 22.20 21.50
31.83 30.89 30.05 29.25 28.53 27.68 26.95 26.25 25.50 24.88 24.21 23.54 22.96 22.33 21.68 21.04 20.61 20.00 19.48
system H
system I"
29.05 28.19 27.39 26.57 25.80 25.13 24.39 23.57 23.00 22.22 21.69 20.99 20.45 19.76 19.29 18.60 18.20 17.64 17.03
26.10 25.40 24.60 23.86 23.25 22.50 21.95 21.18 20.55 19.94 19.38 18.79 18.29 17.71 17.16 16.60 16.12 15.66 15.29
system L" system Ma 22.72 22.21 21.59 21.13 20.59 20.06 19.60 19.06 18.66 18.11 17.75 17.18 16.82 16.35 15.97 15.50 15.16 14.80 14.39
20.03 19.55 19.09 18.63 18.19 17.75 17.35 16.94 16.54 16.17 15.76 15.38 15.02 14.68 14.32 14.05 13.71 13.34 13.01
From ref 3.
terferes with the dipole reciprocal orientation (17). This fact leads to a progressive decrease of the solvent dielectric constant, which certainly corresponds to a lowered dissociating ability toward the ion pairs. The solvent classification made on the basis of the t values (18) is generally accepted: the solvents like water with t 1 80 are considered strongly dissociating, moderately dissociating are those with c ranging from 40 to 80, and slightly dissociating are the ones with c < 40. Therefore the role of the solvent, as regards real systems, should be distinctive, especially in the step involving the dissociation equilibrium characterized by the Kd constant. As a consequence, eq 4 should be coherently written in the general form Kd = Kd(t) (4.1) that is an implicit function of the temperature and perfectly equivalent to eq 4, if the dependence of the dielectric constant on T is known. In the general case of binary solvent mixtures, t may be expressible as a function of two independent variable quantities, i.e. temperature and composition of the solvent system (19): t = c(T,x). If the pure components are characterized by reasonably different t values, the effective microscopic dielectric constant will not coincide with the macroscopic and measurable one. The reason of this fact is known in quite a general way, as well as it is in general known that it is incorrect to use the "massiue" physical properties a t molecular level. However, taking into account that the microdielectric constant evaluation in the neighborhood of the dissolved species involves excessive if not insuperable difficulties, we suggest that one should accept the approximation that the micro property is replaceable by the macroscopic and measurable t (20). This assumption, obviously, involves for mixed solvents deviations from the straight line behavior observed in the pK vs 1 / c plots working in pure solvents, as extensively discussed by Bodenseh, Fuoss, and their co-workers (21, 22). Turning now to the aim of our study, in the past some authors studied the problem of Ki and Kd determination. Kolthoff and Bruckenstein (23) evaluated Ki and Kd values for some solutes in the same solvent by spectrophotometric method, in order to determine the concentrations of the various species involved in the global equilibrium represented by reaction 1. An interesting set of data regarding the Kd evaluation for alkaline and tetraalkylammonium halides (all ionophore solutes) and several ionogen solutes such as dif-
Table 111. Coefficients of Dielectric Constant Dependence on Temperature (Equation 6). for Each Binary Mixture of Gliet/Gliem system
103'~
J
A B C D E F G H I L
-2.221 580 -2.226454 -2.228 749 -2.291 574 -2.304 617 -2.283 828 -2.356 916 -2.558 635 -2.639 848 -2.210539 -2.079 398
1.668952 1.640922 1.613 112 1.584 149 1.552085 1.516500 1.478273 1.437490 1.391407 1.335566 1.280 901
M
ferently substituted triphenylchloromethanes in SOz liquid solutions at various temperatures may be obtained from the papers of Lichtin and co-workers ( 8 , 2 4 , 2 5 ) . These authors have demonstrated that the PKd values increase linearly with 1/ T , deriving this behavior from the inverse dependence of t on T; thus, a direct proportionality between Kd and t is established. On the contrary, in the present case we have studied a single ionogen solute in different solvent systems as reported in our previous papers (2-4). Now, assuming that the cited simplifying hypotheses are valid, we may suggest the following suitable calculation strategy in order to try to separate the ionization and dissociation terms of eq 2.1. The procedure starts from a best fitting equation (12) of the type
