J. Phys. Chem. 1980, 8 4 , 2241-2246
2241
Chloride Complexes of CuCl in Aqueous Solution J. J. Fritz Department of Chemistty, The Pennsylvania State Unlversity, University Park, Pennsylvania 16802 (Received: February 2 1, 1980)
Available data on the solubility of cuprous chloride in HC1-HC104 solutions have been reinterpreted to determine the nature of the principal complexes formed, the thermodynamic equilibrium constants for their formation, and the parameters necessary to represent the activity coefficients of all species present in the solutions. In order to account for the solubility data over the entire range it was necessary to include neutral CuCl(aq),CuC12-, CuClZ-, C U ~ C ~and ~ ~triply - , charged complexes (grouped as c&,c163-). CuClf and CuClZ- are the principal species present below ca. 5 M chloride with triply charged species becoming the major contributions to the solubility at high chloride concentrations. The equilibrium constants have been used to confirm tabulated values for the thermodynamic properties of CuClf and to determine AGf”, AH?,and So for CuC13* (previously unavailable).
Introduction The nature and properties of the complexes formed when cuprous chloride dissolves in aqueous solutions of soluble halides have tantalized investigators for many years. The principal source of information about these complexes has been the solubility of cuprous chloride in various aqueous halides, many examples of which have been rep0rted.l Such data are difficult to obtain because of the ease of oxidation of cuprous ion in solution, and there are major discrepancies and uncertainties even in the available solubility data. The interpretation of these and other data is even more uncertain, with formation constants reported for as many as 19 complexes,2 up to Cu5C1~-.Reported values for formation constants are in serious disagreement even for the simplest complexes, CuC12- and CuC132-. Most past attempts to determine formation constants have been made by using either solubility or electromotive force data at constant (nominal) ionic strength. Of these, the most thorough was that of Ahrland and Rawsthorne3 who carried out both potentiometric and solubility determinations at 25 OC on the system NaC1-CuC1 at a constant (nominal) ionic strength of 5.0 M, using NaC104 as inert electrolyte. They obtained values for the solubility product of CuC1 and for the formation constants of CuClL, CuC1$-, and CuzC142-which fitted their data up to about 1 M chloride but failed to describe their remaining solubility measurements, which extended to 5 M chloride. In any case, measurements at a single ionic strength provide little information about thermodynamic equilibrium constants and related properties at zero ionic strength, because of the difficulty of assigning activity coefficients for the species present. In fact, there are almost no data available on the thermodynamic properties of any of the complex species at zero ionic strength. Data reported for CuC12- (for example, in ref 4)go back to the early work of Noyes and Chow,5who made potentiometric measurements of Cu’. and C1- in dilute solutions of CuCl in HC1 at three temperatures. The values quoted for the formation constant and heat of formation of CuC1,- from CuCl(s) and C1- were derived from their measurements at 0.23 M HC1, without correction for the activity coefficients involved. Two things are necessary for proper evaluation of the stability constants and thermodynamic properties of the complexes: (a) experimental data for a range of ionic strengths, with a number of chloride concentrations for each, and (b) a model capable of sufficiently precise cor0022-3654/80/2084-2241$01 .OO/O
relation of necessary activity coefficients over the entire range for the multicomponent mixtures encountered in the solutions. The first requirement is met by the solubility data of Hikita et aL6 The second is available in theoretical publications of Pitzer and co-worker~.~*~ The successful use of this information to determine the nature of the complexes present, their formation constants, and relevant thermodynamic data is the principal subject of this paper. Hikita et ala6measured the solubility of CuCl in HC1HC104 mixtures at five different (nominal) ionic strengths up to 6.5 M at 15, 25, and 35 “C. For ionic strengths of 0.5, 1.0, and 2.0, they used chloride concentrations from zero to that giving the total ionic strength. Measurements at these ionic strengths were made at all three temperatures. At 25 “C additional measurements were made at ionic strengths of 3.5, 5.0, and 6.5 with chloride concentrations up to the range 1.2-1.5 M. Finally, the solubility of CuCl in aqueous HC1 was measured at seven additional concentrations ranging from 0.75 to 5.0 M. They demonstrate reasonable agreement with less extensive earlier work on the same system. Hikita et ala6interpreted their data in terms of formation of complexes CuC12-,CuClz-, and CuC1:- and give a set of equilibrium “constants” for formation of these species from CuCl(s) as functions of temperature and (nominal) ionic strength. However, they were able to fit their data to only about lo%, and the constants obtained are only very approximate.
