J. Phys. Chem. 1081, 85,3145-3150
expected from the concentration of amine in the droplet. We do not know how an amine arranges itself in a microemulsion droplet, but alcohol cosurfactants move readily from water to microemulsion dropletsBor micellesm (29) Bellocq, A. M.; Biais, J.; Clin, B.; Lalanne, P.; Lemanceau, B. J . Colloid Interface Sci. 1979, 70, 524. (30) Gettins, J.; Hall, D.; Jobling, P. L.; Rassing, J. E.; Wyn-Jones, E. J. Chem. SOC.,Faraday Trans. 1 1978, 74, 1957; Yiv, S.; Zana, R.; U1bricht, W.; Hoffmann, H. J. Colloid Interface Sci. 1981, 80, 224.
3145
and do not enter a rigid structure in the microemulsion. Therefore, by analogy we would expect amines to have considerablemobility in a microemulsion droplet, although they might not have as much conformational freedom as in an aqueous solvent. Acknowledgment. Support of this work by the National Science Foundation Program) is gratefully acknowledged.
Ultrasonic Studies of the Complexation Kinetics of Cadmium Nitrate in Nonaqueous Solvents Shlnklchl Yamada’ and Ronald E. Verrall’ Depaflment of Chemistry and Chemical Engineering, University of Saskatchewan, Saskatoon, Canada S7N OW0 (Received: January 20, 198 1; In Fins1 Form: June 22, 198 1)
Ultrasonic absorption data obtained over the frequency range 5-95 MHz by the pulse method are reported for cadmium nitrate in methanol, dimethylformamide,and dimethyl sulfoxide in the temperature range 15-45 “C and the concentration range 0.02-0.25 mol dm-3. Ultrasonic relaxation spectra show a single relaxation. The kinetic data have been interpreted in terms of the Eigen mechanism. The rate constants for solvent exchange in the first coordination sphere of Cd2+were estimated at 25 “Cto be 1.1 X lo8 s-l in methanol, 6.5 X lo7 s-l in dimethylformamide,and 5.3 X lo’ s-l in dimethyl sulfoxide. Large negative values of the activation entropy suggest that an associative interchange mechanism I, is operative in this process.
Introduction Simple complexation reactions involving divalent cations of the first-row transition metals with unidentate ligands in aqueous solution have been generally represented by an Id mechanism: that is, an interchange process characterized by a dissociative activation mode. According to Eigen, Wilkins, and others,+? the rate and activation parameters for this process are only slightly dependent on the nature of the ligand and are very similar to those of solvent exchange reactions. Recently, kinetic studies of complexation reactions have been extended to nonaqueous systems to examine the applicability of this mechanism in other solvents besides water. At this time, available data show that the reactions involving many unidentate ligands show behavior similar to that of the corresponding aqueous systems. However, the same is not true of multidentate ligands, and discrepancies in rate constants and activation parameters between ligand substitution and solvent exchange have been discusseds in terms of steric requirements of the ligand in the ring-closure step, extra stabi-
lization of the outersphere complex, and solvent structure. The extensive complexation studies in nonaqueous solventa have been done mainly on the first-row transition-metal ions such as Mn2+,Fe2+,Co2+,and Ni2+,9and only limited data are available for the other labile metal ions. Despite the unique property of d’O configuration, there has been little work done on the complexation reaction of cadmium ion as compared to the partially filled d-orbital metal ions. The present study was carried out to obtain mechanistic information on the complexation reaction of cadmium ion in nonaqueous solvents. In this paper we report the kinetic results for the reaction between cadmium and nitrate ions in methanol, dimethylformamide, and dimethyl sulfoxide using ultrasonic techniques and discuss the details of the suggested mechanism. Experimental Section Reagents. Cadmium Nitrate. Reagent-grade cadmium nitrate tetrahydrate was dried over P205under vacuum. The water content in the crystal was determined by Karl Fischer titration to be less than 0.015 mol/mol of Cd(N0312.