+
log t = at p t ("C) (6) which has been applied to each set of experimental dielectric constant values (Table 11) previously determined (3, 4 ) for every investigated solvent system. The coefficients CY and p are reported in Table 111. These equations provide a set of T values corresponding to a set of assigned t values. These T values so obtained are introduced into the appropriate integrated Van't Hoff equations of the 11 solvent systems under study (Table I); as a consequence, isodielectric K values of picric acid are obtained, Table IV. As it appears from the table, this procedure has been performed in the 20-40 c range in order to work with the largest set of isodielectric constant values. Figure 1 also shows the trend of some isodielectric K values; the dotted curves were obtained by fitting each data
ANALYTICAL CHEMISTRY, VOL. 62, NO. 10, MAY 15, 1990
1007
Table IV. Isodielectric Constant Valuesa of Picric Acid in 1,2-Ethanediol/2-Methoxyethanol Solvent System 104~ t
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 a All
system A
19.54 20.70 21.71 22.55 23.23 23.73 24.06 24.22 24.22 24.07
system B
18.66 19.87 20.93 21.84 22.56 23.09 23.43 23.58 23.55 23.33 22.94 22.40
system C
system D
17.07 18.13 19.05 19.80 20.37 20.73 20.89 20.84 20.58 20.14 19.52 18.74 17.82
9.402 10.39 11.32 12.16 12.90 13.50 13.96 14.25 14.37 14.32 14.10 13.71 13.19 12.53 11.77
system E
7.794 8.355 8.903 9.418 9.879 10.26 10.55 10.73 10.77 10.68 10.43 10.05 9.525 8.884
system F system G 3.946 4.264 4.624 5.006 5.390 5.749 6.056 6.280 6.392 6.371 6.200 5.879
5.307 5.778 6.262 6.740 7.193 7.598 7.930 8.166 8.285 8.272 8.115 7.814 7.376
system H
system I
system L
system M
2.815 3.046 3.267 3.469 3.640 3.770 3.847 3.865 3.817 3.702
1.883 2.031 2.177 2.325 2.478 2.641 2.819
1.223 1.550 2.004
0.8912
K values are reported in the molar scale.
set, using a multilinear regression package T S P (26), by an empirical equation of the type
K = PeQJT
for
t
= constant
Table V. Kd Valuesa of Picric Acid in the Gliet/Gliem Solvent System
(7)
or, in the logarithmic form
Q +In P In K = T
(7.1)
where only a term is present as explicit function of the variable quantity T , being P and Q numerical coefficients for each isodielectric set. Considering now the general expression (2.2), for any fixed ii value, we may write
W T , d = f(T,z)g ( d
(2.3) where, having fixed one of the two freedom degrees of the system, the K(T,t) property will be dependent on the variable quantity T and on the parameter t. Therefore, writing eq 2.1 in the logarithmic form
with t being constant, it appears that, from a direct side-to-side comparison, eqs 7.1 and 2.4 should coincide when In & ( Z ) = In P (8) and
f
102Kdcalcd by eq 8
lo2& fitted by eq 10
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
4.416 5.021 5.569 6.665 6.901 7.692 8.318 8.728 11.38 14.40 14.40 15.33 17.20 22.95 25.79 28.85 35.44 38.17 43.53 47.78 49.30
4.218 4.785 5.428 6.158 6.986 7.925 8.990 10.20 11.57 13.13 14.89 16.89 19.16 21.74 24.66 27.98 31.74 36.01 40.85 46.34 52.57
"All K values are reported in the molar scale.
Kd From eqs 2.4 and 8 and these calculating procedures, we have obtained the Kd isodielectric values for picric acid in Gliet/ Gliem solvent system in the range 20 5 t 5 40 (Table V); these values were well fitted by an empirical equation of the type
Kd = Se" (10) which has been chosen from a set of similar relations because (i) it provides the best fit, (ii) it is quite simple, and (iii) it is in good accord with observations mentioned above of Lichtin (8,24,25).This equation has, in its logarithmic form, a linear correlation coefficient r = 0.999, and the trend of Kd vs t is shown in Figure 2. Relation 10 allows us to do a short extrapolation of Kd contribution in order to cover the whole experimentally investigated t range (ca. 13-49), knowing the and U = 1.261 X lo-'. Table 2, values of S = 3.384 X
0.45 0
0.30
-
0.15
-
P +
1 30
20
Figure 2. Plot of K , vs system.