Derivation of Formation Constants from Solubility Data A. General. The equilibrium constants obtainable directly from solubility data are for reactions of the form nCuCl(s) + mC1- = CU,Clm+,m-
(1)
For further reference, these constants will be labelled as K, +n if n = 1and simply as K,,,+, if n > 1. (Note: the suEscript s is inserted to distinguish these constants from those corresponding to addition of Cl- to a lower complex.) In each case the equilibrium constant will be equal to the activity of the complex considered divided by the mth power of C1- activity. For purposes of calculation, it is convenient to use the correspondingequilibrium quotients in terms of concentrations, denoted hereafter with a prime (9,each related to the corresponding equilibrium constant by a suitable ratio of activity coefficients. For a given mixture, the total amount of CuCl dissolved s, is then given by eq 2, where (C1-) is the concentration 0 1980 American Chemical Society
2242
The Journal of Physical Chemistty, Vol. 84, No. 18, 7980
s = (Cu+)
+ (CuC1) + K,,’(Cl-) + (K,,’ + 2K2,‘)(C1-)2 t (K,: + 2K25’ + 3K36’)(C1-)3+ ... (2)
of free chloride ion, and the K s are as defined above. At all chloride concentrations considered, the concentration of free Cu’ is negligible, but that of CuCl [=K,,’] is not, as observed by Ahrland and Rawsthorne3 for their NaC1-NaC1O4 mixtures. The amount of free chloride present is given by eq 3, (C1-) = (HC1)o - (CuClZ-) - 2[(CuC1,2-) + (C~&14~-)] 3[(CuC143-) + ...I ...
+
+
= (HCl)o - Ks,’(Cl-) - 2(Ks,’ K2,‘)(Cl-)2 3(Ks,‘ K23’ + K36/)(C1-)3- ... = (HC1)o - s
+
+ Ksl’ - K,,’(Cl-)’ - ...
(3)
where (HCOois the concentration of HC1 originally added. Hikita et a1.6 took the values of the K’s to depend only on the nominal ionic strengths of their solutions and obtained values for K,,’, K,,’, and K s l graphically in a series of steps where successively better values for (Cl-) were obtained from eq 3 after each application of eq 2. (Note that they neglected Ks[ entirely.) They then represented each of the K’s as an empirical function of ionic strength. The weakness of this approach lies in the fact that each of the K’s will depend (through its activity coefficient ratio) both on a function of the actual ionic strength and on the concentrations of each ionic species present. The treatment described below takes into account both of these factors. B. Procedure. 1. Selection of Constants to be Evaluated. A preliminary graphical treatment of the solubility data indicated that terms in eq 2 up to (Cl-)4 might be required for a proper fit. However, the solubility data are rather insensitive to the distribution of CuCl between complexes of the same charge (for example, between CuCI, and Cu2C1,2-),which occurs explicitly as a small term in eq 3 and implicitly in its effect on the various K’s. For this reason, and to avoid an excessive number of parameters, the set of constants was selected as follows: a. Both K,,’ and K24’ were retained, since Ahrland and Rawsthorne3 found that Cu2C1>- contributed appreciably to the concentration of doubly negative ions. b. K36/ and K48/ were taken to represent the concentration of triply and quadruply charged ions as and Cu&1,4-, respectively. Including Ks,’ and K,; this gave a maximum of six equilibrium quotients to be determined, each as a suitable function of concentration. 2. Introduction of Activity Coefficients. The equilibrium quotients in a given solution are related to the thermodynamic equilibrium constants through suitable ratios of activity coefficients. For example, for the formation of CuC12-by the reaction CuCl(s) + C1- = CuClZ-, (CUClz-) =--(a*)€Ic? (Cl-)
(adHCuC1;
Ks, =
= K,;
(YdHCuCl$ (Y+)HC?
(Y+)HCuC1:
(4) (YdHC?
