Dec., 1961
LEASTS Q U A R E S COMPUTER CALCULATIONS OF STANNOUS CHLORIDE COMPLEXING 2165
in an apparatus in which the sample could be better No evidence for solid state compound formation thermally insulated from its surroundings. was found in any of these mixtures. Exploratory measurements were made on mixFreezing Point of Acetonitrile.-We obtained a tures of several other aromatic hydrocarbons with value for the freezing point of pure acetonitrile of acet>onitrile to check on the possibility of com- 229.30 f 0.05 OK. Eight measurements were pound formation. The procedure consisted of made a t varying rates of cooling and on samples of obtaining freezing curves at several compositions. acetonitrile from two different lot numbers. The If all curves showed the same eutectic temperature measurements all agreed within 0.02O. This freezwith no other temperature halts or irregularities, ing point may be compared with the following it was concluded that no solid compound existed values found in the literature: 228.25,3 228.15,2 in the range between the extreme compositions 227.95,4227.436and 229.2as6 studied. The results are summarized in Table IV. The agreement with the last value, obtained by Mathieq6 is satisfying. The fact that some of the TABLEI V other values are more than a degree and a half lower ACETONITRILE-AROMATIC SYSTEMS SCREENED FOR SOLID is unusual. The solid transition a t lower temperaPHASE COMPLEXES tures suggests the possibility that some of the Range of composition others may have measured a metastable freezing investigated, mole fraction Aromatic component acetonitrile point. However, all attempts by us to supercool the acetonitrile to obtain the metastable freezing o-Xylene 0.30-0.69 point failed. m-Xylene .31- .70 Pseudocuxnene .31- .94 Acknowledgment.-The authors gratefully acAnisole .37- .75 knowledge the support given this project by the Chlorobenzene .27- .66 National Science Foundation and Research CorXitrobenzene .25- .79 poration of America. a-Trifluorotoluene
CY,CY,
.25- .74
The hydrocarbons were chosen so as to have a variety of geometrical structures and both low and high electron density in the ring. The range in composition investigated included compositions corresponding to 1:2, 1 : l and 2 : l complexes.
(3) B. E., Traa. Bur. Int. Et. Phy8.-China. Bmxelles, J . chim. phys., 27,401 (1930). (4) M.Ewert, Bull. soc. chim. Belges, 46,90 (1837). ( 5 ) R. R. Dreishacb, "Physical Properties of Chemical Suhatances,' Dow Chemical Co., Midland, Michigan, 1952. (6) M. P. Mathieu, Acod. roy. BelQ., Classe sei. Mem. Collection in-8, 28, NO. 2 (1953).
LEAST SQUARES COMPUTER CALCULATIONS OF CHLORIDE COMPLEXING OF TIN(II), THE HYDROLYSIS OF TIN(II), AND THE VALIDITY OF THE IONIC MED1UR.I METHOD' BY R. STUART TOBIAS AND Z Z. HUGUS,JR. Department of Chemistry, University of Minnesota, Minneupolis 14, Minnesota Received June 16. 2961
The stability constants of the chloro-complexes of Sn*2 have been redetermined a t 25" for a perchlorate medium a t an ionic strength of 3 by e.m.f. measurements using a cell with a tin amalgam electrode. A computer program which permits the assignment of weights to all experimentally determined quantities is outlined and applied to the computation of the constants. The values for the cumulative stability constants are PI = 15.12 f 0.25 M-1, &,= 54.9 i 2.1.M-2, & = 47.3 f 4.2 M - 3 (standard errors). No evidence was found for mixed chlorohydroxo-complexes in solutions with [H+] from 0.05 t o 0.50 M ,nor was there any evidence for polynuclear complexes involving chloride bridges.
Introduction Recently Rabideau and Moore2 have presented results of least squares calculations of the stability constants of the chloro-complexes of Sn+2using the data of Duke and Courtney3 and Vanderzee and R h o d e ~ . The ~ first set of data was satisfactorily fitted by three (constants for the mono-, di- and trichloro-compIexes instead of the four constants given in the original paper. These values apply to (1) This work was supported, in part, by the United States National Science Foundation under grant NSF-14173. (2) S. W. Rabideau and R. H, Moore, J . Phys. Chem., 66, 371 (1961). (3) F. R. Duke and W. G. Courtney, Iowa State Call. J . Sn'., 94, 397 (1850). (4) C. E. Vanderzee and D. E. Rhodes, J . A n . Chem. Sac., 74,3552 (1852).
