J. Chem. SOC., Faraday Trans. I , 1984,80, 2361-2374 Effect of Ionic Strength on Stability Constants A Study of the Electronic Absorption Spectra of the Mercuric Halides HgX+, HgX,, HgX; and HgXi- in Water BY TREVOR R. GRIFFITHS* AND RICHARD A. ANDERSON Department of Inorganic and Structural Chemistry, The University, Leeds LS2 9JT Received 15th June. 1983 Thermodynamic stability constants log Q and l o g e , at 20 "C, are reported for HgX, + X- + HgX;and HgX; + X- e HgXi-, respectively, in water, where X = I, Br and Cl. The electronic absorption spectra of these reactions are very sensitive to ionic strength ( I ) , and give, by a new approach, log KF = 3.79f0.01, 2.23k0.02 and 0.70+0.03 and log KT = 2.03+_0.02, 1.40+0.03 and 0.50+0.05, for X = I, Br and C1, respectively. Values determined at constant ionic strength, with added NaClO,, compare well with literature values determined by other techniques.To compute stability constants from digitised absorption spectra does not rquire constant ionic strength conditions, and thus the relations between K and I have been studied and they are discussed in terms of activity coefficients. The results are compared with the extended Debye-Huckel equation, employing appropriate distance of closest approach a parameters. The effect of added perchlorate on the reaction HgX, T HgX+ + X- is reported, and the activity coefficients of the neutral species HgX, and HgXY are found to be independent of concentration and probably essentially unity. The reaction between HgX, and added X- always involves a concentration range in which HgX,, HgX; and HgX,2- are in equilibrium.Plots of log K against I: indicate when a two-species equilibrium becomes a three-species equilibrium, and the ionic strength so identified tallies with that noted in appropriate sets of spectra. Since the KT values agree well with existing results this spectroscopic technique has great potential for determining thermodynamic stability constants in non-aqueous solvents, especially when electrochemical methods are not available. The stability constants of mercury(I1) halide complexes were among the first reported. Morsel calculated the first two-step stability constants Kl and K , for the mercury(r1) chloride system from solubility measurements in 1902, and the following year SherriP published the product K3 K4 for mercury(I1) halides, from measurements of the partition of the neutral species between benzene and aqueous halide solutions.The overall stability constants of the complexes were determined potentiometrically. For many years the preferred route to accurate (thermodynamic) stability constants has been via electrochemical measurements. When using spectroscopic procedures the approach has centred on absorbance changes at a few suitable wavelengths3 Stability constants have then been calculated directly or from a graphical technique. We have developed a new procedure (an outline is included herein) which uses complete spectra (digitised at 1 mm intervals) to give accurate concentrations of the various complex ions in solution, and hence accurate (stoichiometric) stability constants (and not under conditions of constant ionic strength). We here report our results and examine our derived (thermodynamic) stability constants and compare them with currently accepted literature values for mercuric halides.23612362 STABILITY CONSTANTS OF MERCURIC HALIDES EXPERIMENTAL SPECTROSCOPIC MEASUREMENTS Details of the Applied Physics Cary 14H spectrophotometer and its Harrison Instruments digitising system have been described previ~usly.