(1) On leave from the Department of Chemistry, Faculty of Science, Nagoya University, Chikusa, Nagoya 464, Japan. (2) C. H. Langford and H. B. Gray, “Ligand Substitution Processes”, W. A. Benjamin, New York, 1965. (3) M. Eigen, 2. Elektrochem., 64, 115 (1960); Pure Appl. Chem., 6 , 97 (1963). (4) R. G. Wilkins and M. Eigen, Adu. Chem. Ser., No.49, 55 (1965). (6) R. G. Wilkins, Acc. Chem. Res., 3, 408 (1970). (6) F. Basolo and R. G. Pearson, “Mechanisms of Inorganic Reactions”, Wiley, New York, 1967. (7) C. H. Langford, “Ionic Interactions”, Vol. 2, S. Petrucci, Ed., Academic Press, New York, 1971, Chapter 6. (8) J. F. Coetzee, “SoluteSolvent Interactions”, Vol. 2, J. F. Coetzee and C. D. Ritchie, Eds., Marcel Dekker, New York, 1976, Chapter 14. 0022-3654/81/2085-3145$01.25/0
Solvents. Reagent-grade methanol (MeOH), dimethylformamide (DMF), and dimethyl sulfoxide (MefiO) were dried over calcium hydride and twice distilled at atmospheric (MeOH) and under reduced (DMF and Me2SO) pressure. The water contents in these solvents were determined by Karl Fischer titration to be less than (MeOH), 3 X lo9 (DMF), and 4 X lo4 (Me2SO) 5X mol dm-3. None of these solvents showed any ultrasonic (9) Rate constants and activation parameters for the complexation reaction in nonaqueous solvents are compiled by J. F. Coetzee (ref 8).
0 1981 American Chemical Society
The Journal of Physical Chetnlstty, Vol. 85,No. 21, 1981
3148 ""1
I.
Yamada and Verrall I
10
20
50
I
100
f (MHz)
relaxation in the frequency range studied. Effect of Water. I t was shown that, at a total concentration of cadmium nitrate equal to 0.15 mol dm", up to 0.1 mol dm" of water had no effect on the ultrasonic absorption spectrum within the experimental error of our measurements. Sound-Absorption Measurements. The apparatus used has been previously described.'*12 The pulse method was used, employing a Matec 6000 radio frequency pulse generator and receiver to drive x-cut quartz crystals on their odd overtones in the frequency range 5-95 MHz. Three absorption cells were used: a single-crystal-reflectortype with crystals of fundamental frequencies 1and 4 MHz for the frequency range 5-25 MHz and 12-36 MHz, respectively, and the send-receive type with two crystals of fundamental frequency 5 MHz (frequency matched within 0.5%) for the frequency range 15-95 MHz. Good agreement between a / f ; values was obtained for the reflection and the send-receive types of cells. Solutions were thermostated at a desired temperature to within f0.03 OC. The absorption coefficient, CY, was measured by varying the sound path length and observing the resulting attenuation in the intensity of the ultrasonic wave by monitoring the first sound echo. Correction for diffraction loss was made at lower frequencies.
= A / ( 1 + (f/fA2)
+B
Flgure 2. Curves of a / f vs. frequency for Cd(NO& In dlmethylformamide at 45 "C: CWwh = 0.06995 (A), 0.05195 (B), 0.03169 (C), and 0.01505 (D) mol dm-3. The arrows show the position of the relaxation frequencies.
TABLE I: Ultrasonic Parameters in Nonaqueous Solutions of Cd(NO,),
101'A, 101 7 4 Np sz Nps' tepp, concn, C r n ~ l d m - ~cm-' cm-' 35
25
15
45
35
25
45
(1)
where f,, A , and B refer to the relaxation frequency, the relaxation amplitude, and the background absorption, respectively. The parameters A , B, and f, were determined by means of a least-squares programl1J2 using a Hewlett-Packard computer. The results of the best fit of the experimental data to eq 1 and the average deviations are summarized in Table I. The solid lines in Figures 1-3 are calculated with the parameters listed in Table I. As seen from Table I, the relaxation frequencies are concentration dependent. This suggests that the complex-formation reaction could likely be the source of the
