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A raman spectrophotometric study of the stability of aqueous coordinatively-saturated mixed bromo-iodo complexes of cadmium
J. inorg, nucl. Chem., 1974, Vol. 36, pp. 1331-1335. Pergamon Press. Printed in Great Britain.
A RAMAN SPECTROPHOTOMETRIC STUDY OF THE STABILITY OF AQUEOUS COORDINATIVELY-SATURATED MIXED BROMO-IODO COMPLEXES OF CADMIUM N. YELLIN* and Y. MARCUS Department of Inorganic and Analytical Chemistry, The Hebrew University of Jerusalem, Israel (First receioed 19 June 1972; in revised form 21 June 1973) Abstract--The substitution equilibrium constants for the reactions CdI 3 _.Br 2~71+ I- ~ CdBr,I 2-n + Br-
(n = 0, 1, 2 and 3) have been measured in aqueous media at a constant ionic strength (1.634 M) and varying bromide to iodide ratios. Quantitative Raman spectrophotometry was used, with dilute (0-167 M) cadmium solutions and an internal standard (LiCIO4). It is shown that the intensity of the Raman scattering of a species is determined by the peak height (rather than area), which is proportional to the concentration. The values of the mixing constants, for the reactions (n/4)CdI~- + (1 - n/4)CdBr~- ~ CdI,Br2=,, corrected for statistical effects, give the stabilization constants 0.4 for CdBr3l 2 -, 0-7 for CdBr2122- and 1.6 for CdBrI~-. Only the latter is thus stabilized beyond the statistically expected level, but the reasons for this are obscure.
INTRODUCTION Tr~ RECENT advance in Raman spectrophotometry caused by the introduction of the high intensity laser light source, has permitted its application for the study of rather dilute solutions. This makes possible the full use of the advantages of this technique, which include the direct proportionality of the signal obtained for single complex species in a complicated equilibrium mixture to the concentration of this species. Under conditions where activity coefficients may be expected to remain constant, i.e. in a constant ionic medium, this permits then the unambiguous calculation of the stability constant of complex species, the existence of which is proven directly by the Raman spectrum. A case where this is of particular advantage is that of mixed complex formation, where most methods give only indirect evidence for the existence of the mixed species, and very complicated relationships between measurable quantities and the total concentrations of the reactants in the solution[l]. As a part of a study of the solvent effect on mixed complex formation in solution[2], it was found advantageous to demonstrate the practical validity of the above method with a system where both the species have already been well characterized by Raman spectrometry, and their stabilities have been determined by conventional methods. One of the few systems where this is possible is the cadmium(II}-bromideiodide system. The Raman spectrum of the tetrahedral complexes CdBr,I~-, (n = 0-4) in aqueous solution, * This work represents a part of the Ph.D. thesis submitted by N,Y. to the Hebrew University, May 1972.
is known[3-5]. Their stability constants have been determined by potentiometric[6] and polarographic[7] techniques. Previous to our work, however, very little quantitative work has been carried out by Raman spectrophotometry. Delwaulle[8] determined the stability constant of HgC1CN in 1949, but even at the present time almost all of the investigations by this technique dealing with mixed ligand complexes do not discuss the quantitative aspects. In this work, we determine the stability constants of the complexes CdBrnI~- . in aqueous solution by Raman spectrophotometry. We also demonstrated that these are coordinatively saturated complexes. EXPERIMENTAL
Analytical reagent quality (Analar) Cdl 2 , LiI and LiC104 were used. Some experiments in anhydrous solvents, for the examination of the Raman peak height-concentration relationship, required dry salts, and CdBr2.2H20 and LiBr. H2 O were dehydrated as follows: CdBr2.2H20 The salt was dehydrated at 25°C for 24 hr, then transferred into a vacuum system (P < 10 -z mmHg) for a further 24 hr at 100°C. The bromide concentration was determined by argentometric titration, and purity was found always to be greater than 99.5 per cent. LiBr2 • H20 The salt was dehydrated at 100°C for 24 hr and the temperature was then raised to 500°C for an additional 24 hr. The bromide concentration was determined by argentometric titration, and purity was found to be always greater than 99.0 per cent.
1331
1332
N. YELLINand Y. MARCUS
Analytical solvents were used, whenever available. The water content of the organic solvents was negligible. The solid salts were weighed in a nitrogen atmosphere because of the hygroscopic nature of LiBr, LiI and LiCIO4. The required amount of solvent was then added. The CIO~scattering band at 938 c m - ' was taken as a quantitative reference. LiC104 was found to be inert in the solutions under examination[9,10], i.e. its constituent ions did not react with the cadmium, iodide or bromide ions and its scattering bands were not in the spectral region of those of the complexes. Spectra were recorded on a Raman spectrophotometer [11] with a Spectraphysics Model 125 Helium-Neon Laser and a Spex 400 II double monochromator. The accuracy of the determination of the peak energy was +_1 cm- ~ at the 95 per cent confidence level. Occasionally, the same, sample was recorded several times, in order to check the reproducibility of the Raman system; the deviation was less than 1 per cent. Overlapping Raman bands were analysed by a nonlinear least-squares computer technique to obtain the best fit to a Gaussian function. Attempts to use a Lorentzian function failed. A Gaussian-Lorentzian gave similar results to a pure Gaussian function, but with greater error limits. As pointed out by IrishE12] and observed in our own work, discretion and a detailed chemical knowledge of the system must be applied in such an analysis, lest spurious results, such as nonexistent lines, are obtained.