t
40
6
for picric acid in the GlietIGliem solvent
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 10, MAY 15, 1990
Table VI. K , Constant Values" of Picric Acid in 1,2-Ethanediol/2-MethoxyethanolSolvent System from Equation 9 103~
system A
c
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
15.31 14.24 11.16 9.827 9.286 8.563 7.511 7.405 7.259 6.442
system B
13.40 13.51 13.06 12.08 9.355 8.172 7.681 7.037 6.121 6.010 5.867 5.163
system C
system D
13.33 12.76 11.18 9.327 9.362 8.980 8.214 6.198 5.324 4.951 4.476 3.824 3.725 3.608 3.119
13.55 11.41 11.46 11.03 10.14 7.754 6.716 6.275 5.708 4.918 4.806 4.669 4.070
system E
11.64 11.22 11.04 10.51 9.121 7.522 7.522 7.173 6.508 4.825 4.096 3.778 3.383 2.853
system F system G
10.20 9.272 9.511 9.100 8.894 8.396 7.196 5.841 5.802 5.483 4.915 3.560 2.972
8.554 8.356 7.861 7.089 7.260 6.909 6.725 6.307 5.342 4.270 4.225 3.966
system H
system I
system L
system M
6.200 6.062 5.694 5.113 5.258 5.001 4.870 4.561 3.834 3.031
4.512 4.387 4.087 3.630 3.723 3.514 3.403
3.180 2.958 2.625
1.828
All Ki values are reported in the molar scale.
Kd
K
~ 1 0 % 15
10
1.0
05
0.5
- - _- _- _
--..
-----
._
- - - - - ...._... 20
.10
50
80
" !
t
Figure 4. Plot of K, vs t ("C) for picric acid in the GlietIGliem solvent
0.C -10
20
50
system for each binary mixture.
80
t Flgwe 3. Plot of K , vs t ("C) for picric acM in the Gliit/Gliim solvent system for each binary mixture from A (top) to M (bottom).
available as supplementary materid, summarizes the Kd values relative to each investigated temperature and each solvent system obtained by using the eq 6 (Table 1111, and Figure 3 shows the trend vs t "C; the dashed lines refer to values extrapolated outside the 20 5 e 5 40 range. Considering the Ki contributions, the values obtained by using the eq 9 are reported in Table VI, where many figures are missing as a consequence of the method of calculation with isodielectric K values. In Table VII, we have reported the Ki values derived by applying eq 6 to the data of Table VI and making a fit by means of eq 5 . This procedure allows us to obtain the K, values at the investigated temperatures. Unfortunately, owing to the lack of isodielectric values in Table IV, many values are absent in Table VII; in particular the data for the systems L and M are completely absent; We have preferred to derive from eq 2 the Ki values by using the experimental K values of Table 1 (supplementary material) and the Kd contributions of Table 2 (supplementary material), in order to avoid excessive extrapolations which would have been necessary starting from eq 9; see Table 3 (available as supplementary material). Since the differences between Ki values calculated
by means of the two above mentioned methods are not excessive, we may conclude that the procedure utilized appears quite acceptable. By examining the values of Table 3 (supplementary material) and Figure 4, we observe an increasing trend of Ki values with temperature from the solvent system A to I; this behavior, relative to the mixtures in which the solvating properties of Gliet are predominant, could suggest that the solv(A+B-)species is more stable at higher temperatures than solv(AB) species (see eq 1). All Kd and Ki values obtained in this way have been fitted for any solvent by the eqs 4 and 5 respectively through a multiple linear regression program (26). The Tables VI11 and IX contain the coefficients of the above equations for dissociation (eq 4) and ionization (eq 5 ) , respectively. The evaluation of the thermodynamic parameters AH" and ASofor the ionization and dissociation steps is clearly possible by using the Van't Hoff equations (4 and 5) in their derived form moqi= R ( b d / i p - C d / i -I-dd/iT)
and ASod/i =
R(Ud/i
+ 2bd/iT + ddji hl T + dd/i)
(11)
(12)
ANALYTICAL CHEMISTRY, VOL. 62, NO. 10, MAY 15, 1990
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Table VII. Ki Constant Valuesa of Picric Acid in 1,Z-Ethanediol/Z-MethoxyethanolSolvent System Calculated by Equations 6 and 5 103~
system A
t , “C
-10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
system B system C
5.434 5.574 5.919 6.446 7.142 7.990 8.962 10.02 11.10 12.12 12.98 13.59 13.84
6.596 6.933 7.316 7.767 8.308 8.970 9.788 10.81 12.09 13.73 15.81
system D system E system F system G system H system I system L system M 3.299 3.541 3.859 4.253 4.726 5.278 5.907 6.609 7.377 8.196 9.048 9.909 10.75 11.53 12.22 12.78 13.18
4.241 4.369 4.632 5.021 5.529 6.154 6.888 7.717 8.620 9.563 10.50 11.38 12.14 12.72 13.04
3.008 3.464 3.972 4.530 5.135 5.780 6.457 7.154 7.857 8.551 9.218 9.838 10.39 10.87 11.24 11.50 11.64
3.214 3.822 4.445 5.069 5.679 6.263 6.812 7.320 7.782 8.197 8.565 8.889 9.172 9.419 9.635 9.827 10.00
3.812 4.248 4.677 5.095 5.496 5.877 6.234 6.567 6.874 7.154 7.409 7.638 7.843 8.027 8.190 8.335 8.464
3.041 3.660 4.188 4.601 4.899 5.097 5.221 5.301 5.368 5.451 5.578 5.780 6.089
3.423 3.454 3.528 3.637 3.773 3.927 4.093 4.262 4.424
All Ki values are reported in the molar scale.