~ Thermostattable cell holders were used, and the water circulated from a thermostat bath maintained the solutions in the cells at _+ 0.1 "C. All spectra were recorded with the appropriate medium in the reference cell. CHEMICALS AND SOLUTION PREPARATION All chemicals were of the highest purity, thoroughly dried, and stored in a vacuum desiccator.Water was distilled and deionised before use. Because of the low and slow solubility of HgI, in water, solutions were prepared by mechanically stirring in water at ca. 40 "C for several hours. After cooling and filtering the solutions were transferred to a graduated flask and made up to volume. An aliquot was mixed with KI solution such that the iodide/mercury ratio was at least 30000 and the solution approximately 1.5 mol dm-3 in KI. HgI, was thus quantitatively converted to HgIi-, which has an absorbance peak at 323 nm. The HgI, concentration was determined from a calibration plot established by dissolving weighed quantities of HgI, in 1.5 mol dm-3 KI solution. Concentrations were accurate and repeatable to within < 0.5%. Standard solutions of KI and NaI were prepared by weighing into graduated flasks.To maximise accuracy the air-conditioned laboratory was maintained at 20 & 1 "C. Solutions for spectral measurement were prepared by transferring known volumes of stock solutions to a graduated flask with a pipette or burette, as appropriate, and making up to volume. Solutions requiring constant ionic strength were prepared by adding the calculated volume of NaClO, solution required. All glassware was grade A. SOLUTION STABILITY For the different concentrations studied, HgI, solutions obeyed the Beer-Lambert law. Solutions containing added iodide were stable for several days in the dark, but for only two hours in the spectrophotometer light beam, because the reversed-beam optics of the spectrophotometer exposed the sample to the full radiation of the quartz-halogen lamp.Test solutions were measured, stored and their spectra recorded again after one, three and nine weeks. After nine weeks the peak maximum of HgI, has decreased by 3%. Fresh solutions were therefore used in all experiments so that hydrolysis was insignificant during the period of use. COMPUTING PROCEDURES The pen noise inherent in spectroscopic measurements may be reduced by multiple scanning, but this is time-consuming and unrealistic for a two hour time-window. Noise reduction was therefore achieved by mathematical smoothing5 of the digitised spectra, which were recorded at 1 nm intervals. Degradation of the original profile was avoided by using a five-point smoothing convolute. CALCULATION OF STABILITY CONSTANTS Of the many techniques available for the determination of stability constants, potentiometric, polarographic, radioactive-tracer studies and spectrophotometric measurements have all been applied to the mercuric halide systems.Direct measurement of the concentration of individual species and curve fitting for various equations are among the methods used to yield values for the stability constants under various conditions of solvent type, ionic strength and temperature. If the molar absorbances of all the species in a solution are known, then the stability constants may be calculated using a series of solutions of different ligand concentrations but constant ionic strength. For this work, the reactions occurring in solution on addition of halide were either HgX, + X- + HgX; (i> or (ii)T.R. GRIFFlTHS AND R. A. ANDERSON 2363 or both. For reaction (i) the following relationship holds, uiz. A I M = [&(HIS,) K3 X&(HgXi)I/(1 i- K3 X) (1) where A is observed absorbance, M is the total molar concentration of mercury, &(Ha,) and &(HgX;) are the molar absorbances of HgX, and H a ; , respectively, K3 is the stability constant and X is the free-ligand concentration. Similarly, for reaction (ii) we have (2) AIM = [&(HgX,)+K,Xe(HgX~-)]/(l + K4X). When both reactions are occurring the following equation is valid: ~(Hgx,) + K3 Xs(HgX;) + K3 K4 P &(Ha:-) 1 + K3 X+ K3 K4 x2 AIM = (3) However, when sets of spectra recorded at constant ionic strength were applied to eqn (1)-(3) the results were not reliable.It was found, as has been noted by that formation constants calculated in this way are very dependent on the values of the molar absorbance used. Instead, therefore, the