In Ksl = In K,,
-
In y2
(5)
where y2 is the ratio of mean ion activity coefficients of eq 4. Similar expressions apply to the other equilibrium quotients. An adaptation of the method of Pitzer et al.’a was used to represent the mean ion activity coefficients needed in
Fritz
equations such as eq 4 and 5. Expressions for these quantities are given explicitly for mixed electrolytes by eq 15 of ref 7. This expression simplified considerably in our application. All summations over cations reduced to a single term, since H+ was the only cation present. In addition, the first summation over anions vanished identically in taking the necessary ratios, an3 did the 6 term of the summation over cations. The remaining small terms in 6’ and # were omitted, leaving a set of expressions involving only f y and the two virial coefficients B (B? and C for each ion pair. Expressions for p , B, and B’are given as eq 12-14 of ref 7 (note typographical errors in their eq 131, with f y a function of ionic strength only and the expressions for B and B’containing the parameters P ( O ) and P ( l ) for the ion pair considered. The C’s are taken as concentration-independent parameters for each ion pair, For HC1 and HC104, we used the parameters given by Pitzer and Mayorgas for 25 “C. For the various complex species, the corresponding P ( O ) , /3(l),and C were taken as parameters to be determined along with the thermodynamic equilibrium constants. An obvious problem in the procedure arises from the fact that the treatment of Pitzer et aL7l8is given in terms of molalities, whereas the data of Hikita et a1.6 (and much of the other solubility data) are given in terms of molarities, None of the information on solution densities required to convert from molarity to molality was available. It was decided to use the equations as they stood, substituting molarity for molality, for the following reasons: 1. Each solubility point represents a combination of a set of thermodynamic equilibrium constants and the corresponding activity coefficients. Correlation of a set of measurements requires only that the expressions for the activity coefficients be adequate to represent them within the accuracy of the data. Provided that the expressions have a reasonable functional form, selection of suitable parameters will accomplish this purpose. 2. For the data used, the ratio of solubility to (total) chloride concentration varied only slowly with concentration. Thus, conversion from one concentration scale to another left the functional form virtually unchanged. It should be observed that the change of concentration units has only a trivial effect on the thermodynamic equilibrium constants. Their determination requires only that the expressions provide suitable functions for extrapolation to infinite dilution. The use, without change, of the parameters given by Pitzer and Mayorgas for HCl and HC104requires further justification. In the present work, Pc0) and C occur only as difference terms involving the corresponding parameters for the various complex species. The extent to which these are inappropriate is absorbed entirely in the selection of parameters for the complexes. p(l) appears both in a difference term and in a summation of minor importance. The latter part must be accommodated by suitable adjustment of all parameters for the complexes. The results presented below provide pragmatic evidence that the procedure used was adequate for the purpose. It should be emphasized that the p’s and C thus obtained are parameters which will predict activity coefficients for concentrations in molarity only. 3. Optimization of Parameters. To begin with, graphical methods were used to obtain approximate values for the equilibrium constants. Initial values for the parameters P ( O ) , PC1), and C were estimated from the tables of Pitzer and Mayorga,s using ions of appropriate charge, size, and molecular weight as examplars for each complex. Thereafter, a computer program was used to optimize the
Chloride Conlplexes of CuCI in Aqueous Solution
set of parameters. This program performed the following functions: a. Using a given set, of parameters it first calculated the solubility predicted for each experimental point, the percentage error in prediction of each point, and the sum of the squares of percentage error for the entire data set. b. In a second set of steps, it predicted the effects of varying each parameter in turn on the individual errors and their sum. c. As a final step, it estimated the changes required to minimize the errors by variation of the parameters separately. Each application of the program produced an improved set of parameters, which was then used as the starting point for another application until step c indicated that minimum error had been attained, i.e., that no significant improvement could be expected by further variation of parameters. Certain features of the procedure merit special mention. First, the concentration of dissolved neutral CuCl (Ks[), which Ahrland and Rawsthorne found to be larger than the ion product (Cu+)(Cl-),had to be treated separately from that of the charged complexes. It was found to be important only for the points with lowest C1- concentration and was taken to be a function of ionic strength only. Initial estimates were taken as 50% of the solubilities given by Hikita et ala6for solutions whose entire ionic strength came from HC104. Thereafter the values were adjusted as necessary to make the points at lowest (Cl-) consistent with the rest. Second, in the early stages of the procedure, the P(O)'s and 0% were constrained to vary together in the manner given for typical ions by Pitzer and Mayorga.s In later stages, the 0% were varied independently. The final sets of values d l fell well within the limits given for Pitzer and Mayorgas for simple inorganic ions. Third, although contributions from quadruply charged ions (K4{) were included at the outset, they were found unnecessary, and the fit was actually improved by removing this term from the solubility. Finally, the third virial coefficient (C) was found necessary for all species considered. The data of Hikita et ala6were used throughout the correlation. However, they did not contain enough points at high chloride concentration to determine adequately the virial coefficients for cu3c163-. These were determined separately, using data of Chang and Cha,9 up to 10 M, along with the points of Hikita et ale6at chloride concentrations above 1 M, in an intermediate stage of the correlation, so as to give a reasonable fit (to lesser accuracy, see below) to the data at molarities above 5 M chloride ion. These virial coefficients were then kept unchanged for the remainder of the procedure. The data at 25 "C furnished values for the equilibrium constants and both virial coefficients for all species considered at that temperature. In treating the much less extensive data at 15 and 35 "C, the virial coefficients were held fixed at their 26 "C value, except for p(O)and p(l) of HCuC12, which were varied slightly (simultaneously) in final stages of the fit,.