Table VIII. Coefficients of Equation 4 for Each Binary Mixture system
ad
1O2bd
cd
dd
A
337.89 88.586 82.704 77.478 72.502 66.217 61.523 56.671 50.619 36.135 36.718
9.4567 2.1582 2.0251 1.9561 1.8526 1.6898 1.6322 1.6466 1.5379 0.91928 0.92851
-7144.4 -753.33 -702.99 -600.72 -570.01 -541.05 -467.33 -288.53 -2 02.4 5 -256.12 -439.53
-60.136 -16.380 -15.361 -14.522 -13.666 -12.548 -1 1.794 -11.113 -10.100 -7.2487 -7.2949
B C D E
F G
H I L M
Table IX. Coefficients of Equation 5 for Each Binary Mixture system
ai
102bi
A B C
-618.08 -133.09 172.59 137.89 1073.7 1140.9 1751.7 923.88 -740.79 -3066.1 -6070.2
-21.706 -8.2118 -0.14366 -2.2027 25.850 27.994 45.842 23.006 -23.132 -93.206 -185.89
D E
F G
H I L M
Ci
4
11471 -1 556.9 -10006 -9 345.5 -33 366 -34 701 -50 524 -27 844 17 765 78 939 155 312
112.12 27.654 -25.213 -18.443 -183.22 -195.36 -302.58 -158.72 130.70 539.40 1070.0
where ad/,, bdli, cd/i, and dd/i are the coefficients of Table VI11 and IX, respectively. The calculated data are reported in Tables 4-7 (available material).
CONCLUSIONS The suggested procedure of calculation can lead to a separation of contributions that allows us to use eqs 4 and 5 in evaluating the Kd and Ki values for any weak electrolyte in a solvent system (in particular for ideal solutions) and at any fixed temperature, if the coefficients of each polynomial are known. This fact could be very interesting for studies and investigations concerning mixed solvents and could represent a remarkable advantage whenever the best conditions for single solute titrations or for differentiating titrations of
various solutes in a given solvent system were to be searched. As shown in previous studies by us and by others (27-31),the acid-base titration curves modify their shape depending on variable quantities and the possibility of varying the T and xWlv these two quantities allows a particular pliability in the research of the best titrimetric conditions. Now, being able to influence the Kd and Ki contributions through the above T and xsolvquantities, the possibility of discriminating between various solutes is considerably extended, allowing the operator to differentiate, for example, acid-base neutralization steps. However, the phenomenology of the acid-base titrations performed in conditions of variability of the solvent system composition should be probably investigated at the microscopic level, in order to clarify, for example, the case of titrations carried out with the titrand solute (or solutes) and the titrating agent dissolved in different solvents.
ACKNOWLEDGMENT The authors wish to thank Professor C. Preti for the helpful discussion and the “Centro Interdipartimentale di Calcolo Automatic0 ed Informatica Applicata (C.I.C.A.I.A.)” of Modena University for the computing facilities. Supplementary Material Available: Tables 1-7 listing experimental K values of picric acid in the Gliet/Gliem solvent system, K values relative to temperature and solvent system, and thermodynamic values for ionization and dissociation steps (7 pages). Photocopies of the supplementary material from this paper or microfiche (105 X 148 mm, 24X reduction, negatives) may be obtained from Microforms & Back Issues Office, American Chemical Society, 1155 16th Street, NW, Washington, DC 20036. Orders must state whether for photocopy or microfiche and give complete title of article, names of authors, journal, issue date, and page numbers. Prepayment, check or money order for $16.00 for photocopy ($18.00 foreign) or $10.00 for microfiche ($11.00 foreign), is required and prices are subject to change.