a medium 2 M in [H+] with an ionic strength of 2.03. The total tin(I1) concentrationwas not held constant during the measurements. In the studies of Vanderzee and Rhodes, the total tin(I1) concentration was held constant a t approximately 0.01 M in a medium with an ionic strength of 3.00. The least squares fitting was carried out with data for solutions with 0.100 and 0.500 M [E+]and for measurements a t four different temperatures. The data for each different temperature and [H+] were fitted with three parameters corresponding to the coefficients in the power series expansion exp(-nFg/RT)
=
1
-+ Al[C1-l +...+ A,[CI-]"
If only mononuclear chloro-complexes are formed, the parameters are the stability constants; how-
R. STUART TOBIAS AND Z Z. HUGUS,JR.
2166
ever, significantly different values were found for the two different total hydrogen ion concentrations. Vanderzee and Rhodes interpreted this as evidence for the hydrolysis of tin(I1) accompanied by the formation of Sn(OH)Cl, and they used the dependence on [H+]to calculate the value 2 X for the equilibrium constant of Sn+2 H2O a SnOH+ H+. Rabideau and Moore found, however, that the variation of the parameters determined by the least squares method did not give consistent values for the hydrolysis constant. Some time ago, one of us published a rather detailed study of the hydrolysis of Sn f 2 in a medium with the total perchlorate concentration held constant a t 3.00 M.5 The lowest total tin(I1) concentration studied was 0.0025 M , and it was found a t this and all higher total tin(I1) concentrations that the protolysis of the aquo Sn+2 cation was followed by a very rapid condensation of the conjugate base to yield mainly a trimeric species. Because of the pronounced tendency to polymerize, it was possible to get a maximum of only about 8% of the total tin in the form of the mononuclear species SnOH+ even in the most dilute Sn+2 solutions. For this reason the value of the constant for the formation of SnOH+, 1 X Jl was not accurately determined. Nevertheless, the experimental measurements showed no significant hydrolysis with 0.01 M total tin(I1) a t a hydrogen ion concentration greater than about 3 X ill, and the hydrolysis constant given by Vanderzee and Rhodes to account for the variation in the A parameters appeared to he much too large. Knowledge of the species present in these tin solutions is of value in the interpretation of rates of tin(I1)-tin(1V) exchange reactions and rates of oxidatiori of tin(I1) by various reagents, in the calorimetric determination of ligational enthalpies and entropies, and in the interpretation of the absorption spectra of tin solutions. In this respect, it is interesting to note that it has been proposed that the variation in the molar extinction coefficient of Sn(I1) in hydrochloric acid solutions as the concentration of HC1 is decreased from 12 to 3 211 is a result of the hydrolysis of Sn+2.6 The extinction coefficient variations in perchloric and sulfuric acid solutions varying from 1 to 10 M in [H+] also have been attributed to the formation of SnOl-f+, and a value of 24.5 f 1 M was given for the first hydrolysis constant.' Vanderzee and Rhodes also suggested that substitution of H + for ITa+ a t constant ionic strength might affect the A parameters because of changes in species activities; however they felt that this was not the major cause of the variation in the parameters. Some years ago, it was suggested that probably half of the stability constants reported in the literature were erroneous because of activity variations caused by such medium changes.8 Since it did not seem likely that mixed chlorohydroxo-complexes were being formed, it appeared
+
+
Vol. 65