35
25
devia10-6fr, tion A: s-l
%
0.05447 0.1058 0.1491 0.1911 0.05281 0.05 57 5 0.07552 0.1078 0.1085 0.1612 0.201 7 0.05694 0.1041 0.1374 0.2112
MeOH 203 40.3 332 43.0 404 41.3 472 44.4 223 45.6 241 38.3 ,310 40.7 400 40.4 381 39.3 498 36.4 611 43.3 285 39.9 444 42.6 521 39.4 678 39.0
22.73 25.31 28.33 29.42 15.93 17.29 17.41 18.85 20.12 22.69 22.07 12.60 14.09 15.75 18.10
3.82 2.50 2.94 2.55 2.35 2.54 3.27 3.61 3.13 2.66 3.64 3.80 3.53 3.58 3.93
0.01505 0.031 69 0.05195 0.06995 0.01922 0.03387 0.05080 0.07054 0.03118 0.04925 0.07218 0.08852
DMF 382 31.9 518 38.9 621 37.1 693 36.1 503 32.0 637 33.9 733 33.7 834 34.4 851 35.7 1006 32.6 1208 34.1 1300 34.4
7.67 9.63 11.38 12.40 6.70 8.04 9.27 10.04 5.24 6.33 6.89 7.36
2.08 4.06 2.79 2.20 2.63 2.45 2.90 2.72 1.21 2.55 2.91 2.27
0.1035 0.1587 0.2138 0.2588 0.09036 0.09768 0.1536 0.2036 0.2496 0.1083 0.1606 0.21 28 0.2442
Me,SO 193 41.3 314 44.2 429 42.6 536 44.8 143 44.2 149 38.5 246 47.1 372 46.3 439 47.5 171 45.7 236 47.7 409 47.5 458 48.5
6.75 8.19 9.88 10.52 4.88 5.81 6.62 7.53 8.80 4.00 5.55 5.70 6.35
3.22 1.92 2.75 3.04 1.39 2.02 1.49 2.32 1.55 0.86 1.15 1.06 1.88
a Calculated by using the equation A = (1/N)ziplN{[(df2)calcd-( a ! l f 2 ) e x p ~ l / ( ~ l f 2 ) c a lxc d100, ) where
N (10)R. E. Verrall and H. Nomura, J. Solution Chem., 6, 1 (1977). (11) R. E.Verrall and H. Nomura, J. Solution Chem., 6, 217 (1977). (12) R. E.Verrall and H. Nomura, J. Solution Chem., 6,541 (1977).
100
f(MHz)
Analysis and Results The absorption coefficient, CY, in units of sound intensity absorbed per unit length, was measured as a function of frequency, f , at various concentrations of Cd(N0J2 and at 15,25,35, and 45 "C.Typical results obtained (Figures 1-3) show the characteristic behavior due to a single relaxation process, which may be described by eq 1 a/f;
I
50
20
10
Flgure 1. Curves of a / f 2vs. frequency for Cd(NO,), in methanol at = 0.1911 (A), 0.1491 (B), 0.1058 (C), and 0.05447 35 "C: C (D) mol dm?the arrows show the position of the relaxatlon frequencies.
IS the
number of data.
relaxation phenomenon. According to Eigen,13one may write
The Journal of Physical Chemistry, Vol. 85, No. 2 I, 198 1 3147
Complexation Kinetics of Cadmium Nitrate
where ay
= YCdz+YN03-/YCdNOs+
If u is the degree of dissociation, neglecting the formation of Cd(N03)2,14one can write the following expression for
5
10
20
3U
1UU
f(MHz)
Figure 3. Curves of a/f2 vs. frequency for Cd(N03)2 in dimethyl = 0.2588 (A), 0.2138 (B), 0.1587 (C), and sulfoxide at 45 O C : Cw* 0.1035 (D) mol d ~ n - ~The . arrows show the position of the relaxation frequencies.
8:
where C is the total concentration of Cd(NO& The approximate values of 7%. and yl:l have been calculated by the Debye-Huckel equation1’ -log ya = S W 2 / ( 1 + AAY1I2) (5) where r is the total concentration of ionic species and is defined by the relation r = 2c(2U + 1) (6) The constants A and S involve the absolute temperature T and the dielectric constant D of the solvents and are defined as follows:
A = (35.56
X
108)(DT)-1/2
S = IZ+Z-J(DT)-3/2 X 1.290 X lo6
8= Y1:l
As generally formulated, the complex-formationreaction in solution involves diffusion-controlledequilibrium of an outersphere complex [Mmt,Ln-]with a solvated metal ion Mm+and ligand Ln- followed by the entrance of Ln- into the innersphere of Mm+and the rupture of an innersphere coordinated solvent molecule (concertedprocess). For this reaction the interchange mechanism2is generally accepted as being operative (solvent molecules present in the innersphere of Mm+are omitted for simplicity) and can be expressed by eq 9. In the case of the intermediate Mm+ + Ln-