LITERATURE CITED Winstein, S.;Ciippinger, E.; Fainberg, A. H.; Robinson, G. C. J. Am. Chem. SOC. 1954, 76, 2597-2598. Franchini, G. C . ; Ori. E.; Preti, C.; Tassi, L.; Tosi, G. Can. J. Chem. 1987, 65, 722-726. Franchini, G. C.; Tassi, L.; Tosi, G. J. Chem. SOC.Faraday Trans. 1 1987, 8 3 , 3129-3138. Franchini, G. C.; Marchetti. A,; Preti, C.: Tassi, L.; Tosi, G. J. Chem. SOC.,Faraday Trans. 11989, 8 5 , 1697-1707. Franchini, G.C.; Marchetti, A.; Tassi, L.; Tosi, G. J. Chem. SOC.Faraday Trans. 1 1988, 8 4 , 4427-4438. Marchetti, A.; Picchioni, E.; Tassi, L.; Tosi, G. Anal. Chem. 1989, 67, 1971-1977.
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(7) Fuoss. R. M.; Hsia, K. L. J . Am. Chem. SOC. 1968, 90, 3055-3060. (8) Lichtin, N. N.; Bartlett, P. D. J . Am. Chem. SOC. 1951, 73, 5530-5536. (9) Harned, H. S.;Embree, N. D. J . Am. Chem. SOC. 1934, 56. 1042-1044. (IO) Harned, H. S.; Ehlers, R . W. J . Am. Chem. SOC. 1933, 55, 652-656. (11) Nims, L. F. J . Am. Chem. SOC.1933, 55, 1946-1951. (12) Handbook of ChemistryandPhysics. 63rd ed.; Weast, R. C., Ed.; The Chemical Rubber Co.: Cleveland, OH, 1982; p D-174. (13) Pimentei, G. C.; Spratiey, R. D. Chemical Bonding Clsrified through Quantum Mechanics ; Holden-Day, Inc.: San Francisco, CA, 1969. (14) Salem, L. Electrons in Chemical Reactions: First Principles; Wiley-Interscience: New York, 1982. (15) Coplan. M. A.; Fuoss, R. M. J . fhys. Chem. 1964, 68. 1181-1185. (16) D'Aprano, A.; Goffredi, M.; Triolo, R. J . Chem. Soc.. Faraday Trans. 7 1976, 72,79-84. (17) Debye, P. Polar Molecules; Dover Publication: New York, 1965. (18) Charlot, G.; Tremillon, 6. Les reactions chimiques dans les solvants et les sels fondus; Gauthier-Villars Editeur: Paris, 1963. (19) Froiich. H. Theory of Dielectrics; Clarendon Press: Oxford, U.K., 1958. (20) Hyne, J. B. J . Am. Chem. SOC. 1963, 85. 304-306.
(21) Bodenseh. H. K.; Rarnsey, J. B. J . fhys. Chem. 1963, 67,140-143. (22) Accascina, F.; Petrucci, S.; Fuoss, R. M. J . Am. Chem. SOC. 1959, 87, 1301-1305. (23) Kolthoff, I.M.; Bruckenstein, S. J . Am. Chem. SOC. 1956, 78, 1-9. (24) Lichtin, N. N.; Leftin, H. P. J . fhys. Chem. 1956, 6 0 , 160-163. (25) Lichtin, N. N.: Rao, K. N. J . Am. Chem. SOC. 1961, 83, 2417-2424. (26) Time Series frocessor - T S f - User's Guide; Hall, Bronwyn H., Ed.; TSP International: Stanford, CA. 1983. (27) Preti, C.; Tosi, G. Anal. Chem. 1981, 5 3 , 48-51. (28) Preti, C.; Tassi, L.; Tosi, G. Anal. Chem. 1962, 5 4 , 796-799. (29) Franchini. G. C.; Preti, C.; Tassi, L.; Tosi, G Anal. Chem. 1968, 6 0 , 2358-2364. (30) Franchini. G. C.; Marchetti, A.; Preti, C.; Tassi, L.; Tosi, G. Anal. Chem. 1989, 67, 177-184. (31) Van Meurs. N.; Dahmen, E. A . M. F. Anal. Chim. Acta 1959, 27, 10-16.