that this system might be one in which the constant ionic medium method9 was proving unsatisfactory. It also is to be noted that the values obtained by Rabideau and Moore from the data of Duke and Courtney and from those of Vanderzee and Rhodes differ much more than one would anticipate on the basis of any reasonable errors in the determination of the solution concentrations and the potential measurements coupled with the change in the medium. Considering all of these uncertainties about the species present in tin(I1) solutions, it appeared necessary to re-examine the tin(I1) chloride system over a wider range of variables before proceeding with further studies on tin(I1)-tin(IV) systems. Improved circuits are now generally available for highly accurate e.m.f. measurements, and the use of high speed digital computers makes it possible to carry out least squares calculations of equilibrium constants with many more data items than would normally have been feasible. Stability constants can he obtained with higher accuracy and false hypotheses more easily discarded. Experimental
Preparation of Solutions.-The Sn +4 solutions were prepared by displacement of Cu+* by tin metal in an oxygenfree system which allowed the Sn(C104)2solutions to be transferred to a storage flask in the thermostat and from there to the buret, all under an atmosphere of nitrogen. The e.m.f. measurements were begun immediately after the tin solutions were prepared. The general design of the apparatus and the preparation of the Sn+2 solutions have been described earlier6; the latest modification of the preparation train had all ground glass joints and Teflon stopcocks. Copper was determined in the Cu(C104)2 solutions by titration with EDTA using murexide as an indirator. All solutions were prepared from freshly boiled distilled water, and nitrogen gas was passed through the C U ( C ~ Osolution ~ ) ~ for an hour before it was reacted with the metallic tin. The preparation of the tin metal, tin amalgams, the preparation and standardization of the sodium and silver perchlorate solutions, and the purification of the nitrogen gas all have been described earlier .5 Sodium chloride solutions were standardized by evaporation and drying to a constant weight and also gravimetrically as AgCl. Hydrochloric acid solutions were standardized gravimetrically as AgCl. E.m.f. Measurements.-The design of the electrochemical cell and the experimental procedure were similar Sn, Hg(satd.) /Tin(II) soln. jj3.000 M NaCIOl (10.010M Ag+, 2.990 M N a + (1) 3.000 M C10,- IAgCl /Ag to that used in the study of the hydrolysis of Sn+2 in a perchlorate medium.6 The titrations were carried oiit bv adding two solutions, one an acidic Sn(ClO& solution and the other a NaCl or a NaCl-HC1 solution. The ionic strength of all solutions was adjusted to 3.00 with NaC104, and they were deoxygenated prior to use by bubbling nitrogen through them. The measurements with the dilute acid solutions were made with a Rubicon type B potentiometer and a spot light galvanometer, and the data with the 0.5 M[H+] solutions were determined with a potentiometer-vibrating reed electrometer circuit. A Leeds and Northrup K-3 potentiometer was used to balance all but 1 mv. of the cell e.m.f., and a Cary 31-V electrometer with a Varian G 11-A recorder was used as a null point detector. I n this way, when the potentiometer is out of balance by 1 mv., a full scale deflection is registered on the recorder (6) R. S. Tobias, Acta Chem. Scand., 12, 198 (1958). chart. This provides a very sensitive method of determin(6) C. I. Browne. R . P. Craig and N. Davidaon, J . A m . Chem. SOL, ing any drift in the otential values with time. Peak to 73, 1948 (1951). peak noise was u ~ u a ofl ~the order of 10 ~ v . ;however, it ( 7 ) G. Gordon and C. H. Brubaker, Jr., ibid., 82,4448 (1960). was not unusual for the potentials to fluctuate over several (8) T. F. Young and A. C. Jones, Ann. Rev. Phyr. Chem., 8, 276
(19521.
(9) L. G.Sillen, J . Inorg. d Nualear Chem., 8, 176 (1958).
:LEAST
Dec., 1961
SQUARES COMPUTER
CALCULATIONS O F STlNNOUS CIILORIDE COMPLEXING
hundredths of a mv. during an hour without showing any consistent drift. The potentials were usually constant within 0.1 mv. overnight. The entire Sn+2 preparation train, the electrochemical cell and thermostat, and the electrometer head all were enclosed within an aluminum cabinet serving ai3 a Faraday cage. The oil-bath thermostat was controlled to 25.0 f 0.1' by pumping water from an external thermostat through copper coils in the oilbath; an air-driven stirring motor was used for agitation.