Values of D required in the calculations were obtained from ref 16 and 17. The quantity B is the minimum distance of closest approach between the solvated free ions and was estimated to be 7 A in MeOH and DMF and 6.5 A in Me2S0. These figures are obtained from previously reported work1&21as the sum of the hydrodynamic radii of the cation and the anion taking into account solvent viscosity dependence of the anion and the crystal radius increment of the cation. The desired differential quantity d In (yat!Y1:12)/d In u in eq 4 was obtained by appropriate differentiation of eq 5 and 6. 0 can then be expressed as (2u + 1)C + 9.212C2u(u
Finally, the overall formation constant for equilibrium 2 is given by eq 8. 2 Y1:l K = CCdNOa’ YCdNOa’ - 1-u (8) C d l + a) Y213 CCd2+CN08- YCd2+YNOa-
2Sl,1- 3Skl + 1)r1l2(1 + AAI’1/2)2
(7) (13) M. Eigen and L. DeMaeyer, “Investigation of Rate and Mechanism of Reaction”,Vol. 8, Part 11, A. Weissberger, Ed., Wiley, New York, 1963. (14) This assumption seems to be reasonable judging from the lower formation constant for the innersphere complexation process (see Table 11). (15) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions”, 3rd ed., Reinhold, New York, 1964. (16) J. A. Riddick and W. B. Bunger, “Organic Solvents”, Wiley-Interscience, New York, 1970. (17) E. M. Washburn, Ed., “InternationalCritical Tables”, McGrawHill, New York, 1930. (18) A. Diamond, A. Fanelli, and S. Petrucci, Inorg. Chem., 12, 611 (1973). (19) M. Vincenzini, B. Sesta, M. Battistini, and S. Petrucci, J. Phys. Chem., 80,2700 (1976). (20) J. E.Prue and P. J. Shervington, Trans. Faraday Soc., 67,1795 (1961). (21) J. Williams, S.Petrucci, B. Sesta, and M. Battistini,Inorg. Chern., 13, 1968 (1974).
& [Mm+,Ln-] & MLm-n kz1
kaz
(9)
[Mm+,Ln-] being present in small concentrations compared with Mm+,Ln-, and ML””, one can derive from eq 9 the following rate law: d[MLm-”]/dt = {k1&23[Mm+l[Ln-l - k21 + k,3[MLm-”1j/(k21 + k23) (10) The mechanism and the rate law of complexation reactions involving many inorganic unidentate ligands have been adequately described by eq 9 and 10, in both aqueous and nonaqueous solvents.* We therefore advance the hypothesis that the observed relaxation in the present study is associated with the coordination of the ligand NO3- into the innersphere of the solvated cadmium ion, this process being loosely coupled to an outersphere diffusion-controlled process which is certainly too small in amplitude to be observed.22 Then ka k,, and the overall formation constant for the process (eq 2) can be shown to be given by the following expressions: kf = k12k23/(Iz21 + k23) (11) k, = k21k32/(k21 + k23) (12) K = ( k 1 2 / W ( l + k23/k32) (13) For a given K , one can calculate the values of u and 6 by (22) It should be noted that the values of B in Table I are definitely 32 X lO-l’, and 39 X higher than those for the pure solvents (30 X Np sa cm-’ for MeOH, DMF, and MezSO, rspectively, at 25 “C). Furthermore, at high frequencies (f > 65 MHz), solutions of Cd(N03)~ in MezSO show a slight decrease in a/f values with increasing frequency. Unfortunately,we have not been able to give a quantitative interpretation of this phenomenon to this time.
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The Journal of Physical Chemistry, Vol. 85, No. 21, 1981
Yamada and Verrall
TABLE 11: Rate and Formation Constants for the Reaction of Cadmium with Nitrate
35 25 15
13.5.t 1.3 10.2 .t 1.5 7.88 f 0.54
45 35 25 45 35 25
90.1 60.7 39.8
7.3 9.3 3.9
7.17 5.88 4.80
5.47 5.12 4.66
9.98 f 0.32 6.90. 0.49 3.87 f 0.45
17.2 f 1.6 16.2f 2.7 13.7 f 3.2
4.83 3.97 3.33
5.11 5.05 4.91
1.92 i 0.14 1.68 f 0.20 1.33 .t 0.30
7.3 f 3.5 5.0 c 4.5 3.2r 7.1
1.98 1.54 1.26
f f f
1.27 f 0.15 1.07 f 0.20 0.915 f 0.077
11.1f 1.2 7.3 f 1.4 4.76 * 0.54
2.45 f 0.05 2.45 ?: 0.11 2.48 t 0.05
DMF
Me,SO 7.97 5.87 4.50
.