concentrations of the individual species were calculated as follows. At any given wavelength, the absorbance of a solution will be given by A = &fEI (4) where c, and E~ are the molar concentration and molar absorbance at a given wavelength of the ith species in solution. This equation holds true for all wavelengths. Thus, if A is measured for n different wavelengths, then n linear equations of i unknowns may be derived. For n % i these linear equations may be accurately solved for ct by means of multiple linear-regression analysis.The output of the program employed was the required concentrations, with their standard error, and various parameters which indicated the accuracy of the main computation and the precision of the fitted data. These latter included the residual sum of squares, the regression sum of squares, F ratio, multiple correlation coefficient and degrees of freedom of the F ratio. A table of residuals and standardised residuals was also obtained. Stability constants, with their standard error, were computed from the regression coefficients. This method had the advantage that conditions of constant ionic strength were not necessary, and hence the variation of stability constant with ionic strength could be studied. This is thus a new approach for determining stability constants from spectroscopic data, and the accompanying statistical data ensure that all erroneous spectra can be identified and eliminated. The resulting stability constants are thus accurate and reliable.To our knowledge this is the first time stability constants have been calculated using complete spectra: previously absorbance values at fixed wavelengths have been used. An account of existing techniques is given in ref. (3). TESTING THE METHOD FOR RELIABILITY AND ACCURACY Advantage was taken of the use of complete spectra in stability constant calculations. Since eqn (4) is valid for any wavelength range, constants calculated from data covering different wavelength ranges should be the same. If they are significantly different it may be assumed that one of the reference spectra is inaccurate over part of the spectrum.The accuracy of the computation, as reflected by the correlation coefficient and standard errors, was improved upon using a correct spectrum, or part thereof. An additional check is that the total metal concentration may be computed and then compared with known concentration in the sample solution. Complete details of our method, which simultaneously generates the spectra of the species H a ; , will be published elsewhere: we restrict ourselves here to the stability constants we have determined and their implications. The symbol K will represent all experimentally determined stoichiometric stability constants and 1% will represent the thermodynamic stability constants obtained from extrapolations back to zero ionic strength.2364 STABILITY CONSTANTS OF MERCURIC HALIDES Table 1.Effect of dilution on the dissociation of HgX2 in water 10-2 0.0035 - 0.123 - 0.575 - - 10-3 0.0106 - 0.389 - 10-4 0.035 0 1.23 0.3 5.75 5 5 10-5 0.106 0 3.89 3.5 18.20 20 18.5 10-6 0.35 0.5 12.30 12.5 57.20 61-73 61.0 - - 1.82 a Calculated from % dissociation = lOO/(Km);, where logK = 10.95, 7.82 and 6.48 for HgI,, Observed % deviation from the Beer-Lambert Since deviation with HgCl, was not independent of wave- HgBr, and HgCl,, respectively [from ref. (8)) law over a wide spectral range. length, this column refers to 200 nm. RESULTS MERCURIC HALIDES AND EFFECT OF ADDED PERCHLORATE The mercuric halides have very high stability constants in but at concentrations of spectroscopic interest, typically < 1 0-4 mol dmP3, dissociation can become significant, according to HgX, + HgX+ + X-.