/
o
/
h C104
/ / ///
/
X=l
X:Br /-
.1_.
/ ./
I/ /
0
i
h
5
10
Cx-/Cc .2 Fig. 1. [X-]/[Cd + z] ratio necessary for total coordination of the Cd +2 ion to CdX 2-, as shown by the normalized
h(vl). of the cadmium ions to form tetrahedral cadmate anions was observed for the ratio [Br-]/[Cd + 2 ] > 6 and for [I-]/[Cd +2] >_ 5. Excess ligand concentration did not produce any change of h(v0, that is it did not produce any new species in the solutions under examination. The maximum coordination number for CdBr 2-" or CdI~ - " complexes is therefore four (see Fig. 1). (c) The correlation between complex concentration and
RESULTS
the intensity of the v I scattering band
(a) Identification of the species in solution Raman spectra of aqueous solutions which contained cadmium ions with various ratios of bromide to iodide concentrations were recorded. The characteristic scattering bands of the complexes C d B r . I 2 : , were found to be in accordance with earlier results (see Table 1). Since the vl symmetric band has the highest intensity, it was used as a measure of the concentration of the complex. (b) Determination of the ratio [X-]/[Cd+2], (X = B r - ,
I-) required for saturation coordination The excess ligand concentration required for coordinatively saturated complexation of the cadmium ions to form CdX~- in aqueous solution was determined as follows. A series of samples was prepared with a constant cadmium concentration (0.167 M) and varying ligand concentrations ranging between 0-2 and 2~ M. A constant concentration of LiCIO 4 (0-470 M) was present in each sample. Saturation coordination
A series of samples containing varying amounts of tetrahalocadmate in the presence of a constant amount of lithium perchlorate were investigated in different solvents. The relationship h~
- -
= Jtv,}c
where htv,) is the peak height at the v1 energy, J is the molar scattering coefficient, and c is the complex concentration, was valid under the present experimental conditions (Figs. 2,3). It was then assumed that if the binary tetrahedral cadmates obey relation (I), then the ternary CdBr~I2-, (n = 1, 2, 3) species would also obey it. (d) Stability constants of CdBr, I ~ - , (n = 0-4) in water A series of solutions was prepared with constant concentrations of cadmium(II) (0.167 M), total ligand
Table 1. vI Scattering bands of the complexes CdBr, I2_n(n = 0-4) CdBr~ 166(62, 185)* 163 (53, 62, 181 ?) 163 (63, 187) 163 (62, 188)
CdBraI =
(1)
h938 era- '
CdBr2If
CdBrI~
141g 144
132
124
142
130
123
I~t
* v2, v3 , v4 are given in parentheses. t The scattering band is in the double-headed arrow range.
CdI2
Ref.
117(37,45, 145) 117 (36, 44, 144) 117 (47, 147) 117 (50, 145)
[4] [3] [5] [this work]
Stability constants of CdBr.I]:.
1333
/ / ~MeOH H
DMA
20
Et0H
4--*
E
C
b
>, O JD
<
z
/
V"
I
I
I
0.0
0.1
0.2
0.3
CCd i2 ,M
I
OO
0.1
012CCdBr4 .M0.3
Fig. 2. The dependence of the vt(Cdl]-) peak height on the complex concentration.
Fig. 3. The dependence of the vl(CdBr~-) peak height on the complex concentration.
(1.00 M) and lithium perchlorate (0.470 M) and various ratios of bromide to iodide, and their Raman spectra were recorded. As the vl scattering energies of the complexes examined are close to each other (see Table 1), the spectra were composed of several superimposed peaks, according to the number of complexes in solution. The computer results gave the vl energy, the peak height at this energy h, and the peak width at half height, for each individual peak. It was assumed that the intensity of all other scattering bands except v~was negligible, and that the spectrum is one of superimposed v~ peaks alone. This assumption is correct to a very good approximation, because the low intensity of the v2 - v6 peaks of the mixed complexes prevents their identification with the sensitivity attainable with present-day Raman instrumentation. The results obtained by the computer analysis were assumed to be reliable if the energy values agreed with previously known values of v~ energies, within their standard deviation (Table 1). The determination of the peak heights was reproducible within 0.5 per cent (maximal error) and the peak width within + 60 per cent (maximal error), as given by the computer. The peak height was taken as a measure of the complex concentration. The molar scattering coefficients of tetrabromo- and tetraiodocadmate were obtained from solutions which contained the binary complexes only, with the same amount of LiC104 and the same ionic strength as the whole series. The concentrations of the other species and their molar scattering coefficients were obtained
sequentially from the intensities of the resolved peaks. The concentrations of free bromide and iodide were obtained from the total concentrations CB~- and C~by difference. The equilibrium quotient K, (n = 0-3) for the substitution reactions CdBr4_,I,z- + I- m CdBr3_,I,Z.~l + Br-
(2)
is given by K.=
[CdBr 3_.12+1] [Br- ] [CdBr4_.I2_]Ei_ ] .