1.332 f 0.055 1.061 f 0.091 0.647 f 0.087
2.17 1.96 1.55
f f
0.22 0.36 0.39
2.83 2.70 2.54
0.853 * 0.067 0.715 f 0.096 0.53 f 0.14
0.80 0.56 0.36
f f f
0.39 0.52 0.82
2.46 f 0.30 2.6 i 1.1 2.6 r 1.2
f
f f
0.05 0.11 0.15
25'C
1 0.5
10
8 x 102(mol d ~ n - ~ ) Figure 4. Relationship between Prf,and ionic concentration 8 for Cd(NO& In methanol.
0.5
1I)
8 x IO2 (mol dm-3) Figure 5. Relationship between 2?rfr and Ionic concentration 8 for Cd(N03)* in dimethylformamide.
eq 8 and 7, respectively, for given concentrations of the electrolyte, and a plot of 27rfrvs. 6 (calculated)should yield a straight line with a slope of kf and an intercept of k,. From the overall rate constants thus obtained, one can estimate ka and k32 by eq 11 and 12, assuming that kI2and kZ1are expressed by23 k12 = [8NkT/(30007)](-b/[exp(-b) - 11) (14)
kzl = [2kT/(7rA37)l(-b/[l - exp(b)lI (15) where b = 2e2/(WkT),k is the Boltzmann constant, N is the Avogadro number, 7 is the solvent viscosity, and e is the electronic charge. The values of 7 required in the calculations were obtained from ref 16 and 17. On the other hand, the calculated overall formation constant derived from the experimental data using eq 11-13 should be the same as that postulated. Consequently, one can find a reasonable set of constants by iterative procedures such that they interpret the results in a self-consistent manner. Plots of 2rf, vs. I3 are shown in Figures 4-6. Slopes (kJ,intercepts (k,),calculated rate constants, and overall formation constants with standard deviations based on a least-squares analysis are summarized in Table 11. Finally, using the Eyring equation k23 = W/h)[exp(-mZ3*/RT) exp(AS23*/R)I the activation parameters for ka were evaluated as follows: for AH%*(kJ mole1),9.6 f 0.2 (MeOH), 22.6 f 5.3 (DMF), (23) S. Petrucci, J. Phys. Chem., 71, 1174 (1967).
e x 102(rnol d n ~ ' ~ ) Figure 6. Relatlonshlp between 2 r f r and ionic concentration 0 for Cd(N03)2In dlmethyl sulfoxlde.
and 14.2 f 2.5 (Me2SO);for ASz3* (J mol-l K-l) -60 f 1 (MeOH), -19 f 17 (DMF), and -49 f 8 (Me,SO). In order to examine the effect of the value of A on the kinetic results, the calculation of I3 was carried out with A = 6 and 8 A for MeOH and DMF, and 7.5 and 8.5 8, for Me2S0. The plot of 2rfr vs. I3 showed that the slopes increase with decreasing magnitude of A. However, the rate constants kzs and kS2and the formation constant K remain almost the same within the experimental error for a given temperature, as compared to the results shown in Table 11. It appears that the rate of the innersphere complexation step is not too sensitive to a change in the value of
A.
Complexation Kinetics of Cadmium Nitrate
Discussion It is now generally accepted that complex formation in aqueous solution occurs by a two-step mechanism M(HzO)6m++ L"-
The Journal of Physical Chemistry, Vol. 85, No. 27, 1981 3140
TABLE 111: Kinetic Parameters for Solvent Exchange at Divalent Metal Ions AH*, AS*, k -s at kJ Jmol-l solvent Mz+ 25'C. s-' mol'' K-I ref methanol
Cd Mn Fe Co Ni Cd Mn Fe
1.1 X 3.7X 5.0 X 1.8X 1.0 x 6.5X 2.4 x 1.7 x 3.9 x 3 . 8 5.3 X 6.3 x 1.0 x 3.1 X 3.2 x
10'
lo5 lo4 lo4
9.6 25.9 50.2 67.7 66.0 22.6 37.2 48.9 56.8 62.7 14.2 31.0 47.2 51.0 54.3
-60 -50 13 30 33 -19 3 38 53 33 -49 -10 29 41 6
a b b
in which the diffusion-controlled formation of the outerc sphere complex [M(HzO)6m+,L"-]between the aquated 10' c metal ion M(H20)p+and the unidentate ligand L"- preDMF 10' a 10' d cedes the loss of a coordinated water molecule as the lo6 e rate-determining step and the overall formation rate conco 105 f stant is given by K,kM-H20 where K, is the formation Ni ~l o 3 f constant of the outersphere complex. However, there has Me,SO Cd l o 7 a been R report of complexation between highly charged Mn 10' g cations and anions where a three-step mechanism involving Fe 10' e Co lo5 h an outer-outersphere complex has been proposed.24 Ni lo3 h Studies of complexation reactions involving multidentate ligands have shown that some features of the chemical F. W. Breivogel, Jr., J. Chem. Phys., 51, a This work. system alter the rate-determining step. For example, Z. Luz and S. Meiboom, J. Chem. Phys., 445 (1969). T.