(iii) Spectra were therefore recorded at various concentrations and the results are summarized in table 1. Essentially no reaction was found for HgI,, but below and mol dm-3 for HgBr, and HgCl,, respectively, dissociation is apparent. The percentage reduction in the molar absorbance of the peaks is comparable with the percentage dissociation. Solutions containing HgI, maintained the same spectral profile throughout the whole concentration range. Solutions of HgBr, behaved similarly, though the peak became less resolved as dilution increased, but the peak at 200 nm for HgCl, at lo--, mol dmP3 had flattened at 4 x mol dm-3 and at lower concentrations only an absorption edge was seen (fig.1). The Beer-Lambert law was thus obeyed by HgI, at all concentrations used, but by HgBr, and HgC1, only at the higher concentrations. The spectra of various concentrations of the mercuric halides in aqueous NaC10, solutions with concentrations from 1.0 to 0.0001 mol dm-3 were not significantly affected by change in ionic strength. The Beer-Lambert law was obeyed by HgI, and HgBr, for halide concentrations from lov4 to mol dm-3 and by HgCl, above mol dm3. A similar observation has been made previouslyl0 for HgBr,. At lower molarities of HgCl,, e.g. 5 x mol dm-3, as the ionic strength was increased the 200 nm peak increased slightly, so that in 0.5 mol dm-3 NaClO, solution it was 2% higher than in pure water. Thus the perchlorate was affecting the activities of the ionic species in reaction (iii) and causing the equilibrium to be displaced towards undissociated HgCl,.That perchlorate should exert a salting-out effect under these conditions was thus surprising and unexpected.4 - I E 3 - 0 E E - a 2 0, CI m . UJ 1 T. R. GRIFFITHS AND R. A. ANDERSON 2365 200 210 220 230 2 40 wavelength/nm Fig. 1. Effect of dilution on the electronic absorption spectrum of aqueous mercury@) chloride at 20 "C. 1, maximum concentration, 2 x 10-3 mol dm-3; 2, minimum concentration, 2 x mol dm-3. MERCURIC HALIDES IN PERCHLORIC ACID In aqueous perchloric acid (2 mol dm-3) the spectra of HgX, had lower molar absorbances than those in water. A plot of the percentage difference between the two sets, relative to HgX, in water, has minima at 255 and 208 nm for HgI,, at 217 nm for HgBr, and at 196 nm for HgCl, (fig. 2).It is therefore suggested that HgX+ has absorbance maxima around 255 and 208 nm. Furthermore, since for HgI, the percentage difference at 255 nm approaches zero, the molar absorbance ( E ) of HgI+ at that wavelength must be approximately equal to that of HgI, (viz. 4500). Our results for HgI+ may be compared with the value of 245 nm reported by Griffiths and Symons,ll who observed a shoulder at this wavelength on the spectrum of HgI, in 72% HClO,, and the value of 266 nm reported by van Eck,' who calculated the spectrum of HgI+ in 0.5 mol dm-3 NaC10, solution using SillCn's stability constants.s Van Eck also reported peaks at 221 and 238 nm (both with E = 4000) for HgBr+ and HgCl+, respectively.' However, if HgCl+ had a peak at 238 nm of the reported molar absorbance it should be seen to appear on dilution of HgC1, solutions.We found no peak or shoulder here, even after repeated attempts, and van Eck's results must be considered doubtful. MERCURIC IODIDE WITH ADDED IODIDE The stability constant K3 was here obtained by two different methods, but by only one for K,. Our results, at 20 "C, for ionic strength 0.5 mol dm-3, with added NaClO,, are compared with those of Sillens and Marcus,12 at 25 OC, in table 2. Our two values for log K3 are within experimental error and our findings for log K3 and log K4 compare well with those of Marcus,12 who used an extraction into benzene procedure. They do not, however, compare well with those of Sillen,s who employed solubility measurements.Each reported error limit, which is the same as or better than previous values, reflects the maximum error value obtained. Upon examining the role of ionic strength we noted that for a given R value (R = mole ratio X-/HgX,), the conversion into HgXf was greater in NaClO,2366 STABILITY CONSTANTS OF MERCURIC HALIDES 200 220 240 I , 260 1 280 300 320 200 220 240 260 200 220 24 0 wavelength/nm Fig. 