(3)
The ionic strength, I = 1,634, was constant, so it can be assumed that activity coefficient ratios do not change appreciably in the series of solutions. Thus, if a constant value for the quotient K. is obtained at several compositions, its value as an equilibrium constant is valid. The results are given in Table 2 and Fig. 4. The values of KI for experiments 9-13 were obtained by assuming an average value of 5.3 for Ko in these solutions. The values of K 2 scatter widely, because there are always three species present when the concentrations of CdBr2I~- and CdBrI]- are comparable. A weighted average of K2 ~ 5 is consistent with the data. It appears however from Fig~ 4, which shows the primary data from the resolved peaks, which are independent of the K. values, that CdBrI 2- is the most stable mixed complex in the present system. DISCUSSION
The present quantitative work is based on relation (1). Some workers[12] prefer to take the peak area as a
N. YELLINand Y. MARCUS
1334
affect the v~ symmetric vibration of the complex. 015
0.10
g
o
0.05 t,
_ 0.00 bOO
"/
_
\
0.25
0.50
0.75
C I-
1.00
Fig. 4. The dependence of the concentrations of the complexes CdBr, l,2_-,(n = 0-4) on the [I-]/[Br-] ratio.
measure of the concentration of the species, but the peak height is a satisfactory measure of the concentration of the species, as long as there is no line broadening with a change in concentration. Line broadening is caused by an interaction of the species with molecules of the solvent. Our results show clearly that a linear relationship exists between the height h of the v~ scattering band and the complex concentration (Figs. 2 and 3), in all solvents studied. It is concluded that there is no interaction with the solvent which would
Conversely, whenever relation (1) is not observed, there exists an interaction between the solvent and the solute as, for example, in the rapid exchange of a proton between the hydrogen sulphate anion and water molecules[13]. The deviation from linearity may serve as a quantitative criterion for this solute-solvent interaction, but this aspect requires further study. It should be noted that deviations from linearity exist even when the peak area is taken as a measure of the concentration of the species[12]. In that case, there is no doubt that the deviation indicates solute-solvent interaction. When dealing with computer analysis, a considerable physical knowledge of the system must be applied, since the mathematical results do not always express the chemical situation. In order to limit the possibilities of error, the energy value was taken as a varying parameter, even though it was known exactly. F r o m the energy values obtained by the computer, the reliability of the peak height results was determined. The best results are obtained in the case where there are only two peaks in the spectrum (the range of error for the calculated K values is within + 10 per cent), and the accuracy decreases as the number of peaks in the spectrum increases. G o o d accuracy can be achieved by increasing the number of data points fed to the computer, but in the present case this was impossible, because the work was manual.
Technical improvements in the last few years allow Raman spectrophotometric measurements of quite
Table 2. Substitution equilibrium constants (Eqn 3) for tetro(bromo-iodo) cadmate ions in aqueous solutions The concentrations in columns 2-8 are in M. No. 1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
C l-
CdBr~
1.00
--
0-958 0.950 0.916 0.900 0.875 0.833 0.792 0.750 0-708 0.700 0.650 0.625 0-600 0.583 0.500 0.400 0.292 0.250 0-208 0.200 0.167 0.150 0.125 0.100 --
0.042 0-050 0.084 0.100 0.125 0.167 0.208 0-250 0.292 0.300 0.350 0.375 0-400 0.417 0.500 0-600 0.708 0-750 0.792 0.800 0.833 0.850 0.875 0.900 1-00
0.167 0.138 0.132 0.111 0.103 0.093 0.083 0.071 0.062 0.052 0.050 0.039 0.036 0.031 0.030 0.020 0.009
CBr-
CdBr31= 0.029 0.035 0.056 0.061 0-061 0.033 0.012 ------
-----
CdBr21 ~
0.003 0.013 0.051 0.084 0.105 O.113 0.113 0.098 0.086 0.068 0.050 0.015 --
* From solution No. 7 onwards K o was assumed to be 5.3.