Computational Procedure Input Information.-The usual Leden graphical procedureio for treating CsncII,/ [Sn +2], where CS~(II) is the total tin concentration and [Sn+2] the equilibrium concentration of the aquo-tin cation, was used to obtain preliminary values for the cumulative stability constants. As a first approximation, it was assumed that CCI- = [Cl-] where C a - is the total chloride concentration and [CI-] the equilibrium chloride ion concentration. These preliminary 0's together with the sets of data E, UE, Ccl-, aCcl-, CSn(II), O C S ~ ( I I )were used as input for a computer program using the Univac Scientific (ERA 1103) Computer a t the University of Minnesota. E is the difference in the potential values of cell (1) with total chloride concentration Cc1- and with no chloride ion. The a's are estimated errors in the experimentally determined quantities and were based on the replication experiments and the anticipated errors in the analytical data. Computation of the B's.-The first step in the program was the calculation of preliminary values for [Cl-] using the stoichiometric mole balance condition for chloride ion [el-]
cci-
+
N
NL[s~+~I[c~-I"
(2)
n-1
The values of I [ S ~ +were ~ ] obtained directly from the input E vz~lixes,the preliminary @s were used, and values for [CI-] were calculated by a NewtonRaphson iteration." The residuals for the least squares analysis are obtained from the other mole balance condition, that for the total tin(I1) cS~(II)
+
N
B ~ [ S ~ + ~ I [ C ~ -(3) I"
== [ ~ n + 2 1
n-1
and the function to be minimized is I wx(-CBn,iI)i
r=l
--
+ [Sn+*Ii + ~ ~ [ S n + * l , [ C 1 - 1 ~ ~ ) * I wi
i-1
(4)
In order to obtain the normal equations, the exact residuals are replaced by approximate residuals obtained by expanding the expression for C'~,+~ in a power series in the small corrections to be applied to the preliminary p's, neglecting terms of degree higher than the first. The reciprocal of the variance ui2 is chosen for the weight wi. The variance of the quantity, the residual of which (10) I. Leden, Z . physik. Chcm., 8188, 160 (1941); dissertation, Lund, 1943; we, e.g., J. C. Sullivan and J. C. Hindman, J . Am. Chem. SOC.,72, 6091 (1952).
(11) E. Whittaker and G. Robinson, "The Calculus of Observa(ions." Fourth Edition, Blackie and Son, Glasgow, 1844. p. 84-87.
2167
appears in (4), is computed using the provisional
6 values and the variances u2Csn(1~), u2E and Ccl-.
u2-
If G is the residual in (4),then
The partial derivatives of G are obtained from the mole balance condition for tin (3), and the partials of [Cl-] are obtained from the mole balance condition for chloride ion. The elements of the matrix formed from the coefficients of the adjustments to the p's in the normal equations are computed, the matrix is inverted, and it then is multiplied into the column vector formed from the constant terms in the normal equations to give the column vector, the elements of which are the adjustments to the p's. The standard errors in the constants were calculated from the relation where Ann-1 is the nth diagonal element in the inverse matrix, S is obtained from (4) with the calculated constants, and I - N is the number of degrees of freedom. The entire cycle of calculations then is repeated in an iterative procedure until convergence is obtained. The final set of constants together with the final iterated values for [Cl-1, and the CSn(1I)i are used in the mole balance expression for tin (3) to calculate values for [Sn+2]i and hence for the e.m.f. values E,. In these calculations del- was taken as A0.4010 of the total chloride, and U C ~ . ( ~ ~was ) taken as *0.4% of the total tin(I1) concentration. UE was estimated from duplicate experiments and observations of the fluctuations in the potentials recorded on the strip charts. The values rose to a maximum of f 0.5 mv when 0.03 M < C a - < 0.16 M and then decreased to f 0.1 mv. for Ccl- > 0.28 M . Results The data are plotted in Fig. 1 as 7 = log(Csn!rr)/ [Sn+*]) as a function of the iterated equilibrium chloride ion concentration. The back titration points correspond to a dilution of the tin(I1)chloride system with Sn(C10& solution and indicate that the equilibria are reversible. Slow changes are absent, since 3 hours elapsed between the readings. The interesting feature of these data is the absence of any trend in the points as the total analytical hydrogen ion concentration is varied from 0.05 to 0.50 ill while maintaining the ionic strength constant at 3.00. Two runs were made with 0.005 M total tin(I1) in order to determine if there were any interference from chloride ion bridging to form polynuclear complexes. The points describe the same curve as the 0.01 211 tin(I1) data and hence polynuclear complexes are absent. These measurements could not be extended to as high ligand concentrations as with the more concentrated tin(I1) solutions, for the potentials became erratic at high chloride ion
R. STUART TOBIAS SND
2168 1.4 1.2 1.o
0.8 6 0.6
0.4 0.2
-1.8 -1.4 -1.0 -0.6 -0.2 log [Cl-I. Fig. 1 . 7 as a function of log [Cl-] . Concentrations are in moles per liter. The curve is calculated with the set of constants reported in Table I. A, data from two runs with [H+] = 0.500 M ; 0, data from two runs with [H+] = 0.100 M ; 0 , data from two runs with [H+] = 0.050 M . Only about ]/a of the experimental points, selected a t random, are shown for clarity; A, data obtained by dilution with Sn(Cl0a)z-NaClOa solutions.