2. Effect of perchloric acid on the spectra of the mercury@) halides in water at 20 "C. 1, HgX, in water; 2, HgX, in 2 mol dm-3 HC10,; 3, percentage difference. solution than in aqueous solution, The reverse was true for HgX;. This is in agreement with reported studies showing an increase in K4 with ionic strength.13 This phenomenon was studied in greater detail by recording the spectra of solutions of the same R value at different NaClO, concentrations and at different mercury concentrations [fig.3 (a) and (b)]. The two-species equilibrium between HgI; and HgIt- [fig. 3(c)] at R = 100 became a three-species equilibrium as dilution caused the ionic strength, and hence the activity of the tri- and tetra-halide species, to be reduced. Stability constants were calculated for all solutions used in the absence of NaClO,. K3 remained constant at low ionic strength, with logK3 = 3.79k0.01. Above fi GZ 1.6 x this plot deviated to higher K values [fig. 4(a)]. A plot of log K4 against @ [fig. 4(b)] gave a straight line at higher ionic strength, extrapolating toT.R. GRIFFITHS AND R. A. ANDERSON 2367 Table 2. Formation constants for HgX; and HgX,2- in water at 20 "C constant ionic X K strengtha at infinite dilutionb ref. (12)c ref. (8)d I logK3 3.69f0.03 ~ 2.38 k 0.02 Br log K3 2.34 k 0.02 1.91 f0.03 C1 IogK, 0.81 kO.10 - log K4 K4 1% K4 K4 1% K4 K4 - - - 3.67f0.02" 3.79k0.01 3.67f0.02 3.78f0.14 - 2.03 & 0.02 2.37 f 0.05 2.23 & 0.02 - 2.03 +_ 0.03 2.25f0.06" 2.23t0.02 2.27f0.02 2.41k0.11 1.87 +_ 0.02" 1.40 f 0.03 2.04 k 0.05 1.75 f 0.03 - 1.36 f 0.03 - 0.70 +_ 0.03 0.95 f 0.03 0.85 k 0.15 - 0.50 f 0.05 1.05 & 0.06 1 .OO f 0.06 - 0.49 & 0.06 - - - - - - a For I and C1, ionic strength was made up to 0.5 rnol dm-3 with NaClO,; for Br, to Extrapolation oflog K3, log K4 and K, against It plots, respectively, 0.49 mol dm-3 NaClO,+0.01 mol dm-3 HClO, 1 .O rnol dm-3 with NaC10,. for each halide, for two-species equilibria.(25 "C). 0.5 rnol dm-3 NaC10, (25 "C). Independent calculation from same data set. l o g q = 2.03k0.02 for P = 0, but this line deviated towards the origin below fi = 0.01, intercepting the abscissa at fi x 3 x MERCURIC BROMIDE WITH ADDED BROMIDE Studies at constant ionic strength (made up to 1 .O mol dm-3 with NaClO,) at 20 "C yielded values of 2.34 0.02 and 1.91 k 0.03 for log K3 and log K,, respectively. A less precise procedure gave 2.25 & 0.06 and 1.87 & 0.02, respectively. Our results are intermediate between those of SillCn6 and Marcus12 (table 2). In pure water, the formation constants again varied with ionic strength at given R values.K3 was constant only at low ionic strength, giving l o g e = 2.23 f 0.02 [fig. 4(a)] and increasing rapidly at higher ionic stren ths. The variation of log K4 with fi is shown in fig. 5(b), being linear above lfz 9 x and extrapolating to log = 1.40 0.03 at fi = 0. At lower ionic strength the plot deviates from linearity to intercept the abscissa at fi w 4 x lov2. MERCURIC CHLORIDE WITH ADDED CHLORIDE Using an ionic medium made up to 0.5 mol dmd3 with NaClO,, when R values > 500 were exceeded, salting-out occurred, thus preventing study over the whole CI- concentration range. At equal R values, with and without NaClO,, the conversion into HgCl; was more pronounced in the presence of NaClO,. The effect of ionic-strength variation at different R values is shown in fig.6. Log K3 was calculated as 0.8 I f 0.10 at ionic strength 0.5 mol dmd3 (including NaClO,). This is slightly lower than previous values8, l4 (table 2). In the absence of perchlorate, at low ionic strength log K3 remained constant at 0.70+0.03, but above 1: x 6 x it increased rapidly [fig. 7(a)]. A plot of log K4 against 14 was similar to that for HgBrg- [fig. 7(b)]. The straight line at high ionic strength gave an intercept at zero ionic strength of log KT = 0.50 k 0.05. Below 1; = 3.0 x '10-1 this line deviated towards the abscissa giving an intercept at r: w 1.5 x 10-1.2368 STABILITY CONSTANTS OF MERCURIC HALIDES 2 I , 3 2 CI 250 300 350 4 00 E E 0 U m . u, 3 2 1 0 3 2 50 3 00 3 50 400 k 2 50 300 3 50 400 260 300 3 4 0 wavelength/nm Fig. 3.Effect of ionic strength [(a) and (b)] and dilution [(c) and (d)] on the spectra of HgI, + I- in water at 20 "C. Mercury concentration 3.2 x mol dm-3. (a) and (b) Ionic strength adjusted with added NaClO, : (a) R = 20, I/mol dmP3 : 1,O.O 1 ; 2,O. 1 ; 3 , O . 