J. Phys. Chem. 1987, 91, 4596-4599
4596
Ultrasonic Absorptlon Study of the Complex Formation of Cadmium( I I ) Monothiocyanate in Aqueous Solution Kiyoshi Tamura Department of Chemistry, National Defense Academy, Yokosuka 239, Japan (Received: February 6, 1987)
Ultrasonic absorption measurement of aqueous cadmium(I1) thiocyanate solutions reveals a single-relaxation phenomenon in the metal-rich concentration region. The characteristics of the absorption data indicate that the relaxation process involves the formation of the cadmium(I1) monothiocyanate complex. The concentration dependences of the relaxation frequency and amplitude are consistent with the Eigen-Tamm mechanism of stepwise association, M
+X& M(OH2)-X& MX kll k32
where M and X denote cadmium and thiocyanate ions, respectively; the charges of the ions are omitted. The formation of the outer-sphere complex M(OHz)-X is considered to be in rapid equilibrium and the formation of the inner-sphere complex MX the rate-determining step. The reaction parameters determined are KI2 (=kI2/k2,)= 1.05, kz3 = 4.8 X lo8 s-', k3* = 2.1 X lo7 s-l, AVI2 = -5.8 cm3/mol, and AV23 = 10.6 cm3/mol, at 25 "C and at ionic strength 3 M. The kinetic behavior is similar to those accepted widely with metal-complexation reactions, while it is very different from the case of zinc(I1) thiocyanate previously reported.
Introduction Relaxation kinetics' has enabled us to study rapid reactions involved in metal-ligand interactions. Complex formation reactions of labile metal ions with various ligands have been widely s t ~ d i e d , and ~ , ~ most of them can be interpreted well by the Eigen-Tamm mechanism,2 which consists of the rapid formation of an outer-sphere complex and the subsequent formation of an inner-sphere complex; the rate-determining step is the release of a solvent molecule from the inner coordination sphere of the metal. In a previous paper: we reported the ultrasonic absorption study of aqueous zinc(I1) thiocyanate solutions at ionic strength 3 M and showed that the absorption data over a wide concentration range could be explained by four successive coupled complexation reactions, each of which is represented virtually by a single-step mechanism in contrast to the Eigen and Tamm's. The result raises the question whether it is of general applicability under the conditions of high ionic strength used or not; the high ionic concentration might serve to reduce the relevant outer-sphere association constants to very small value^.^ Examination of this point may be important because ultrasonic absorption studies on metal-complexation reactions must often be carried out at high ionic concentrations to cover a wide concentration range and/or to obtain significant absorption. The absorption measurements under such conditions enable us to determine the reaction mechanism involved entirely from the concentration dependences of both the relaxation frequencies and amplitudes. For the above reasons, we adopted in the present work the cadmium(I1) thiocyanate system as analogous to zinc(I1) thiocyanate and carried out an ultrasonic absorption study under similar experimental conditions. Since few ultrasonic absorption studies on the formation reactions of cadmium(I1) complexes can be found in the l i t e r a t ~ r e , the ~ ? ~results may be of interest also from this point of view. Experimental Section All chemicals used were of reagent grade. Sample solutions were prepared by dissolving Cd(N03)2.4H20 and NaSCN in distilled water. The ionic strength, I , of the solutions was kept at 3.0 M by the addition of NaNO,. The pH of the solution was adjusted, when necessary, with HNO, and/or NaOH. (1) Eigen, M.; De Maeyer, L. Technique of Organic Chemistry, 2nd ed.; Friess, S . L., Lewis, E. S., Weissberger, A,, Eds.; Wiley-Interscience: New York, 1963; Vol. VIII, Part 11, Chapter 18. (2) Eigen, M.; Wilkins, R. G. Adu. Chem. Ser. 1964, 49, 5 5 . (3) Hewkin, D. J.; Prince, R. H. Coord. Chem. Reu. 1970, 5, 45. (4) Tamura, K. J. Chem. Phys. 1985, 83, 4539. (5) Spiro, T. G.; Revesz, A,; Lee, J. J . A m . Chem. Soc. 1968, 90, 4000.