CdBrl~
Cdl~
Ko
K1
K2
K3
5.15 5.60 5.60 5.40 5.05 (1.8)
0.002 0.004 0.030 0.045 0.068 0.085 0.120 0.131 0.119 0.105 0.094 0.094 0.074 0-070
(17.1) 8.5 8.4 8.3
6.3 8-5 0.002 0.012 0-027 0.048 0.062 0.073 0.073 0.093 0.097
0.058
0.109
0.047
0.120 0.167
8.3
1.3 2.0 4.5 8.7 0.44 0.49 0.44 0.46 0.41 0.36 0-49 0.44 0.47 0.49
Stability constants of CdBr, I24-
1335
Table 3. Substitution constants of CdBr4_ ~I~-(n = 0-3) in water determined by different techniques Ko
K1
K2
5.3 + 0.5 8.0 7.1
8.5 6.0 7.1
5 2.9 0.3
Technique
[Cd +z]
[Brl + [I]
I
Rarnan Spect. Potentiometry[6] Polarography[7]
0.167M 0.089M 0.002M
1.00M 3.00M 2.00M
1.53M 6M 2M
K3
0-45 + 0-05 1.8 0.8
dilute solutions (to about 0.1M), but it is not sensitive enough for 10w concentrations. E.M.F. techniques, on the other hand, can be applied to very dilute solutions (about 10-4M), i.e. quite different experimental conditions. Nevertheless, there is agreement between the K n results obtained by these two methods (Table 3). Where there is disagreement, i.e. for the values of K2 and K3, there is a similar disagreement between potentiometric and polarographic results, which apply essentially to the same experimental conditions. Although the present determination of K : is not accurate, it is definitely concluded that K 2 > 1 (in agreement with the potentiometric value) and that K s < 1 (in agreement with the polarographic value). The dimensionless equilibrium constants calculated according to eq. (3) pertain to the substitution reaction
(2) CbBr4_nI 2- + I - ~ CbBr3_nI2~-I + Br-
(2)
where there is no difference in charges between the reactants and the products. This formulation is preferable to addition reactions for obtaining the data, e.g. Cd 2+ + h i - + (4 - n)Br- ~ CdlnBr2-,
(4)
CdI 2-n + (4 - n)Br- ~ CdlnBr2=,.
(5)
or
In these reactions, there is participation of solvent, which must leave the coordination sphere around the cadmium, where it completes to four the coordination number of a species such as CdI~ [14], as well as noncancelling activity coefficient terms. On the other hand, the substitution equilibrium constants Kn of Eqn (3) for equilibrium (2) may be used to calculate dimensionless mixing constants Ku(~} for the reactions -
4)CBr
#- CdI.Br~2~
(6)
shown in Table 4. These include a statistical contribution, the binomial factor (~), so that by dividing the KMO ) , KM(z~and KM~3)values by 4, 6 and 4 respectively, the stabilization constants K s shown in Table 4 are obtained. Of these, only Ks~3~, for CdBrI~-, is larger
J.I.N~C.,Vol. 36. No. 6--J
Table 4. Stabilization constants of CdBr4_nl~ -(n = 0-3) in water
KM Ks
CdBr3 I2-
CdBr21~-
CdBrI~-
1.62 0.4
4.2 0.7
6.5 1.6
than unity, denoting that this complex is more stable than predicted statistically, though only slightly. The others are less stable, but not by large factors. These findings are m agreement with previous reports[l], as required by the entries in Table 3. It is not immediately obvious why CdBrI 2- should be favoured and not the others. The analogous mercury (II) species are all favoured above the statistical expectation (in aqueous solutions[l]), and if anything, the smaller cadmium ion should lead to ligand crowding in CdBrI~- and destabilization rather than the observed behaviour. REFERENCES
1. Y. Marcus and I. Eliezer, Coord. chem. Ret'. 4, 273 (1969). 2. N. Yellin and Y. Marcus, J. inorg, nucl. Chem. 36, 1323 (1974). 3. M. L. Delwaulle, Bull. Soc. Chim. 1=1".1294 (1955). 4. J. A. Rolt'e, D. E. Sheppard and L. A. Woodward, Trans. Faraday Soc. 50, 1275 (1954). 5. J. E. D. Davies and D. A. Long, J. chem. Soc. (A), 2054 (1968). 6. Ya. D. Fridman, S. D. Sarvaev and R. J. Sorochan, Zh. neorg. Khim. 5, 791 (1960). 7. A. Swinarski and A. Grodzicki, Roczn Chem. 41, 1205 (1967). 8. M. L. Delwaulle, C.r. hebd. Sdanc. Acad. Sci. Paris 208, 999 (1939). 9. R. Hester and R. A. Plane, lnorg. Chem. 3, 769 (1964). 10. K. Heizinger and R. E. Weston, J. chem. Phys. 42, 272 (1965). 11. H. H. Claassen, H. Selig and J. Shamir, Appl. Spectroscop. 23, 8 (1969). 12. D.E. Irish and H. Chen, Appl. Spectroscop. 25, 1 (1971). 13. D.E. Irish and H. Chen, J. phys. Chem. 74, 3796 (1970). 14. N. Yellin and Y. Marcus, Symposium on Coordination Chemistry. Debrecen, Hungary (Sept. 1970).