5 ; 4, 1 .O. (b) R = 200, I/moldm-3: 1, 0.01; 2, 0.1;3, 0.5; 4,l.O. (c) and ( d ) Ionic strength due to added halide: (c) R = 100, I/mol dm-3: 1, 0.0071; 2, 0.005; 3, 0.0035; 4, 0.0018; 5, 0.0007. ( d ) R = 1000, I/moldm-3: 1, 0.036; 2, 0.025; 3, 0.018; 4, 0.007. DISCUSSION The thermodynamic stability constant Kr for reactions (i) and (ii), which take the form A + B + AB, is given by fl = Jww/y(A) Y(B) ( 5 ) where K is the stoichiometric stability constant, reported here, and y(A) is the activity coefficient of species A etc.KT values are more commonly obtained by extrapolating K values to infinite dilution. Plots of log K against both I and fi are used and give reliable values of KT for reactions of the type studied here.15 We chose to examine mainly the function log K(fi) because of its relation to the Debye-Hiickel equation.T. R. GRIFFITHS AND R. A. ANDERSON 2369 4.0 3.9 G 00 - 3 . 8 3.7 2.4 G ?? - 2.0 200 150 d 100 50 0 0 0.01 0.02 0.03 Ii/mol* dm-) Fig. 4. Effect of ionic strength on K3 and K4 stability constants for HgI, +I- in water at 20 "C. (a) Extrapolated thermodynamic log K3 = 3.79 f 0.01 : dashed line, K3 values calculated assuming a two-species equilibrium between HgI and HgI; ; solid line, two species equilibrium up to fi = 0.013 and a three-species equilibrium, including HgI:-, above.(b) Extrapolated thermodynamic log K4 = 2.03 k0.02. (c) K4 intercept at 106 f 7, giving thermodynamic log K4 = 2.03 k 0.03. Dashed lines in (b) and ( c ) give K4 values calculated assuming that a two-species equilibrium between HgI; and Hg1:- holds below = 0.05. log K3 VALUES AND IONIC-STRENGTH DEPENDENCE If we assume that for neutral species, here HgX,, activity coefficients are unity and independent of the ionic strength of the medium, then the relationship between log K3 and ionic strength may be explained qualitatively. Eqn ( 5 ) may be re-written as (6) log K = log KT - log y(AB) + log y(A) + log y(B) where AB = H a ; , B = X- and A = HgX,. Thus for logK3 to be essentially independent of ionic strength at low concentrations shows that the activity coefficients2370 1 .5 e 21 .o d 0 . 5 0 6 0 L 40 20 0 STABILITY CONSTANTS OF MERCURIC HALIDES d 0.3 Fig. 5. Effect of ionic strength on K3 and K4 stability constants for HgBr,+Br- in water at 20 "C. (a) Extrapolated thermodynamic log K3 = 2.23 & 0.02. (b) Extrapolated thermodynamic log K4 = 1.40 f 0.03. (c) K4 intercept at 22.4 _+ 1.6, giving thermodynamic 10gK4 = 1.35f0.03. of HgX; and X- are the same within experimental error in this region. Unfortunately this does not provide the activity coefficients of the individual ions, but the rate of decrease of the absolute activity coefficients of these two anions can be said to be the same at low ionic strengths with concentration increase. Using the extended Debye-Hiickel equation concepts implies that the mean distance of closest approach for X- is greater in water than for H a ; .The strong, and hence bulky, hydration shell of X- prevents the close approach of other ions. The larger HgX; ion is consequently expected to be less strongly solvated. log K4 VALUES AND IONIC-STRENGTH DEPENDENCE Plots of log K4 against fi (fig. 4, 5 and 7) yielded straight lines at high ionic strength, the slopes of which increased from chloride to iodide; the line for HgC1;- wasT. R. GRIFFITHS AND R. A. ANDERSON 237 1 I L 2 00 2 20 240 2 60 220 240 2 60 wavelengt h/nm Fig. 6. Effect of ionic strength upon the electronic absorption spectrum of HgC1, + CI- in water at 20 "C, with R value constant and ionic strength varied by