-M. Chen and L. 0.Morgan, J. 40, 2686 (1964). anomalously low values of rate constants for Hnta% (H3nta Phys. Chem., 7 6 , 1 9 7 3 (1972). e S. Funahashi and R. B. = nitrilotriacetic acid)%and H2egta2ethylene Jordan, Znorg. Chem., 1 6 , 1 3 0 1 (1977). f N. A. glycol bis(2-aminoethyl ether)tetraacetc acid) with Cd2+ Matwiyoff, Znorg. Chem., 6, 788 (1966). g J. Boubel and are interpreted to be due to the rate-determining proton J. Delpesech, Adv. Mol. Relaxation Processes, 7, 209 transfer occurring before chelate ring closure. As well, L. S. Frankel, Inorg. Chem., 10, 814 (1971). (1975). chelatn ring size sometimes may affect the kinetic behavior in certain complexation reaction^.^^*^ However, this mining step.41 The aquacadmium ion is known to be two-step mechanism seems to be applicable to almost all six-coordinated.42 On the other hand, for anionocadmium complexation reactions involving the multidentate ligands complex formation, equilibrium and enthalpy measurewhich have no extra stabilization of an outersphere complex% and no steric hindrance due to their b u l k i n e ~ s . ~ ~ments ~ ~ ~ indicate that the coordination changes from an octahedral to a tetrahedral structure at the third step of Numerous kinetic studies of cadmium have been done the successive reaction for halides43 and selenocyanate in aqueous solution primarily with multidentate ligands systems.44 The same situation has also been observed for such as ethylenediaminetetraacetic acid,=* nitrilotriacetic acetate and azide systems.& Thus, the reported values a ~ i d , ~pyridine-2-a~o-p-dimethylaniline,~~ ~ J ~ 1,lOlo8" (ref 39) and 108*6(ref 4) s-l at 20 "C for the comof phenanthroline,37terpyridyl,37murexide,- ethylene glycol plexation of Cd2+ with acetate and chloride, respectively, bis(2-aminoethyl ether)tetraacetic 1,3-propyleneobtained by ultrasonic techniques appear to be a measure diaminetetraacetic acidto and ethylenediaminediaceticof the water exchange rate at cadmium ion as judged by dipropionic acid.40 The overall rate constants (K,kM-H@) . this one the similarity in magnitude with k ~ d - ~ z OFrom reported range from 2 X lo6to 4 X lo9 mol-' dms 8' at 25 may conclude that the complexation process involving "C with appropriate estimates of K, yielding rate conaquated cadmium ion is "normal" and the rate-determinstants for the inner-coordinated water exchange at Cd2+ ing water exchange rate is around 108.5s-' a t 25 "C. (ka-Hd') to be around 10ass-l at 25 "C for the normal mode However, only limited information is available on the of thermodynamics and kinetics of the complexation reaction There is some evidence that complexation reactions in nonaqueous solution as compared to aqueous systems. which involve a change in coordination number and geIn one case, X-ray diffraction measurements of cadmium ometry about the metal ion may exhibit anomalous kinetic perchlorate in Me2S0 were interpreted as showing the behavior if the configurational change is the rate-deterformation of a regular octahedral hexasolvate with MezSO coordinated via the oxygen atom.47 The structural change (24) A. Bonsen, W. Knoche, W. Berger, K. Giese, and S. Petrucci, Ber. from an octahedral coordination in the solvated ion to a Bumenges. Phys. Chem., 82,678 (1978). tetrahedral coordination in an anionocomplex might also (25) D.L. Rabenstein and R. J. Kula, J. Am. Chem. Soc., 91, 2492 (1969). be anticipated to occur in nonaqueous solution at some (26) G. H. Reed and R. J. Kula, Znorg. Chem., 10,2050 (1971). particular step in the reaction. In fact, by means of po(27) K. Kustin, R.F. Pasternack, and E. M. Weinstock, J. Am. Chem. tentiometric and calorimetric titration methods, Ahrland Soc., 88, 4610 (1966). (28) A. Kowalak, K. Kustin, R. F. Pasternack, and S. Petrucci, J. Am. and Bjork have reported