0022-3654/87/2091-4596$01 .50/0
The ultrasonic absorption was measured in the frequency range 3-260 MHz by the pulse technique, and the velocity of sound at 3 MHz. The details of the measurements were described prev i o ~ s l y . ~The density of the solutions was determined by a Gay-Lussac pycnometer. All the measurements were carried out at 25.00 Et 0.05 "C. Results Table I shows the experimental conditions together with the density p and the velocity of sound c. Here, ZCd and ZSCN denote the stoichiometric concentrations of cadmium(I1) and thiocyanate ions, respectively. As shown in Table I, the experiments were carried out in the concentration range of ECd = 0.2-1.0 M and ZSCN = 0.2-0.6 M, and only in the metal-rich concentration region (1 I ZCd/ZSCN I4) because of the solubility limitation in the ligand-rich region (ZCd/ZS.CN < I). Representative sound absorption spectra are shown in Figures 1 and 2. All the absorption spectra can be expressed by the single-relaxation equation
_a -f 2
A 1+
+B
Cr/"o2
where a is the absorption coefficient and j t h e frequency of sound;
f, and A are the relaxation frequency and amplitude, respectively; B is the high-frequency value of a/f. The absorption parameters j r , A , and B were determined by fitting the data to eq 1. Here, a nonlinear least-squares routine, in which the rms percentage deviation between the computed and observed values of a/f is minimized, was employed. The absorption parameters obtained are listed in Table I. The results in Table I indicate the following features. (a) The relaxation absorption is independent of the pH; variation of pH from 2.6 to 4.6 proved to have no observable effect on the absorption. (b) When the concentration ECd increases under a definite concentration of ZSCN, the relaxation frequency increases and the relaxation amplitude decreases. (c) When the concentration ZSCN increases under a definite concentration of ZCd, the relaxation frequency decreases and the relaxation amplitude increases. That is, when the ratio ZCd/ZSCN decreases to approach unity, the relaxation frequency decreases and the relaxation amplitude increases in both the cases of (b) and (c). Treatment of Data Relaxation absorption was observed in all solutions containing cadmium and thiocyanate ions, while blank solutions of either Cd(N03)2or NaSCN showed no discernible relaxation effect in the same frequency range. This result implies that the relaxation 0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 17, 1987 4597
Complex Formation of Cadmium(I1) Monothiocyanate
TABLE I: Experimental Conditions and Ultrasonic Absorption Parameters4for Aqueous Cadmium(I1) Thiocyanate Solutions at 25 O C and I = 3.0 M
sample ZCd, M 0.200 0.400 0.400 0.400 0.400 0.600 0.600 0.800 0.800 0.800 1.oo 1.00
no. 1 2 3 4 5 6 7 8 9 10 11 12
ZSCN, M 0.200 0.200 0.400 0.400 0.400 0.300 0.400 0.200 0.400 0.600 0.400 0.600
PH 3.7 3.5 2.6 3.6 4.6 3.4 3.2 3.0 3.1 3.4 3.1 3.4
P, g
cm-' 1.1743 1.1828 1.1933 1.1931 1.1933 1.1956 1.2005 1.1955 1.2086 1.2220 1.2148 1.2292
c, m
s-'
fr,
1623 1588 1609 1607 1610 1587 1587 1560 1581 1587 1549 1562
MHz
A,
11.9 f 0.7 19.8 f 1.2 16.5 f 1.0 16.4 f 0.8 16.6 f 0.8 22.5 f 1.1 22.5 f 1.0 33.3 f 2.8 29.6 f 1.6 25.6 f 1.4 35.6 f 1.4 33.5 f 1.8
cm-I s2 127 f 7 87 f 4 191 f 10 194 -+ 8 192 f 7 111 f 4 148 f 5 52 f 2 109 f 4 186 f 7 92 f 2 146 f 5
B, 1O-I' cm-' s2 23.3 f 0.6 22.7 f 0.5 23.8 f 1.0 23.6 f 0.7 23.7 f 0.7 23.2 f 0.7 23.2 f 0.7 23.7 f 0.9 24.4 f 0.9 26.0 f 1.2 24.5 f 0.7 25.0 f 1.3
"The error interval denotes the 99.7% confidence area. 5
0
0
s
1
TABLE II: Reaction Parameters for the Formation of CdSCN' at 25 OC and Z = 3.0 Mu AV12= -5.8 f 0.3 cm3 mol-' Klz = 1.05 f 0.06 AV2, = 10.6 f 0.2 cm3 mol-' K23 = 23.4 f 1.3 kZ3= (4.8 f 0.2) X lo8 s-I k32 = (2.1 f 0.1) x io7 s-I 'The equilibrium constants used (ref 7): K, = 25.5, K2 = 6.86, K3 = 1.7, and K4 = 1.0, at 25 OC and I = 3 M.