dilution. (a) R = 1000, I/mol dm-3: 1, 0.01; 2, 0.02; 3, 0.06; 4, 0.12. (b) R = 10000, I/mol dm-3: 1, 0.06; 2, 0.12; 3, 0.29; 4.0.58. horizontal within experimental error. With decreasing ionic strength, the value at which the plots deviated from linearity towards the abscissa decreased from chloride to iodide. However, at lower ionic strengths the points at which these plots intersected the abscissa could not readily be extrapolated. We also plotted K4 against fi (fig. 4, 5 and 7). Surprisingly, although there is no theoretical justification, good linear plots were obtained, now comprising two straight lines, and the intercept on the abscissa was determined. Furthermore, our plots have many more K values than are normally determined. The results are interpreted thus. The straight line at low ionic strengths corresponds to that concentration range when HgXi- is in a three-species equilibrium with HgX; and HgXi-. After the change in slope a two-species equilibrium, between HgX; and HgX,, is present.The positive intercept on the abscissa shows that no HgXi- can form until HgX; has been formed, and HgX; will only form in the presence of an excess of halide and not by disproportionation of HgX,. The distance of the intercept from the origin affirms the ease of formation of HgXZ- and is in the order I < Br c C1 ( I = 1 x loF5, 1.6 x and 2.3 x mol dmV3, respectively). These values are also the approximate minimum ionic strengths at which formation of HgX,2- will occur and they are consistent with the spectral evidence.14 > 0.001 mol dm-3 with logK (or K ) are not expected, or common.Excluding our results for chloride, where there is more scatter, linear relationships for log K3 are here observed up to around 0.0002 and 8.0006 mol dm-3 for iodide and bromide, respectively. However, for log K4, above a critical concen- tration, when all the HgX, has reacted, a linear relationship was found up to the maximum ionic strengths used, namely 0.017 and 0.09 mol dm-3 for iodide and bromide, respectively. We thus have Interestingly, we further have where m is the slope of the line. This reduces to Linear relationships for log K4 = log - log y(HgXi-) +log y(HgX;) + log y(X-). (7) (8) y(HgX,) m-) = Y(HgX,2-)m. (9) 1% Y(HgX,) + 1% y(X-) = m 1% Y(HgX:-)2372 STABILITY CONSTANTS OF MERCURIC HALIDES I 1 I 1 I i 0 -10 0.20 0 0 0 4 J Do - 0.2 4 0 (b) I I I I I I I 0 I- 0 0 d 31- 2 0 00 0 0 0 0 1 I I 1 1 I 1- 0.4 0.8 1.2 I f / m o d dm-3 Fig.7. Effect of ionic strength on K3 and K4 stability constants for HgC1, + Cl- in water at 20 "C. (a) Extrapolated thermodynamic log K3 = 0.70 k 0.03 ; dashed line, K3 values calculated assuming a two-species equilibrium between HgCl, and HgCl; ; solid line, K3 values calculated assuming a three-species equilibrium, including HgC1,2-. (b) Extrapolated thermodynamic log K4 = 0.50 f 0.05. (c) K4 intercept at 3.1 f 0.15, giving thermodynamic log& = 0.49+0.06. Unfortunately at this time this relationship cannot be usefully employed : accurate activity coefficients for the individual halide ions are required. APPLICATION OF EXTENDED DEBYE-HUCKEL EQUATION The extended Debye-Huckel equation can be applied to the formation of HgX- in water using our data, provided appropriate closest approach parameters (a) are chosen.ls For example, for the formation of HgI,2- two sets of results were obtained,T.R. GRIFFITHS AND R. A. ANDERSON 2373 Table 3. Application of extended Debye-Huckel theory to the formation of Hg1;- in water after D-H I / mol dm-3 experimental correctiona 5.8 7.3 8.5 10.0 11.5 13.0 16.6 20.3 27.4 41.5 48.9 56.3 63.5 70.9 141.6 288.3 1.91 1.87 1.99 1.95 2.03 1.97 2.07 1.99 2.08 2.00 2.10 2.02 change of slope 2.13 2.05 2.14 2.08 2.16 2.06 2.19 2.07 2.20 2.08 2.22 2.06 2.23 2.07 2.27 2.06 2.29 2.07 2.41 2.1 1 a The distance of closest approach, a, employed for I-, HgI; and HgIq- was 4, 3 and 4.5 ( x lo-*) cm, respectively.corresponding to a three-species equilibrium where log K4 increased