that, for cadmium halide systems, Chem. SOC.,89, 3126 (1967). the change of structure takes place at an earlier stage (the (29) R. W. Taylor, H. K. Stepien, and D. B. Rorabacher, Inorg. Chern., second step) in M e a 0 than in water,48because of the fact 13, 1282 (1974). (30) T. S. Turan, Inorg. Chem., 13, 1584 (1974). (31) C. T. Lin, D. B. Rorabacher, G. R.Cayley, and D. W. Margerum, Znorg. Chem., 14, 919 (1975). (32) N. Tanaka,.R. Tamamushi, and M. Kodama, 2. Phys. Chem. (Frankfurtam Main), 14, 141 (1958). (33) G.H. Aylward and J. W. Hayes, Anal. Chem., 37, 195 (1965). (34) J. L. Sudmeier and C. N. Reilly, Inorg. Chem., 5, 1047 (1966). (35) J. Koryta, 2.Elektrochem.,64, 196 (1960). (36) R. G.Wilkins, Znorg. Chem., 3, 520 (1964). (37) R. H. Holyer, C. D. Hubbard, S. F. A. Kettle, and R. G. Wilkins, Inorg. Chem., 5, 622 (1966). (38) G.Geier, Helv. Chim. Acta, 51, 94 (1968). (39) G. Maass, 2.Phys. Chem. (Frankfurtam Main), 60,138 (1968). (40) B. J. Fuhr and D. L. Rabenstein, h o g . Chem., 12,1868 (1973).
~
~~~
(41) K. Tamura, J. Phys. Chem., 81, 820 (1977). (42) H. Ohtaki, M. Maeda, and S.Ito,Bull. Chem. SOC.Jpn., 47,2217 (1974). (43) P. Gerding, Acta Chem. Scand., 20, 79 (1966). (44) S. Ahrland, E. Avsar, and L. Kdlberg, Acta Chem. Scand., Ser. A, 28, 855 (1974). (45) P. Gerding and B. Johanason, Acta Chem. Scand., 22,2255 (1968). (46) P. Gerding, Acta Chem. Scand., 20, 2771 (1966). (47) M. SandstrBm, I. Persson, and S. Ahrland, Acta. Chem. Scand., Ser. A, 32, 607 (1978). (48) S. Ahrland and N. BjBrk, Acta Chem. Scand., Ser. A, 30, 257 (1976).
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t'
Yamada and Verrail
i
itive values of AV*/'c" are always associated with highly positive values of AS* (methanol exchange for Ni2+, AV*/ VO = 0.28, and for Co2+,0.22;5@3 water exchange for Ni2+= 0.39;5of acetonitrile exchange for Ni2+ = 0.18&), 0 whereas negative values of AV*/ 'c" correlate with highly 0 0 negative values of AS* (methanol exchange for Mn2+, AV*/'c" = -0.12608) and small positive values of AV*/'c" OI 0 0 I with small positive values of AS* (methanol exchange for 3 *v, Fe2+,AV*/'c" = 0.01%). - 40 In Figure 7, the activation entropy for solvent exchange 4 is plotted against the ionic radius of the metal It is clear that the associative character increases with inN'*: C6Fez* . creasing ionic size of the cation. As well, for a given metal L. I . 1 ion, associative character decreases in the order of MeOH 0.6 0.8 1.o > MezSO > DMF, except for Ni2+,and this order is conIonic Radius(A 1 sistent with the increasing order of solvent molar volume Flgure 7. Plot of activation entropy against ionic radius: (0)MeOH, VO. Although some additional properties of the cation and (0)DMF, (a)Me,SO. solvent may be also reflected in AS*, it is reasonable to assume that the entropy of the solvent exchange process that solvent molecules are more crowded in the Me2S0 will be governed mainly by the size of the cation and hexasolvate than in the hexahydrate. Unfortunately, there solvent molecule and that, judging from the highly negative is little additional information available on the complexvalues of activation entropy obtained, the complexation ation involving cadmium ion. However, by analogy with involving cadmium ion proceeds associatively in nonathe halide systems in MefiO, it seems reasonable to expect queous solvents used in this study. The higher positive that the coordination change presumably does not take value of AS* for water exchange at Mn2+(12 J mol-l K-1)62 place at the first stage in MeOH, DMF, and MezSO soluthan that for the DMF exchange suggests that AS* for tions of cadmium nitrate. It is therefore pertinent to water exchange at Cd2+may be higher than the correconsider that the complexation reactions of solvatosponding value for DMF. This will lead to increased cadmium and mononitratocadmium ion involve CdSe2+ dissociative character for water exchange at Cd2+and will and Cd(N03)S5+,respectively (S stands for one of the