Results A. Quality of Fit. The entire data set at 25 "C consisted of 57 points. Excluding a single point which deviated by 6 % , the remaining solubilities were fitted to an average (root mean square) error just over 1.0%. The maximum error of any of the remaining 56 points was 2.6%. Deviations in the ten points measured with only HCl present (no HC104)were slightly less than for the remainder, averaging 0.8%. Overall, the errors were random with the single exception that points at ionic strengths near 5.0
The Journal of Physical Chemktry, Vol. 84, No. 18, 1980 2243
TABLE I : Parameters for 25 " C ~~
equilibrium constant
parameters
value 0.0604 0.0128 8.2X 3.4 X lo-' 2Kz4 0.0144
species
K.2 Ks 3 K24
K36 Ks3 +
p(0)
0.2072 0.2746 0.3666 0.4498
p(') C 0.3215 0.0107 1.587 0.0264 1.774 0.0076 4.567 0.0218
TABLE 11: Parameters for 15 and 35 " C value constant at 15 " C at 35 " C 0.0409 0.0869 K.2 0.0105 0.0150 K.3 5.4 x 10-4 9.5 x 10-4 K.4 2.4 X 5.1 x 10-5 K36 KS2 + 2KZ4 0.0116 0.0169 for K8, p(O) 0.1905 0.21 64 for Ks, p(') 0.3048 0.3307 1.00
I
I
I
I
I
I
2
3
4
5
MHCI
Figure 1. Distribution of dissolved CuCl between singly, doubly, and triply charged complexes as a function of the molarity of HCI used, at 25 "C.
tended slightly negative, while those near 3.5 tended slightly positive; this suggests that the fit could be improved slightly by allowing the third virial coefficient to vary with ionic strength, but the number of data points did not warrant this elaboration. The 23 data points at 15 OC were fitted to an average (rms) error of 0.7%, with only one point deviating more than 2% and deviations randomly distributed. The points at 35 "C were not so consistent. The best overall fit obtained was to 1.2%, with two points of the 23 deviating by more than 2%; deviations were randomly distributed, however. B. Equilibrium Constants and Viral Coefficients. Table I gives the equilibrium constants and other parameters obtained for 25 O C . The sum (Ks2 2K2,) represents the total contribution of both species with double negative charge, while that for KN represents the total concentration of all triply negative ions. K48(not included) is less than
+
10-10.