A RAMAN SPECTROPHOTOMETRIC STUDY OF THE STABILITY OF AQUEOUS COORDINATIVELY-SATURATED MIXED BROMO-IODO COMPLEXES OF CADMIUM N. YELLIN* and Y. MARCUS Department of Inorganic and Analytical Chemistry, The Hebrew University of Jerusalem, Israel (First receioed 19 June 1972; in revised form 21 June 1973) Abstract--The substitution equilibrium constants for the reactions CdI 3 _.Br 2~71+ I- ~ CdBr,I 2-n + Br-
(n = 0, 1, 2 and 3) have been measured in aqueous media at a constant ionic strength (1.634 M) and varying bromide to iodide ratios. Quantitative Raman spectrophotometry was used, with dilute (0-167 M) cadmium solutions and an internal standard (LiCIO4). It is shown that the intensity of the Raman scattering of a species is determined by the peak height (rather than area), which is proportional to the concentration. The values of the mixing constants, for the reactions (n/4)CdI~- + (1 - n/4)CdBr~- ~ CdI,Br2=,, corrected for statistical effects, give the stabilization constants 0.4 for CdBr3l 2 -, 0-7 for CdBr2122- and 1.6 for CdBrI~-. Only the latter is thus stabilized beyond the statistically expected level, but the reasons for this are obscure.
INTRODUCTION Tr~ RECENT advance in Raman spectrophotometry caused by the introduction of the high intensity laser light source, has permitted its application for the study of rather dilute solutions. This makes possible the full use of the advantages of this technique, which include the direct proportionality of the signal obtained for single complex species in a complicated equilibrium mixture to the concentration of this species. Under conditions where activity coefficients may be expected to remain constant, i.e. in a constant ionic medium, this permits then the unambiguous calculation of the stability constant of complex species, the existence of which is proven directly by the Raman spectrum. A case where this is of particular advantage is that of mixed complex formation, where most methods give only indirect evidence for the existence of the mixed species, and very complicated relationships between measurable quantities and the total concentrations of the reactants in the solution[l]. As a part of a study of the solvent effect on mixed complex formation in solution[2], it was found advantageous to demonstrate the practical validity of the above method with a system where both the species have already been well characterized by Raman spectrometry, and their stabilities have been determined by conventional methods. One of the few systems where this is possible is the cadmium(II}-bromideiodide system. The Raman spectrum of the tetrahedral complexes CdBr,I~-, (n = 0-4) in aqueous solution, * This work represents a part of the Ph.D. thesis submitted by N,Y. to the Hebrew University, May 1972.
is known[3-5]. Their stability constants have been determined by potentiometric[6] and polarographic[7] techniques. Previous to our work, however, very little quantitative work has been carried out by Raman spectrophotometry. Delwaulle[8] determined the stability constant of HgC1CN in 1949, but even at the present time almost all of the investigations by this technique dealing with mixed ligand complexes do not discuss the quantitative aspects. In this work, we determine the stability constants of the complexes CdBrnI~- . in aqueous solution by Raman spectrophotometry. We also demonstrated that these are coordinatively saturated complexes. EXPERIMENTAL
Analytical reagent quality (Analar) Cdl 2 , LiI and LiC104 were used. Some experiments in anhydrous solvents, for the examination of the Raman peak height-concentration relationship, required dry salts, and CdBr2.2H20 and LiBr. H2 O were dehydrated as follows: CdBr2.2H20 The salt was dehydrated at 25°C for 24 hr, then transferred into a vacuum system (P < 10 -z mmHg) for a further 24 hr at 100°C. The bromide concentration was determined by argentometric titration, and purity was found always to be greater than 99.5 per cent. LiBr2 • H20 The salt was dehydrated at 100°C for 24 hr and the temperature was then raised to 500°C for an additional 24 hr. The bromide concentration was determined by argentometric titration, and purity was found to be always greater than 99.0 per cent.
1331
1332
N. YELLINand Y. MARCUS
Analytical solvents were used, whenever available. The water content of the organic solvents was negligible. The solid salts were weighed in a nitrogen atmosphere because of the hygroscopic nature of LiBr, LiI and LiCIO4. The required amount of solvent was then added. The CIO~scattering band at 938 c m - ' was taken as a quantitative reference. LiC104 was found to be inert in the solutions under examination[9,10], i.e. its constituent ions did not react with the cadmium, iodide or bromide ions and its scattering bands were not in the spectral region of those of the complexes. Spectra were recorded on a Raman spectrophotometer [11] with a Spectraphysics Model 125 Helium-Neon Laser and a Spex 400 II double monochromator. The accuracy of the determination of the peak energy was +_1 cm- ~ at the 95 per cent confidence level. Occasionally, the same, sample was recorded several times, in order to check the reproducibility of the Raman system; the deviation was less than 1 per cent. Overlapping Raman bands were analysed by a nonlinear least-squares computer technique to obtain the best fit to a Gaussian function. Attempts to use a Lorentzian function failed. A Gaussian-Lorentzian gave similar results to a pure Gaussian function, but with greater error limits. As pointed out by IrishE12] and observed in our own work, discretion and a detailed chemical knowledge of the system must be applied in such an analysis, lest spurious results, such as nonexistent lines, are obtained.