with increasing ionic strength, and a two-species equilibrium (between HgI; and HgIi-) where log K4 remained constant at 2.07f0.02. The a parameters chosen were (3, 4 and 4.5) x cm for HgI;, I- and HgIi-, respectively, and the results are given in table 3. Obviously a better correspondence between the experimental and Debye-Hiickel corrected log K4 values could be obtained upon varying the a values, but there would not be one unique set of a values. Note the change in slope at Z = 1.5 x low3 mol dm-3 after correction, corresponding to the observed change in the observed data, and that for the two species a straight line of approximately zero slopelS was obtained up to 0.03 mol dm-3, the limit of measurement.The extended Debye-Huckel equation is normally linear up to 0.1 mol dmm3. ACTIVITY COEFFICIENTS OF NEUTRAL HALIDES We finally note that Spiro and HumelB have claimed that the stability constant of HgXY in aqueous 0.5 rnol dm-3 NaCIO, would be 0.11 log units greater than in the absence of perchlorate. They studied the reaction of the neutral halides HgX, and HgY, and assumed that the activity coefficients of the reactants were dependent upon the ionic strength of the medium but that of the product, HgXY, was independent. We have found that the spectra of HgX, and HgYz mixtures in 0.1 rnol dm-3 NaCIO, exactly superimpose the respective mixtures in water alone. Our earlier assumption that the activity coefficients for the neutral dihalides in water are independent of concentration, and essentially unity, is thus supported.The only alternative explan- ation for our observation would be that the activity coefficients of all three species cancel, which implies that y(HgXY), x y(HgX,) y(HgY,).2374 STABILITY CONSTANTS OF MERCURIC HALIDES CONCLUSIONS The electronic absorption spectra of the various halogeno-mercury(I1) complex ions are very sensitive to the ionic strength of the medium. Stability constants calculated from digitised spectra recorded in the presence of added NaCIO, compare well with those obtained by a distribution technique. Plots of log& against fi are independent of concentration at low ionic strengths, implying equivalence of y(HgX;) and y@-) values.At high ionic strengths, the positive deviation reflects the effect of the size of the reacting halide ion and correlates qualitatively with extended Debye-Huckel theory. The concentration dependence of log& reveals the ionic strength at which the change from a three- to a two-species equilibrium occurs and parallels data derived using the extended Debye-Hiickel equation in the range where it is applicable. The activity coefficients of HgX, and HgXY are independent of concentration. Finally, this approach is equally applicable to similar spectra obtained in non-aqueous systems. Electrochemical methods are not always possible, and as the reliability of our technique is now established it has considerable potential for the future. We thank the S.E.R.C. for the provision of the Cary 14H spectrophotometer and the UKAEA for the digitising equipment (purchased under EMR 1913). R.A.A. thanks the University of Leeds for a Research Studentship. T.R.G. thanks the Chemistry Department, Michigan State University, East Lansing, Michigan 48824, U.S.A. for their hospitality while on leave from the University of Leeds. Valuable discussions with Dr S. R. Crouch, Michigan State University, are gratefully acknowledged. H. Morse, Z . Phys. Chem. Leipzig, 1902, 41, 709. M. S. Sherrill, 2. Phys. Chem. Leipzig, 1903, 43, 705. F. R. Hartley, C. Burgess and R. Alcock, Solution Equilibria (Ellis Horwood, Chichester, 1980). T. R. Griffiths and R. A. Anderson, J. Chem. SOC., Faraday Trans. 2, 1979,75, 957. A. Savitsky and M. J. E. Goley, Anal. Chem., 1964,36, 1627. S . Feldberg, P. Klotz and L. Newman, Inorg. Chem., 1972, 11, 2860. L. C. Sillen, Acta Chem. Scand., 1949, 3, 539 and references therein. 'I C. 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