Table I1 gives the equilibrium constants for 15 and 35 "C and the parameters @ ( O ) and pCufor HCuCl,, with the remaining parameters as for 25 "C. The concentration of neutral CuCl(Ks[) as a function of ionic strength at 25 "C appears as part of Table 111. Corresponding values were about 20% lower at 15 "C and 20% higher at 35 "C. C. Concentration of Complex Species Present. The parameters of Tables I and I1 permit calculation of concentrations of all species present at saturation in any
2244
The Journal of Physical Chemistry, Vol. 84, No. 18, 1980
Fritz
TABLE 111: Concentrations of Species Present in “Pure” HCl Solutions at 25 C s o h bil ity concn calcd c1CuCl cuc1,cuc1,zMHCl 0.499 0.750 1,010 1.50 2.00 3.00 3.50 4.00 4.50 5.00
0.0338 0.0555 0.0825 0.147 0.232 0.463 0.608 0.772 0.957 1.163
0.4595 0.6797 0.8987 1.284 1.639 2.251 2.521 2.775 3.01 9 3.256
0.00042 0.00032 0.00028 0.00026 0.00025 0.00024 0.00023 0.00022 0.000 21 0.00021
TABLE IV : Representative Values of Equilibrium Quotients at 25 C molarity ionic HCl HC10, strength Ks2‘ KS,l 0.499
1.010 2.000 3.000 4.000 5.000 1.490 0.994 0.497 0.973
0 0 0 0 0 0 3.500 4.000 4.500 5.53
0.506 1.041 2.146 3.556 4.655 6.042 5.071 5.032 5.010 6.535
0.0577 0.0549 0.0487 0.0417 0.0344 0.0273 0.0273 0.0273 0.0272 0.0179
0.0289 0.0360 0.0480 0.0565 0.0589 0.0548 0.0411 0.0405 0.0400 0.0265
AT 6610 3170
298
* 50 * 110
K36’
0.00031 0.00041 0.00087 0.0017 0.0028 0.0041 0.0016 0.0015 0.0015 0.0017
As“ 2 9 8 16.6 2.0
HC1-HC104 mixture within the range covered. Table I11 gives the calculated solubility along with the concentration of chloride ion and all copper containing species for 10 solutions at 25 “C with total HCl concentrations from 0.50 to 5.0 m (no added HC104). Figure 1 displays graphically the fraction of dissolved CuCl present in the form of each charged complex species (note that the fraction present as neutral CuCl was too small to appear on the scale of this graph and that the best fit to the solubility data gave about 10% of the doubly charged species as Cu2C1t-). D. Equilibrium Quotients as a Function of Concentration. Each calculation of solubility included evaluation of the equilibrium quotients for the ionic strength and ionic concentrations present in the solution. Table W gives the values for these quotients for a number of representative solutions. The table contains the original molarities of HC1 and HC1 and HC104, the equilibrium ionic strength, and the three most significant reaction quotients. E. Heats and Entropies of Solution. The equilibrium constants K,,, K,,, and K36 can be represented quite well by Arrhenius-type equations, with least-squares fit giving In K,,= 8.3487 - 3326/T In K,, = 0.9869 - 1597/T In K36 = 1.2069 - 3420/T
0.0061 0.0150 0.0291 0.0695 0.1289 0.2863 0.3721 0.4538 0.5 254 0.5815
c u 2c1,2-
cu,c1,+,3-
0.00034 0.00078 0.001 5 0.0033 0.0058 0.01 23 0.0168 0.0214 0.0263 0.0314
0.00003 0.00010 0.00030 0.0013 0.0039 0.0191 0.0353 0.0599 0.0957 0.1430
of the fact that K36 represents the total contributions of the three triply charged complexes, no attempt is made to interpret the slope of the equation.
TABLE V: Heats and Entropies of Solution of CuCl species produced cuc1,cuc1,2-
0.0265 0.0383 0.0493 0.0667 0.0799 0.0939 0.0959 0.0954 0.0930 0.0890
(6)
This was not true for KZ4,apparently because the data at 15 and 35 OC were not extensive enough to discriminate clearly between CuC12- (K,) and CuzC12-(K2J.The heats and entropies of solution of CuCl to produce CuC1,- and CuC13- at 298 K are given in Table V. The uncertainties listed for the heats come from the standard deviations of the slopes in the least-squares deviations of eq 6. In view
Discussion A. Evaluation of Other Experimental Results. The parameters obtained above can be used to assess the reliability and consistency of other experimental results at temperatures and concentrations where direct comparison of the data is not feasible. Among these are those of Noyes and Chow,5on which most reported thermodynamic data are based; of Chang and Cha: summarized by Gmelin;lo of McConnell and Davidson;l’ of Vestin et al.;12of Morozov and Ustav~hikova,’~ presented in Linke;l of O’Connor et al.;14 and of Glodzinka and Zembura.16 All of the data except that of O’Connor14are at 25 OC. The data of 0’Connor14and Glodzinka15are in volume concentrations, like the present data; the remainder are in molality (or its equivalent). The data of McConnell and Davidsonl’ are for a constant (nominal) ionic strength of 1.0 m, while those of Vestin et al.12 are for a nominal ionic strength of 4.0 m; in both of these cases HC104was used as inert electrolyte. All other data are for aqueous solutions of HC1 with no inert electrolyte. In order to compare the data, it was necessary to put all of them on the basis of molarity. Those data given in terms of molality were converted to molarity by using the concentration of water in pure HC1 solutions of the same acidity as the solution investigated. This procedure is obviously approximate but should produce no large error in the molarities used. The results of the comparisons are as follows: 1. The data of Noyes and Chow5 at 25 “C agree remarkably well with the present work. Although their point at 1.14 M appears about 16% high, the remaining three points, below 0.5 M, agree within 2.5% (average). 2. The fit to the data of Chang and Chag is also good, considering the uncertainties in conversion of concentration scales. For 10 points between 0.7 and 9.6 M, the (rms) average deviation is 3.5% and the maximum 5.1 YO,with positive and negative deviations nearly equal in number. The agreement at the highest concentrations is surprising, considering that a representation of this simplicity is inadequate to represent activity coefficients of “pure” HCI solutions above about 6 m. 3. The fit to the Vestin12 data above 0.5 M is equally good. Except for one point deviating by 11% (possibly misreported), the average deviation in the range 0.5-3.7 M is 2.4% (maximum 3.3%). Below 0.5 M the Vestin data are high by 6-12%. 4. The remaining data are available only in graphical form, with substantial uncertainties in making comparison. They agree, by and large, with present work within those uncertainties, except that all appear high at low concentrations and show scatter and a smooth curve.