'00
the following complex According to equilibrium formation equilibria exist in solution under the present experimental conditions
50
MXW1+ X
t
1 100
10
1
f , MHz
Figure 1. Ultrasonic absorption spectra of aqueous cadmium(I1) thiocyanate solutions; ZCd = 0.2-0.8 M and ZSCN = 0.2 M, at 25 OC and I = 3 M; The number in parentheses corresponds to the sample number in Table I. The solid curves are the calculated single-relaxation curves. The arrows indicate the relaxation frequencies.
MX,
K,,, n = 1-4
where M and X denote cadmium and thiocyanate ions, respectively; the charges of the ions are omitted for simplicity. The K,,k (n = 1-4) are the equilibrium constants for the successive complexation equilibria. The values of the K i s used in this study are those of Gerding obtained from the potentiometric studies' and are given in the footnote of Table 11. The results of the equilibrium analysis on the system of Table I, together with the already mentioned fact that the relaxation amplitude increases when the concentration ratio ZCd/ZSCN decreases to approach unity, indicates that the relaxation absorption under study can be ascribed mainly to the formation equlibrium of cadmium(I1) monothiocyanate complex. If we adopt the Eigen-Tamm mechanism of stepwise association: the complexation reaction may be described as follows
M
+X& M(OHz).X & MX kl, k32
I
X
1
1
100
10
(3)
where M(OH2).X and M X denote the outer-sphere and innersphere complexes, respectively. The first step, involving the ion association and dissociation processes, is very fast and can be cqnsidered to be in equilibrium at all times in the frequency range studied. Therefore, the second-step ligand substitution reaction is the rate-determining step of the complexation. The relaxation frequencyf, for the above scheme is given by
'-'
I
(2)
f , MHz
Figure 2. Ultrasonic absorption spectra of aqueous cadmium(I1) thiocyanate solutions; ZCd = 0.8 M and ZSCN = 0.2-0.6 M, at 25 OC and Z = 3 M. The notations and remarks are the same as in Figure 1.
absorption under study is due to cadmium(I1)-thiocyanate interactions. Contribution to the relaxation absorption from the hydrolysis reaction of Cd2+ or protonation reaction of SCN- can be ruled out by the pH independence of the absorption.
where the square brackets indicate molar concentrations a t equlibrium. The quantities K,,( = k 1 2 / k 2 ,and ) K,, ( = k z 3 / k 3 2 ) are the equilibrium constants of the first- and second-step reactions, respectively, of eq 3 and are related to the complex formation constant K 1 as K1 = KlZ(1
+ K23)
(5)
(6) Sillen, L. G., Martell, A. E., Eds. Stability Constants of Metal-Ion Complexes, 2nd ed.; Chemical Society: London, 1964; Supplement No. 1, 1971. (7) Gerding, P. Acra Chem. Scand. 1968, 22, 1283.
4598
The Journal of Physical Chemistry, Vol. 91, No. 17, 1987
t
Tamura
' I
I 10
-
5-
0-
05
I
I
I
1
06
07
08
09
1 1 + K,,(IMI
[XI)
Figure 3. Concentration dependence of f, for aqueous cadmium(I1) thiocyanate solution at 25 OC and I = 3 M.
Figure 4. (2RTfl#m/aI')'/2vs. (1 + Kl,([M] [XI)]-' plot for aqueous cadmium(I1) thiocyanate solution at 25 O C and I = 3 M.