RECEIVED for review August 24, 1989. Accepted February 2, 1990. The Minister0 della Pubblica Istruzione (M.P.1,) of Italy is acknowledged for the financial support.
Electrolyte Dropping Electrode Polarographic Studies. Solvent Effect on Stability of Crown Ether Complexes of Alkali-Metal Cations ZdenBk Samec*,' and Paolo Papoff Istituto d i Chimica Analitica Strumentale del CNR, Via Risorgimento 35, 56100 Pisa, Italy
Polarography with the electrolyte dropping electrode (EDE) was pioneered by Koryta et al. (1, 2 ) . In the further development, the four-electrode assembly was designed ( 3 ) and employed without a substantial modification in double layer studies ( 4 , 5 )or in measurements of the ion transport across liquid-liquid interfaces (6-14). Fundamental factors in polarography with the EDE were examined (11)for both possible configurations, i.e. for the electrolyte solution dropping upward, called by some authors (6, 7) the ascending solvent (e.g. water) electrode, and for the electrolyte solution dropping downward. In addition to the classical potential-scan polarography ( I , 2 ) , current-scan polarography has been intro-
duced (6) and used in a number of studies (7-14). The advantage of this method is an easy compensation of the ohmic potential drop. On the other hand, the enormous current density a t the very beginning of the drop life can cause irreversible changes in the boundary state and conditions (15). In either case, the cell and apparatus deserve an experienced and skillful experimental approach. The observation (16) that macrocyclic polyethers form stable complexes with alkali and alkaline earth metal cations has stimulated a great deal of interest in these compounds for their possible applications in various branches of chemistry and biology (17). Extensive thermodynamic data (18, 19) suggest that the stability of macrocyclic complexes depends on the relative cation and ligand cavity size, the number and spacial arrangements of the ligand binding sites, the substitution on the macrocyclic ring, and the solvent effects. While these data refer mostly to studies in homogeneous media, an analysis of the interfacial complex formation is obviously of a closely related significance. It has been shown (9, 10,20-25) that a powerful insight into its mechanism, kinetics, and thermodynamics can be gained from measurements of the faradaic ion transport across a liquid-liquid interface in the presence of the ligand. However, systematic electrochemical studies of the factors listed above are lacking. In the present paper we intend to demonstrate the use of a simple three-electrode assembly with the EDE for the study of the interfacial ion transport. In particular, wer focus on the transfer of alkali-metal cations from water to nitrobenzene or 1,2-dichloroethane facilitated by dibenzo crown ethers. We wish to throw some light on the stability of crown ether complexes and the selectivity of ion-ligand interactions in various organic solvents.
'Present address: The J. Heyrovskg Institute of Physical Chemistry and Electrochemistry, Czechoslovak Academy of Sciences, DolejSkova 3, 182 23 Prague 8, Czechoslovakia.
Chemicals. Reagent grade chemicals from Carlo Erba, 1,2dichloroethane (1,2-DCE),nitrobenzene (NB),LiC1, NaC1, KCl,
A simple three-electrode polarographic assembly with the electrolyte dropplng electrode for the study of the Ion transport across a IIquM-Hquid Interface was presented. Transfer of alkall-metal catlons from water to nltrobenzene (NB) or 1,2-dlddwoethane (1,2-DCE) facimatd by complex formation with dlbenzo-18trown-6, dlbenzo-24trown-8, or dlbenzo30-crown-10 was studied. Experimental current vs potential data were used to clarlfy the mechanism of the ion transport and to evaluate the stablllty constants of crown ether complexes. The stabNlty constants are 105-107 larger in NB and 10'o-10'2 larger In 1,P-DCE than those In water. The selectlvlty sequence changes with the solvent, comparing water (K' > Na' > Rb' > Cs') wlth NB (Na' > K' > Rb' > Cs', )'lL and 1,2-DCE (Ll' > Na' > K' > Rb' > Cs'). Solvent effects can be understood In terms of dlfferences in cation solvatlon, which plays a dominant role In low polar media.
0003-2700/90/0362-10 10$02.50/0
EXPERIMENTAL SECTION
IC 1990 American Chemical Society