-2.6
-2.2
concentrations. For this reason, these points were not included in the least squares analysis. A set of 171 data items was treated in the least squares computation of the equilibrium constants. Since the maximum value of the average ligand number, E, which was attained in these measurements was about 1.73, the data were fitted in terms of three constants. An attempt to fit them in terms of 4 constants for the mono-, di-, tri- and tetrachloro-complexes gave a negative value for P 4 . The average ligand number is given by the stope of the curve in Fig. 1 a t a given ligand concentration. The values of the cumulative equilibrium constants for the mono-, di- and trichloro-complexes together with their standard errors are given in Table I. Least squares constants also were calculated from the data of Vanderzee and Rhodes4and are included for comparison.
z z. HUGUS,JR.
Vol. 65
It should be noted that the standard deviations given for the data of Vanderzee and Rhodes do not indicate the reliability of the constants, since only smoothed data were reported. The data were also insufficient to permit the assignment of weights to all of the experimental parameters, so all of the error was assumed to be in the e.m.f. values; and 0 - ~= f 0.2 mv. was assigned. This procedure gives virtually the same sets of constants reported for these data by Rabideau and Moore3 who, in addition, re-evaluated the data of Duke and Courtney and obtained ,& = 11.4 f 0.26 M-l, 02 = 52.3 f 1.8 M - 2 , and 83 = 31.4 =k 2.3 iM-3 by a least squares procedure assuming Ccl- = [Cl-1. Again the standard deviations indicate only the goodness of the fit of a single set of data and not the reliability of the constants. These data were insufficient for use with the computer program described here, since the total tin(I1) concentration is given only for the first point in the titration; values cannot be calculated for the other points as the tin(I1) solution is diluted by the addition of the chloride solution, for no volume data are given. The standard errors, 0-, of the constants obtained in this work should give a reliable estimate of the accuracy of the constants. Since the number of degrees of freedom is so large, 168, tables of the '(t" test of significanceI2 can be entered using an infinite number of degrees of freedom. Thus 0.6740- is the probable error a t the 507, confidence level and 2.5760- is the error a t the 99yGconfidence level.
Discussion The lack of any evidence for the formation of mixed chlorohydroxo-complexes explains the inability of Rabideau and Moore to obtain consistent values for the hydrolysis constant from the data of Vanderaee and Rhodes. The constants determined in this work for the chloride complexing are slightly larger than those obtained from the data of Vanderzee and Rhodes in the most acid solutions. The values for the smoothed potentials reported by these authors differ by about 470 a t high chloride concentrations for the solutions with 0.5 and 0.1 M [H+]. In this work almost all of the e.m.f. values were reproduced within 0.67, a t high chloride concentrations by the three constants even though the analytical hydrogen ion concentration was varied by a factor of 10. The TABLE I values of p1 and Pa obtained from the data of THE CUMULATIVE STABILITYCONSTANTS FOR THE MONO-, Vanderzee and Rhodes are, in turn, considerably DI- A N D TRICHLORO-COMPLEXES OF Sn+2OBTAINED BY THE larger than the values obtained from the data of LEASTSQUARES COMPUTATION Duke and Courtney. The presence of tin(1V) This work = 15.12 It 0 . 2 5 M-' to be the most likely reason for these disseems p2 = 54.9 If 2 . 1 M - 2 crepancies, since Duke and Courtney took no 63 = 47.3 i 4 . 2 AI-3 special precautions to prevent contamination with tin (IV). Vanderzee and Rhodes If the simplest ionic model is used to predict the A1 = 12.98 f O.10M-' 0.100 M [H+] stability of the hydroxo-complex SnOH+ as comA2 = 44.7 If 1.0 M-2 pared to HgOH+, one would expect similar staA , = 32.4 f 1 . 7 bility constants for these complexes. The crystal A1 = 13.71 f 0 . 0 8 M - ' 0.500 M [H +I A2 = 49.7 f 0.8 M-2
Aa = 45.7 f 1 . 4 M-8
(12) R . A. Fisher, "Statistical Methods for Research Workers." Hsfner Publishing Co., New York, N. Y., 1954, p. 174.