If we known the value of the outer-sphere association constant K,,, we obtain K23 from eq 5 and then the quantity in braces on the right-hand side of eq 4 can be calculated. Therefore, the observedf, was fitted to eq 4 by using KI2as adjustable parameter. The result is shown in Figure 3. The straight line in the figure expresses the calculated& which agrees well with the observed one in the whole concentration range studied. The determined values of the equilibrium constants, KI2 and K23, and the rate constants, k23 and k32, are shown in Table 11. The maximum excess absorption per wavelength, kUm (=cAf,/2), for the reaction mechanism is given bys
or four coupled reactions. The above results are very different from the case of the zinc(I1) thiocyanate ~ y s t e mwhere ,~ all the absorption data in the metal-rich concentration region (1 I BZn/ZSCN I4) were explained by the three coupled successive complexation reactions ( n = 1-3 in eq 2 ) . Thus, the reaction mechanism represented by eq 3 proved to be the most appropriate one consistent with the absorption data.
where R is the gas constant, T the absolute temperature, and 6, the adiabatic compressibility of the solution; AV12and AV23 are the reaction volume changes of the first and second steps, respectively, of eq 3 . The I" term represents the following quantity:
From eq 6 , we obtain
As shown in Figure 4, a graph of (2RT@&,,,/?rr)'/*vs. (1 + K I 2 ( [ M ] [XI))-' gives a straight line. From the slope and intercept of this line, the volume changes AVI2 and AV23 were obtained and are shown in Table 11. Alternative mechanisms, which consist of the conventional single-step complexation reactions as expressed by eq 2, were also tested, unsuccessfully. The single-step complexation reaction, M X M X (Le., n = 1 in eq 2), cannot quantitatively explain the relaxation data in Table I; the simulation analysis showed that, even with the optimal values of rate constant and volume change, the rms percentage deviation between the observed and calculated values offi is 14 and that of 30, in contrast to the corresponding values of 4 and 6 for the reaction mechanism of eq 3 . The reaction mechanisms involving two, three, or four coupled successive single-step complexation reactions also gave unsatisfactory results. Here, the simulation analysis, in which the a/f values are calculated from trial values of rate constants and AVs and directly compared with the experimental v a l ~ e swas , ~ applied. The rms percentage deviation between the observed and calculated values of a/f was 6 for the two coupled reactions ( n = 1 and 2 in eq 2), and no further improvement was found even by using three
+
+
(8) Tamura, K.; Schelly, Z . A. J . Chem. Phys. 1985, 83, 4534.
+
Discussion The association constant of outer-sphere complexes is usually difficult to assess experimentally and has been estimated from the Fuoss e q ~ a t i o n . ~However, the application of this equation to the present system requires the knowledge of the pertinent activity coefficients at an ionic strength of 3 M. As is seen in eq 5 , the formation constant K1 is a composite constant consisting of the outer-sphere association constant Ki2 and inner-sphere formation constant K23. If we assume that the activity coefficient factors of K1 and K12are approximately equal, we may estimate the variation of K,, with ionic strength from the variation of K,. Adopting Gerding's experimental Kl's in the range I = 0.25-3 M? we may expect K12at I = 3 M to be 6% less than that at I = 0.25 M. Thus, evaluation of the latter from the Fuoss equation, by setting the minimum approach distance between the reaction partners at 5 A, gave K I 2= 1.4 at I = 3 M. The experimental value of Table I1 agrees reasonably well with this value. According to the Eigen-Tamm mechanism, the rate of formation of inner-sphere complex is controlled by the rate of release of a water molecule from the inner coordination sphere of the metal and thus is nearly independent of the nature of the entering ligand. The present result is consistent with the above concept; the rate constant k23 of Table I1 agrees in magnitude with the corresponding value obtained by Maasslo for the formation of cadmium(I1) monoacetate complex, Le., 2.5 X lo8 s-' (at 20 "C). The signs of the volume changes are not revealed by the absorption data alone since the square of the linear combination of volume changes is involved in the equation for pm, Le., eq 6. Therefore, the sign of the volume change AV23 was taken positive so as to be consistent with what would be expected on the basis of electrostriction effects of the metal ion. As shown in Table 11, the AVI2 value thus obtained is negative in contrast to the positive values found for transition-metal sulfates."-13 Unambiguous discussions about this point may be very difficult without taking into account the effects of ionic concentration on the partial molar volumes of ions. Therefore, only a tentative interpretation shall be given as follows. In view of the large partial molar (9) Fuoss, R. M. J . Am. Chem. SOC.1958, 80, 5059. (10) Maass, G. 2.Phys. Chem. (FrankfurtlMain) 1968.60, 138. (11) Jackopin, L. G.;Yeager, E. J . Phys. Chem. 1970, 7 4 , 3766. (12) Bonsen, A.;Knoche, W.; Berger, W.;Giese, K.; Petrucci, S. Ber. Bunsen-Ges. Phys. Chem. 19'78.82, 678. (13) Hemmes, P.J. Phys. Chem. 1972, 76, 895.