Chloride Complexes of CuCl in Aqueous Solution
The Journal of Physical Chemistry, Vol. 84, No. 18, 1980 2245
TABLE VI: Reported Values for Formation Constants at 25 'C ref nominal ionic strength K8, present work 0 0.0604
Ks3
K,,
Kn,n+a
0.0128
8 . 2 ~10-4
3.5 x 10-5
0.0212
0.00703 0.0021
5
(0.5) 0 1 m (HCIO,) 0 0 5 M (NaClO,)
9 11
4 6 3
0.0661 0.066 0.075 0.0618 0.0551 0.042
B. Formation and Stability Constants. The formation constants can be used to calculate stability constants for formation of the various complex species from Cu+ and C1-, provided a reliable value of the solubility product of CuCl(s) is available. At zero ionic strength, tabulated to 2.3 X For present values-range from 1.2 X purposes, we select 2.0 X lo-'. Using this value, we obtain, for zero ionic strength p 2 = 3.0 x 105 c u + t 2c1- = cuci2Cu+ 4- 3C1- = C U C ~ , ~ ~ C Ut+ 4C1-
:=
Cu2Cl:-
p s = 6.4 X lo4 p24
= 2.1 X lo1'
(7)
It is not possible to derive stability constants at other ionic strengths for lack of data on the concentration dependence of the solubility product. Many values of formation constants have been reported in the literature (see, for example, ref 16). Those derived in works cited above are listed in Table VI along with present results. Of previous resulta for K,,, that derived from ref 4 agrees best with the present work. The higher results of Noyes and Chow,5 of Change and and of McConnell and Davidsonll reflect both the neglect of (CuCl)' concentration (KJ and spuriously highresults at low concentrations. The low results of Mikita et a1.6 for both Kszand K,, apparently result from over-assignment of triply charged species in a relatively crude fit to the data. The data of Ahrland and Rawsthorne, are best compared with our equilibrium quotients for 0.5 M HCl, 4.5 M HC104in Table IV. Their values are all higher, reflecting the higher solubility of CuCl in NaC1-NaC104 solutions displayed in their data. They find a substantially larger contribution from Cu2C142-than we observe, but they regard their K 2 i value as highly uncertain. The equilibrium quotients of Table IV provide striking evidence of the interplay between ionic strength and the virial terms in determination of activity coefficients. The large changes in KS/depend primarily on the acidity, with the ionic strength entering only indirectly (and not significantly) through itri effect on the virial coefficient B. For the other quotients the ionic strength is a major contributor to variation in activity coefficients, but its effect is strongly modulated by the effect of acidity on the virial coefficient terms. The observed behavior points up the weakness in the common practice of reporting stability constants as a function of ionic strength alone. Where charged complexes are formed, this procedure may be quite misleading, for two reasons. First, the actual ionic strength may be substantially different from the nominal ionic strength because of formation of complexes with charges different from that of the ligand ion, as evident in Table IV. Second, the virial coefficient contributions can depend strongly on the nature of "spectator ions", as indicated by the sizable differences between equilibrium quotients for solutions containing H+ (Table IV) and those for the same nominal ionic strength with Na+ quoted in Table VI. This weakness extends to
0.020 0.034 0.00492 0.0415
TABLE VII: Thermodynamic Properties of CuC1,and CuCLa- at 25 'C
cuc1,A Gf" A Hf"
I 9
- 58.1
-65.6 51.6
cuc1,z- 87.9 - 109.0 50.0