be consistent with the earliet discussion on the mechanism solvents studied here). in aqueous solution. Recently, kinetic studies of complexation reactions have The relatively low values of activation enthalpy observed been extended to nonaqueous systems in order to examine for the complexation reaction may be anticipated from the applicability of the Id mechanism in other solvents crystal field stabilization considerations.6 For example, besides water and to find a correlation between kinetic it seems reasonable to assume that the total activation parameters and fundamental solvent properties. Considenergy is made up of a crystal field contribution and a erable work has been done, mainly on the first-row transolute-solvent contribution. In the case of a Cd2+dl0 sition-metal ions in methanol, dimethyl sulfoxide, acetocation, the contribution of the crystal field stabilization nitrile, dimethylformamide,and other solvents (see review to the activation energy will be small for any postulated by J. F. Coetzee*). Rate constants and activation parammechanism. A similar argument would hold for the Mn2+ eters for solvent exchange at divalent metal ions in MeOH, d5 cation. The higher values of AH* for Mn2+relative to DMF, and Me2S0 are summarized in Table 111. As can Cd2+indicate that the solvent-solute contribution to the be seen from this table, the solvent exchange for cadmium activation energy is not constant for metal ions of the same ion is characterized by highly negative values for the accharge and, as one would expect, the solute-solvent intivation entropy and lower activation enthalpies, which teraction is very much dependent on the charge density leads to a higher exchange rate. The entropy of activation of the cation involved in the complex. has been considered the useful parameter for judging Finally, insofar as the thermodynamics of this reaction whether a reaction mechanism is associative or dissociative, are concerned, Table I1 shows that the formation constant particularly when the entropy for closely related systems between cadmium and nitrate ions has no temperature is highly negative or positive.49 dependence within experimental error. This suggests that More recently the use of volumes of activation has been emphasized for the diagnosis of reaction mechanism~,4~1~ the cadmium-solvent bond-breaking energy is largely compensated by cadmium-nitrate bond-making energy. and the ratio of the volume of activation to the solvent This result is not too surprising since oxygen is the donor molar volume, AV*/VO, has been proposed for a measure atom involved in both processes. of solvent exchange mechanism: 5@ AV*/V" = 1 for dissociative (D) mechanism, 1-0 for dissociative interchange Acknowledgment. Financial support from the Natural (Id) mechanism, 0 to -1 for associative interchange (I,) Sciences and Engineering Research Council of Canada and mechanism, and -1 for associative (A) mechanism. Posthe President's NSERC Award Fund of the University of Saskatchewan is gratefully acknowledged. We thank Dr. (49) T.W. Swaddle, Coord. Chem. Rev., 14, 217 (1974). H. Nomura (Nagoya University) for helpful discussions, (50) (a) A. E. Merbach and H. Vanni, Helu. Chim. Acta, 60, 1124 and S.Y.thanks Nagoya University for allowing a leave (1977); (b) W. L. Earl, F. K.Meyer, and A. E. Merbach, Inorg. Chim. of absence to perform this work. Acta, 25, L91(1977); (c) K.E. Newman, F. K. Meyer, and A. E. Merbach,
-
I
1
,
0
i' i'
,
J. Am. Chem. SOC.,101,1470 (1979); (d) F. K.Meyer, W. L. Earl, and A. E. Merback, Inorg. Chem., 18,888 (1979); (e) Y.Docommun, W. L. Earl, and A. E. Merbach, ibid., 18,2754 (1979); (0H.Vanni and A. E. Merbach, ibid., 18,2758 (1979); (9) F.K.Meyer, K. E. Newman, and A. E. Merbach, J. Am. Chem, SOC.,101,6588 (1979).
(51) All ionic-radii data are taken from R. C. Weast, Ed., "Handbook of Chemistry and Physics", 60th ed., CRC Press, B o a Raton, FL, 1979. (52) T.J. Swift and R. E. Connick, J. Phys. Chem., 37, 307 (1962).