J . Phys. Chem. 1987,91, 4599-4602 volumeI4 and low ionic charge of the thiocyanate ion, water molecules around the ion, being subjected to weak electrostriction, form probably a bulky hydration structure through hydrogen bonding with the ion. Thus, when the outer-sphere complex forms, dehydration from the anion produces volume contraction. For the purpose of examining the present results as a whole, the total volume change, AVl, of complexation was evaluated from the relationI3 AV, = AV12 K23(l K23)-'AV23. The data in Table I1 yield AV, = 4.4 cm3 mol-', which seems reasonable compared with the value 4.0 cm3 mol-' obtained previously for the zinc(I1) monothiocyanate complex4 and also with the AVs found for the monoglycinate complexes of bivalent metals.I5 Thus, not only the concentration dependences of the relaxation parameters but also the obtained values of the reaction parameters are wholly consistent with the Eigen-Tamm mechanism. That is, the complex formation of cadmium( 11) monothiocyanate proceeds via the stepwise mechanism even a t the high ionic strength of 3 M, and the high ionic concentration does not reduce the outer-sphere association constant to very small values, against
+
+
(14) Millero, F. J. Chem. Reu. 1971, 71, 147. (15) Grant, M. W. J. Chem. SOC.,Faraday Trans. 1, 1973, 69, 560.
4599
Spiro's expectation.s The present study demonstrates that ultrasonic absorption measurements over a wide concentration range are very effective for determining the reaction mechanism involved and also that the high ionic strength needed for this experimental condition does not necessarily alter the reaction mechanism. The present investigation together with the previous one reveals different kinetic behavior from the chemically similar systems of zinc(I1) and cadmium(I1) thiocyanate. We have also noticed that ultrasonc absorption data obtained on aqueous cadmium(I1) halides16 are inconsistent with the reaction mechamism proposed for zinc(I1) halides." Elucidation of these points requires further studies.
Acknowledgment. I thank Dr. Shoji Harada of Hiroshima University and Professor Z. A. Schelly of the University of Texas at Arlington for reading the manuscript and offering helpful comments. Registry No. Cd, 7440-43-9; SCN-, 302-04-5; cadmium(I1) thiocyanate, 865-38-3. (16) Tamura, K.; Harada, S.; Yasunaga, T., unpublished results. (17) Tamura, K. J. Phys. Chem. 1977, 81, 820.
Effect of Solvent on the Rate Constant for the Radiative Deactivation of Singlet Molecular Oxygen ('Ago,) Rodger D. Scurlock and Peter R. Ogilby* Department of Chemistry, University of New Mexico, Albuquerque, New Mexico 871 31 (Received: February 9, 1987; I n Final Form: April 3, 1987)
-
Relative rate constants for the radiative deactivation (k,) of singlet molecular oxygen (3Z;02 lLigo2) have been determined in 15 solvents. A substantial solvent effect is observed. Changes in the value of k, can exceed a factor of 20. A reasonably good correlation exists between the solvent polarizability, defined as a function of the solvent refractive index, and the radiative rate constant. We suggest that our data support a model in which 'Ago2 is perturbed through the formation of a discrete oxygen-solvent collision complex.