the determination of the stability constants to begin with, since typical methods depend for their validity on the assumption that the stability constants are fixed if the nominal ionic strength is held constant. C. ThermodynamicProperties. The data of Table I can be used to obtain the thermodynamic properties at 25 OC of CuClf and CuCl?-. Using values from ref 4 for CuCl(s) and C1-, one obtains the values given in Table VII. The properties for CuClF are not significantly different from those of ref 4 and mainly serve to confirm their validity. Those for CuC12- will facilitate future work with solutions containing this complex. D. Species Present in Solu,tion. The correlation of the solubility data corroborates past observations that at modest chloride concentrations dissolved CuCl exists primarily as CuC12-and CuCll-, with the latter the major species above ca. 1.5 M. It also agrees with the observation of Ahrland and Rawsthorne3 that Cu2C1?-, the dimer of CuC12-,contributes to the solubility, but assigns it relatively less importance than they do. Triply charged complexes, represented here by Cu3ClG3-,become noticeable above 1M. They account for almost 40% of the solubility at 5 M C1- and apparently become the major species present at higher C1- concentrations (see Figure 1). On the other hand comparison with the limited data available above 5 M C1- gives no indication that any quadruply charged species are needed to explain the solubility in this region. The existence of the manifold and highly charged complexes postulated by Sukhova et a1.2 seems highly unlikely. Although the solubility data are not sufficient to determine the nature of the triply charged species present, it seems reasonable to expect that Cu3C11-, the trimer of CuClf, is a major contributor, for reasons similar to those which make cu3c16 (but not Cu2C14)a major constituent of gaseous cuprous ch10ride.l~
Summary and Conclusions Correlation of the solubility data of Hikita et a1.,6representing activity coefficients by a model based on that of Pitzer and c o - w ~ r k e r sgives , ~ ~ ~equilibrium constants for the solution of CuCl(s) to produce CuCl,-, CUC~,~-, Cu2C1?-, and complexes with triple negative charge. The equilibrium constant for formation of CuCl, is nearly indentical with that derivable from ref 4 and leads to AGp, AHfo, and Sofor this species essentially the same as those therein. The corresponding formation constant for CuC1:is substantially lower than most values previously reported, though nearest to that of Chang and Cha.9 It leads to thermodynamic properties (not previously available) for this complex (see Table VII). This work confirms that fact that (CuCl)omakes significant contributions to the solu-
J. Phys. Chem. 1980, 84, 2246-2254
2246
bility at low Cl-, as reported by Ahrland and R a ~ s t h o r n e . ~ References and Notes .It indicates that complexes with charges greater than three See, for example, W. F. Linke, “Solubility of Inorganic and Metal Organic Compounds”, Prentice-Hall, Princeton, 1958, and references are highly unlikely, even at very high C1- concentrations. therein. Application of this correlation to literature data on the T. G. Sukhova, 0. N. Temkin, R. M. Flld, and T. K. Kaliga, Russ. J . solubility of CuCl in HCl solutions indicates that most Inorg. Chem. (Engl. Trans/.), 13, 1072 (1968). reported data are too high at chloride concentrations below S. Ahrland and J. Rawsthorne, Acta Chem. Scand., 24, 157 (1974). F. D. Rossini et al., Nat/. Bur. Stand. (U.S.), Circ., 500 (1952). 1.0 M. This is probably because of the great ease of oxA. A. Noyes and M. Chow, J . Am. Chem. Soc., 40, 739 (1918). idation of Cu+ to Cu2+mentioned in the Introduction. The H. Hikita, H. Ishikawa, and N. Esaka, Nippon Kagaku Kaishi, 1, 13 data of Noyes and Chow5 below 1m and those of Chang (1973) (text in Japanese, but figures, tables, and abstract in English). K. S. Pitzer and J. J. Kim, J . Am. Chem. Soc., 96, 5701 (1974). and Chagboth appear reliable as do those of Vestin et K. S. Pitzer and G. Mayorga, J . Phys. Chem., 77, 2300 (1973). above 0.5 M chloride. All of these data agree with the K. S. Chang, and J. T. Cha, J . Chin. Chem. SOC. (Talpei),2, 298 present correlation (where applicable) within 5% or less. (1939). “Gmelin’s Handbuch der Anorganischen Chemie”, Vol. 60B1, Verbg All other data in the literature gives values which are either Chemie, Weinheim, 1958, p 228. substantially high or show a large degree of scatter. H. McConnell and N. Davldson, J. Am. Chem. Soc., 72,3168 (1950). The data on the formation constant of CuC132- should R. Vestin, A. Somersalo, and B. Mueller, Acta Chem. Scand., 7, 745 (1953). be of substantial aid in interpreting the solubility