/
o
/
h C104
/ / ///
/
X=l
X:Br /-
.1_.
/ ./
I/ /
0
i
h
5
10
Cx-/Cc .2 Fig. 1. [X-]/[Cd + z] ratio necessary for total coordination of the Cd +2 ion to CdX 2-, as shown by the normalized
h(vl). of the cadmium ions to form tetrahedral cadmate anions was observed for the ratio [Br-]/[Cd + 2 ] > 6 and for [I-]/[Cd +2] >_ 5. Excess ligand concentration did not produce any change of h(v0, that is it did not produce any new species in the solutions under examination. The maximum coordination number for CdBr 2-" or CdI~ - " complexes is therefore four (see Fig. 1). (c) The correlation between complex concentration and
RESULTS
the intensity of the v I scattering band
(a) Identification of the species in solution Raman spectra of aqueous solutions which contained cadmium ions with various ratios of bromide to iodide concentrations were recorded. The characteristic scattering bands of the complexes C d B r . I 2 : , were found to be in accordance with earlier results (see Table 1). Since the vl symmetric band has the highest intensity, it was used as a measure of the concentration of the complex. (b) Determination of the ratio [X-]/[Cd+2], (X = B r - ,
I-) required for saturation coordination The excess ligand concentration required for coordinatively saturated complexation of the cadmium ions to form CdX~- in aqueous solution was determined as follows. A series of samples was prepared with a constant cadmium concentration (0.167 M) and varying ligand concentrations ranging between 0-2 and 2~ M. A constant concentration of LiCIO 4 (0-470 M) was present in each sample. Saturation coordination
A series of samples containing varying amounts of tetrahalocadmate in the presence of a constant amount of lithium perchlorate were investigated in different solvents. The relationship h~
- -
= Jtv,}c
where htv,) is the peak height at the v1 energy, J is the molar scattering coefficient, and c is the complex concentration, was valid under the present experimental conditions (Figs. 2,3). It was then assumed that if the binary tetrahedral cadmates obey relation (I), then the ternary CdBr~I2-, (n = 1, 2, 3) species would also obey it. (d) Stability constants of CdBr, I ~ - , (n = 0-4) in water A series of solutions was prepared with constant concentrations of cadmium(II) (0.167 M), total ligand
Table 1. vI Scattering bands of the complexes CdBr, I2_n(n = 0-4) CdBr~ 166(62, 185)* 163 (53, 62, 181 ?) 163 (63, 187) 163 (62, 188)
CdBraI =
(1)
h938 era- '
CdBr2If
CdBrI~
141g 144
132
124
142
130
123
I~t
* v2, v3 , v4 are given in parentheses. t The scattering band is in the double-headed arrow range.
CdI2
Ref.
117(37,45, 145) 117 (36, 44, 144) 117 (47, 147) 117 (50, 145)
[4] [3] [5] [this work]
Stability constants of CdBr.I]:.
1333
/ / ~MeOH H
DMA
20
Et0H
4--*
E
C
b
>, O JD
<
z
/
V"
I
I
I
0.0
0.1
0.2
0.3
CCd i2 ,M
I
OO
0.1
012CCdBr4 .M0.3
Fig. 2. The dependence of the vt(Cdl]-) peak height on the complex concentration.
Fig. 3. The dependence of the vl(CdBr~-) peak height on the complex concentration.
(1.00 M) and lithium perchlorate (0.470 M) and various ratios of bromide to iodide, and their Raman spectra were recorded. As the vl scattering energies of the complexes examined are close to each other (see Table 1), the spectra were composed of several superimposed peaks, according to the number of complexes in solution. The computer results gave the vl energy, the peak height at this energy h, and the peak width at half height, for each individual peak. It was assumed that the intensity of all other scattering bands except v~was negligible, and that the spectrum is one of superimposed v~ peaks alone. This assumption is correct to a very good approximation, because the low intensity of the v2 - v6 peaks of the mixed complexes prevents their identification with the sensitivity attainable with present-day Raman instrumentation. The results obtained by the computer analysis were assumed to be reliable if the energy values agreed with previously known values of v~ energies, within their standard deviation (Table 1). The determination of the peak heights was reproducible within 0.5 per cent (maximal error) and the peak width within + 60 per cent (maximal error), as given by the computer. The peak height was taken as a measure of the complex concentration. The molar scattering coefficients of tetrabromo- and tetraiodocadmate were obtained from solutions which contained the binary complexes only, with the same amount of LiC104 and the same ionic strength as the whole series. The concentrations of the other species and their molar scattering coefficients were obtained
sequentially from the intensities of the resolved peaks. The concentrations of free bromide and iodide were obtained from the total concentrations CB~- and C~by difference. The equilibrium quotient K, (n = 0-3) for the substitution reactions CdBr4_,I,z- + I- m CdBr3_,I,Z.~l + Br-
(2)
is given by K.=
[CdBr 3_.12+1] [Br- ] [CdBr4_.I2_]Ei_ ] .