Introduction In recent years, it has become evident that singlet molecular oxygen (IA,O2) is an ideal model system for the study of a sol'$0, vent-induced Since the transition 32;02 is fobidden as an electric dipole p r o ~ e s s ,the ~ , ~radiative lifetime in the absence of collisions (e.g., the upper atmosphere) of 'Ago2 is quite long ( 7 , = l/k, 1 h).5 However, in the presence of a perturbing environment, the 32-02 'Ago2 transition probability increases dramatically.'s2*b The total rate constant for IA,02 deactivation ( k A )in solution is determined by two components: a radiative (k,) and a nonradiative (knr)channel. In general, for any molecule, the rate constant for a radiative process will depend intrinsically on the refractive index of the ~olvent."~
-
-
~
______
(1) Wayne, R. P. In Singlet Oxygen; Frimer, A. A., Ed.; CRC: Boca Raton, FL, 1985; Vol. I, p 81 and references cited therein. (2) Monroe,8. M. Reference 1, p 177 and references cited therein. (3) Herzberg, G. Molecular Spectra and Molecular Structure. I. Spectra ofDiatomic Molecules; Van Nostrand Reinhold; New York, 1950; p 279. (4) Herzberg, L.;Herzberg, G. Astrophys. J. 1947, 105, 353-359. ( 5 ) Badger, R. M.; Wright, A. C.; Whitlock, R. F. J. Chem. Phys. 1965, 43, 4345-4350. (6) This is also observed, as a change in the absorption cross section, for (ref 7, 8). In order to observe an absorption the procws 'Ago2 3Z-02 signal, however, these exkriments were performed at elevated pressures. Due to the danger of combustion, the number of solvents accessible for study was restricted. (7) Long, C.; Kearns, D. R. J. Chem. Phys. 1973, 59, 5729-5736. (8) Cho, C. W.; Allin, E. J.; Welsh, H. L. Can J. Phys. 1963, 41, 1991-2002. (9) Andrews, J. R.; Hudson, B. S. J. Chem. Phys. 1978,68,4587-4594.
-
0022-3654/87/2091-4599$01.50/0
This relationship appears in the Einstein coefficients and in Planck's blackbody radiation law." However, even for a substantial change in the solvent refractive index, the magnitude of this effect on k, does not exceed a factor of about 1.5.9Jo Consequently, other models have been presented to account for large solvent effects on the radiative rate constant of a solute molec ~ l e . ~ For J ~ Jexample, ~ the formation of a discrete solute-solvent complex and, by definition, a new set of molecular eigenfunctions, may allow a process forbidden in the isolated solute to "steal intensity" from an allowed t r a n ~ i t i o n . ~ ~ ' ~For - ' * the particular example of molecular oxygen, the perturbation offered by the solvent could, therefore, make the transition 3z;02 '4,02more probable. This, in turn, would be manifested as an increase in the value of k,. In solution, the nonradiative channel dominates deactivation process ( k A= k, + k,,, with k,, >> the total 'Ago2 k,). This results in an extremely small quantum efficiency for '$0, phosphorescence ($ 10-3).19 Under these circumstances,
-
=
(10) Giniger, R.; Amirav, A. Chem. Phys. Lett. 1986, 127, 387-391. (1 1) Birks, J. B. Photophysics of Aromatic Molecules; Wiley-Interscience: London, 1970; pp 87-88. (12) Birks, J. B. Z . Phys. Chem. 1976, 101, 91-104. (13) Olmsted, J. Chem. Phys. Left. 1976, 38, 287-292. (14) Robinson, G. W. J. Chem. Phys. 1967, 46, 572-585. (15) Hoytink, G. J. Arc. Chem. Res. 1969, 2, 114-120. (16) Dijkgraaf, L.; Sitters, R.; Hoytink, G. J. Mol. Phys. 1962, 5, 643-644. (17) Rettschnick, R. P. H.; Hoytink, G. J. Chem. Phys. Lett. 1967, I , 145-148. (18) Ogilby, P. R.; Foote, C. S. J. Am. Chem. SOC.1983, 105, 3423-3430.
0 1987 American Chemical Society