of CuCl I. S. Morosov and G. V. Ustavshlkova, Izv. Akad. Nauk SSSR, 451 in halide solutions other than HC1. The fraction of doubly (1944). charged species existing as Cu2C12-appears to depend on j. J. OConnor, A. Thomasion, and A. F. Armington, J . Electrochem. Soc., 115, 931 (1968). the particular halide considered. In addition, the distriW. Glodzinka and 2. Zembura. Rocz. Chem., 48, 341 (1974). butions of triply charged species still remains as an inL. G. Silien and A. E. Martell, “Stability Constants of Metal-Ion triguing problem, for whose solution considerably more Complexes”, Chemical Society, London, 1964. experimental data will be needed. L. Brewer and N. Lofgren, J . Am. Chem. Soc., 72, 3038 (1950).
Electron Donor-Acceptor Complexes. 1. Linear Free Energy Correlation of the Charge-Transfer Transition Energy with the Kinetics of Halogenolysis of Alkylmetals S. Fukuruml and J. K. Kochi” Department of Chemistry, Indiana University, Bloomington, Indiana 47405 (Received: February 13, 1980)
Mulliken charge-transfertheory is used to relate the properties of transient donor-acceptor complexes between alkylmetals and halogens with the kinetics of the accompanying cleavage reaction (halogenolysis). The formulation derives from the charge-transfertransition energy hvCT which is proportional to the second-order rate constant for halogenolysis of a variety of tetraalkyltin compounds in hexane or carbon tetrachloride solutions. The description of the activation process for halogenolysis as an electron transfer in the CT complex, e.g., [R4SnBrz] [R4Sn+Brz-],leads to a linear free energy relationship in which the activation free energy is equal to the driving force for [R4Sn+Brz-]ion pair formation. The latter is equated to the charge-transfertransition energy plus a contribution from the solvation energy, by employing a comparative procedure for the evaluation of alkylmetals. An independent measure of the solvation energy obtained from the gas-phase ionization potentials of alkylmetals and their free energy changes in solution supports the electron-transfer formulation of the activation process. The charge-transfer mechanism is generalized for the halogenolysis of alkylmetals.
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Introduction Electron donor-acceptor complexes have been studied extensively since the early development of the Mulliken charge-transfer (CT) theory.’ Most of these investigations have focussed primarily on the physical characterization of persistent CT complexes,2and rather less attention has been paid to transient CT complexes. Some earlier, sporadic attempts to apply CT theory to various types of reactions have been restricted to qualitative discussion^.^ However, no quantitative treatment of kinetic phenomena has been forthcoming, largely owing to the paucity of suitable chemical systems in which both the reaction rate and the CT phenomenon can be examined ~irnultaneously.~ The interaction of organometals RM with halogens merits special attention for several reasons. First, transient charge-transfer absorption bands can be observed, as we recently reported for a variety of alkylmetals and iodine (reaction l).5Second, the accompanying cleavage of the 0022-3654/80/2084-2246$0 1.OO/O
alkyl-metal bond by halogen, or halogenolysis, is one of the most common reactions of organometallic compounds,6 reaction 2 where Xz = Iz, Br2, Clz, or F2, Third, as repRM + Xz RX + MX ( 2) +
resentatives of organome’tals generally, the tetraalkyl derivatives of the group IVA metals (silicon, germanium, tin, and lead) are substitution stable and well behaved in solution to allow meaningful kinetic ~ t u d i e s .More ~ importantly, they are sufficiently volatile to enable the vertical ionization potentials to be accurately determined by UV photoelectron spectroscopy.8 By the proper choice of alkyl ligands, the steric properties of these alkylmetals can be systematically varied and finely tuned to cover a wide range of subtle molecular effects of the electron donor. Finally, the study of halogens as the electron acceptor 0 1980 American Chemical Society