(3)
The ionic strength, I = 1,634, was constant, so it can be assumed that activity coefficient ratios do not change appreciably in the series of solutions. Thus, if a constant value for the quotient K. is obtained at several compositions, its value as an equilibrium constant is valid. The results are given in Table 2 and Fig. 4. The values of KI for experiments 9-13 were obtained by assuming an average value of 5.3 for Ko in these solutions. The values of K 2 scatter widely, because there are always three species present when the concentrations of CdBr2I~- and CdBrI]- are comparable. A weighted average of K2 ~ 5 is consistent with the data. It appears however from Fig~ 4, which shows the primary data from the resolved peaks, which are independent of the K. values, that CdBrI 2- is the most stable mixed complex in the present system. DISCUSSION
The present quantitative work is based on relation (1). Some workers[12] prefer to take the peak area as a
N. YELLINand Y. MARCUS
1334
affect the v~ symmetric vibration of the complex. 015
0.10
g
o
0.05 t,
_ 0.00 bOO
"/
_
\
0.25
0.50
0.75
C I-
1.00
Fig. 4. The dependence of the concentrations of the complexes CdBr, l,2_-,(n = 0-4) on the [I-]/[Br-] ratio.
measure of the concentration of the species, but the peak height is a satisfactory measure of the concentration of the species, as long as there is no line broadening with a change in concentration. Line broadening is caused by an interaction of the species with molecules of the solvent. Our results show clearly that a linear relationship exists between the height h of the v~ scattering band and the complex concentration (Figs. 2 and 3), in all solvents studied. It is concluded that there is no interaction with the solvent which would
Conversely, whenever relation (1) is not observed, there exists an interaction between the solvent and the solute as, for example, in the rapid exchange of a proton between the hydrogen sulphate anion and water molecules[13]. The deviation from linearity may serve as a quantitative criterion for this solute-solvent interaction, but this aspect requires further study. It should be noted that deviations from linearity exist even when the peak area is taken as a measure of the concentration of the species[12]. In that case, there is no doubt that the deviation indicates solute-solvent interaction. When dealing with computer analysis, a considerable physical knowledge of the system must be applied, since the mathematical results do not always express the chemical situation. In order to limit the possibilities of error, the energy value was taken as a varying parameter, even though it was known exactly. F r o m the energy values obtained by the computer, the reliability of the peak height results was determined. The best results are obtained in the case where there are only two peaks in the spectrum (the range of error for the calculated K values is within + 10 per cent), and the accuracy decreases as the number of peaks in the spectrum increases. G o o d accuracy can be achieved by increasing the number of data points fed to the computer, but in the present case this was impossible, because the work was manual.
Technical improvements in the last few years allow Raman spectrophotometric measurements of quite
Table 2. Substitution equilibrium constants (Eqn 3) for tetro(bromo-iodo) cadmate ions in aqueous solutions The concentrations in columns 2-8 are in M. No. 1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
C l-
CdBr~
1.00
--
0-958 0.950 0.916 0.900 0.875 0.833 0.792 0.750 0-708 0.700 0.650 0.625 0-600 0.583 0.500 0.400 0.292 0.250 0-208 0.200 0.167 0.150 0.125 0.100 --
0.042 0-050 0.084 0.100 0.125 0.167 0.208 0-250 0.292 0.300 0.350 0.375 0-400 0.417 0.500 0-600 0.708 0-750 0.792 0.800 0.833 0.850 0.875 0.900 1-00
0.167 0.138 0.132 0.111 0.103 0.093 0.083 0.071 0.062 0.052 0.050 0.039 0.036 0.031 0.030 0.020 0.009
CBr-
CdBr31= 0.029 0.035 0.056 0.061 0-061 0.033 0.012 ------
-----
CdBr21 ~
0.003 0.013 0.051 0.084 0.105 O.113 0.113 0.098 0.086 0.068 0.050 0.015 --
* From solution No. 7 onwards K o was assumed to be 5.3.