Dcc., 1961
LEASTSQUARES c 0 l l l F ~ T E RC A L C U L A T I O N S OF
radii of Sn+2 and Hg+2 are given by WyckoffI3 as 1.02 and 1.04 .$., respectively, and these can be used to approximate the cation radii in the complexes. The hydrolysis of Hg+2 has been carefully studied,‘? and one can calculate the value 2 X l0l0 ill-1for the stability constant of HgOH” in 0.5 ;11SaC104. The hydrolysis constant reported by Vanderzee and Rhodes for a medium with an ionic strength of 3.00 corresponds to a stability constant of 2 X 10l2 J1-l for SnOH+. The suggestion that Sn+2 is hydrolyzed to a significant extent in solutions with a hydrogen ion concentration of 3 Jl and larger seems even more irnplausihle. The hydrolysis constant reported earlier,5 which corresponds to a stability constant of 1 ;K 10’” for SiiOH+, is more consistent with this model and the results of this investigation. This simple ionic model is, however, insufficient to account for the details of the aquo-acidity of Sn+2 and Hg-2. The constant for the formation of aqueous Hg(OH)2 from HgOH+ is larger than the formation constant for HgOH+ from the aquocation, and no polynuclear complexes are formed. The Hg T? ion frequently forms compounds with tn-o strong bonds at an angle of B O 0 , and this ivould account for the hydrolytic behavior. On the other hand, the strength of Sn+?as an aquoacid is principally a result of the rapid polymerization of the mononuclear conjugate base. The Sn+’ ion is known to deviate from spherical symmetry in solid compounds containing tinoxygen bonds, ciid this can be explained by the addition of l f p ” character to the lone pair of 5s electrons’5 giring a “pear shaped” ion. This mould teiid to arcount for the formation of two or more strong IjolLds to oxygen which are directed in such a way as to permit polymerization by ~ which ring formation in solution. The C C I + ion differs only by the absence of the pair of 5s electrons is an extremely weak aquo-acid ; the stability constant for the formation of CdOH+ is only IO5 J1-1. (13) R TV. G Wjckoff, ”Crystal Structures,” Interscience Publisher&, Ne* York, N Y 1948 T H ~ *calculated ” from the HgFn distance i l l ) S Hietsnen a n 3 I G. sillen, Acta Chem. Scand , 6, 747 (1952). (15) L E Orgel, J Chenl S o c , 3816 (1959: (16) Y 31aiciis icia Chem S c a n d , 11, 690 (1957).
STAXNOUS C H L O R I D E C O M P L E X I N G
2169
The absence of any measurable variation in !he q ( [Cl-1) curves as H+ was substituted for Na+ is encouraging. This indicates that so long as one works with a high concentration of supporting electrolyte, e.g., 3 M , and does not make any more drastic change in the medium than the substitution of up to 16% of one univalent cation by another, activity coefficient effects will be small. I t must, of course, be assumed in the interpretation of the data in this work that the substitution of up to 15y0 of the medium Clo4- ions by C1- also has a negligible effect on the species activity coefhients. In the course of this investigation with Sn(C104)? solutions we have found it essential to carry out the entire procedure for the preparation, handling, and titration of the tin(I1) solutions in a glass system with oxygen carefully excluded. Tin(I1) perchlorate solutions are strong and fairly rapid reducing agents, and the tin(I1)-tin(1V) potential is undoubtedly more positive than the value EOox = -0.15 v. given in the l i t e r a t ~ r e ’ ~ because of the extensive polymerization of tin(1V) hydrolysis products in perchlorate solutions.’* Exposure of Sn(C104)zsolutions to the atmosphere for short periods of time gave rise to a strong absorption in the blue region of the spectrum, presumably the result of a tin(I1)-tin(1V) interaction complex with hydroxo or oxo bridging groups.
Conclusions The measurements described above show that only the mono-, di- and trichloro-complexes of Sn+2 need be considered in systems with [ C1-] I 0.4 M and [H+]20.05 M . KO evidence was found for Sn(0H)Cl as required by Vanderzee and Rhodes to fit their data, and this accounts for the inability of Rabideau and Moore to obtain a consistent hydrolysis constant from those data using least squares calculations. The absence of mixed chlorohydroxo complexes in these solutions is in accord with predictions based on ionic models and with independent studies on the hydrolysis of Sn(ClO& solutions. (17) W. 31. Latimer, “The Oxidation States of the Elements and Their Potentials in Aqueous Solution,” 2nd Edition, Prentlce-Hall Inc., New York, N. Y . , 1952 (18) J. S Johnson and K. A . Kraus, J . Phys Chem. 63, 440 (1959)