CdBrl~
Cdl~
Ko
K1
K2
K3
5.15 5.60 5.60 5.40 5.05 (1.8)
0.002 0.004 0.030 0.045 0.068 0.085 0.120 0.131 0.119 0.105 0.094 0.094 0.074 0-070
(17.1) 8.5 8.4 8.3
6.3 8-5 0.002 0.012 0-027 0.048 0.062 0.073 0.073 0.093 0.097
0.058
0.109
0.047
0.120 0.167
8.3
1.3 2.0 4.5 8.7 0.44 0.49 0.44 0.46 0.41 0.36 0-49 0.44 0.47 0.49
Stability constants of CdBr, I24-
1335
Table 3. Substitution constants of CdBr4_ ~I~-(n = 0-3) in water determined by different techniques Ko
K1
K2
5.3 + 0.5 8.0 7.1
8.5 6.0 7.1
5 2.9 0.3
Technique
[Cd +z]
[Brl + [I]
I
Rarnan Spect. Potentiometry[6] Polarography[7]
0.167M 0.089M 0.002M
1.00M 3.00M 2.00M
1.53M 6M 2M
K3
0-45 + 0-05 1.8 0.8
dilute solutions (to about 0.1M), but it is not sensitive enough for 10w concentrations. E.M.F. techniques, on the other hand, can be applied to very dilute solutions (about 10-4M), i.e. quite different experimental conditions. Nevertheless, there is agreement between the K n results obtained by these two methods (Table 3). Where there is disagreement, i.e. for the values of K2 and K3, there is a similar disagreement between potentiometric and polarographic results, which apply essentially to the same experimental conditions. Although the present determination of K : is not accurate, it is definitely concluded that K 2 > 1 (in agreement with the potentiometric value) and that K s < 1 (in agreement with the polarographic value). The dimensionless equilibrium constants calculated according to eq. (3) pertain to the substitution reaction
(2) CbBr4_nI 2- + I - ~ CbBr3_nI2~-I + Br-
(2)
where there is no difference in charges between the reactants and the products. This formulation is preferable to addition reactions for obtaining the data, e.g. Cd 2+ + h i - + (4 - n)Br- ~ CdlnBr2-,
(4)
CdI 2-n + (4 - n)Br- ~ CdlnBr2=,.
(5)
or
In these reactions, there is participation of solvent, which must leave the coordination sphere around the cadmium, where it completes to four the coordination number of a species such as CdI~ [14], as well as noncancelling activity coefficient terms. On the other hand, the substitution equilibrium constants Kn of Eqn (3) for equilibrium (2) may be used to calculate dimensionless mixing constants Ku(~} for the reactions -
4)CBr
#- CdI.Br~2~
(6)
shown in Table 4. These include a statistical contribution, the binomial factor (~), so that by dividing the KMO ) , KM(z~and KM~3)values by 4, 6 and 4 respectively, the stabilization constants K s shown in Table 4 are obtained. Of these, only Ks~3~, for CdBrI~-, is larger
J.I.N~C.,Vol. 36. No. 6--J
Table 4. Stabilization constants of CdBr4_nl~ -(n = 0-3) in water
KM Ks
CdBr3 I2-
CdBr21~-
CdBrI~-
1.62 0.4
4.2 0.7
6.5 1.6
than unity, denoting that this complex is more stable than predicted statistically, though only slightly. The others are less stable, but not by large factors. These findings are m agreement with previous reports[l], as required by the entries in Table 3. It is not immediately obvious why CdBrI 2- should be favoured and not the others. The analogous mercury (II) species are all favoured above the statistical expectation (in aqueous solutions[l]), and if anything, the smaller cadmium ion should lead to ligand crowding in CdBrI~- and destabilization rather than the observed behaviour. REFERENCES
1. Y. Marcus and I. Eliezer, Coord. chem. Ret'. 4, 273 (1969). 2. N. Yellin and Y. Marcus, J. inorg, nucl. Chem. 36, 1323 (1974). 3. M. L. Delwaulle, Bull. Soc. Chim. 1=1".1294 (1955). 4. J. A. Rolt'e, D. E. Sheppard and L. A. Woodward, Trans. Faraday Soc. 50, 1275 (1954). 5. J. E. D. Davies and D. A. Long, J. chem. Soc. (A), 2054 (1968). 6. Ya. D. Fridman, S. D. Sarvaev and R. J. Sorochan, Zh. neorg. Khim. 5, 791 (1960). 7. A. Swinarski and A. Grodzicki, Roczn Chem. 41, 1205 (1967). 8. M. L. Delwaulle, C.r. hebd. Sdanc. Acad. Sci. Paris 208, 999 (1939). 9. R. Hester and R. A. Plane, lnorg. Chem. 3, 769 (1964). 10. K. Heizinger and R. E. Weston, J. chem. Phys. 42, 272 (1965). 11. H. H. Claassen, H. Selig and J. Shamir, Appl. Spectroscop. 23, 8 (1969). 12. D.E. Irish and H. Chen, Appl. Spectroscop. 25, 1 (1971). 13. D.E. Irish and H. Chen, J. phys. Chem. 74, 3796 (1970). 14. N. Yellin and Y. Marcus, Symposium on Coordination Chemistry. Debrecen, Hungary (Sept. 1970).