6481
Kinetics of Oxygen Exchange, Racemization, and Aquation in Tris (oxalato ) rhodate (111) Ion132 Lenore Damrauer and Ronald M. Milburn* Contribution from the Department of Chemistry, Boston University, Boston, Massachusetts 02215. Received January 13, 1971 Abstract: A n earlier study of acid-catalyzed oxygen exchange between R h ( C ~ 0 ~ ) 3a ~n d- solvent water has been extended t o a reexamination of the acid-catalyzed racemization a n d aquation reactions. Racemization over the [H+] range 0.0-0.4 M requires a two-term rate law: R = (kr2[H+] k,3[H+]2}[Rh(C~04)3a-]. At 56.4" a n d p (ionic M-, sec-l, AH*,, = 23.3 =t 1.5 kcal mol-', AS*,, strength) = 0.54, k,, = 4.2 X 10-5 M-1 sec-1, kr3 = 2.4 X
+
= -8.2 + 4.0 eu, AH*,, = 26.8 i 1.5 kcal mol-', A S S r 3 = 5.8 i 4.0 eu. F o r inner-oxygen exchange a t 56.3" a n d p = 0.54, ki2 (= kl/[H+]) = 8.5 X 10-5 M-l sec-l, AH+iz = 23.4 =t 2.0 kcal mol-', AS*iz = -6.3 =t 6.0 eu. T h e rate constants a n d activation parameters, corresponding to rate law terms which are first order in [H+], are remarkably similar for racemization a n d inner-oxygen exchange, a n d the results strongly suggest a parallelism in the mechanisms. The aquation of Rh(C204)3a-t o Rh(C20r)z(Hz0)2-a n d free oxalic acid, which was examined over the [H+] range 0.0-0.5 M , also requires a two-term rate law: R = (k,z[H+] k,3[H+]2}[Rh(C~04)33-]. A t 56.3" M-2sec-',AH*,~ = 25.5 f 2.0 kcal mol-', AS*,, a n d p = 0.54, ka2 = 1.67 X 10-8 M-lsec-1, ka3 = 1.16 X = -7.8 =k 6.0 eu, AH*,, = 25.9 f 2.0 kcal mol-', AS*a3 = -2.9 i. 6.0 eu. F o r the conditions under which racemization a n d inner-oxygen exchange were examined, the aquation is significantly slower. Thus, a t 56.3 O with [H+] = 0.20 M and p = 0.54, when 50% of the inner oxygens have exchanged, -4% of the complex has aquated; when 50% of the optically active complex has racemized, ~3 % of the complex has aquated. Outer-oxygen exchange is considered t o proceed by the previously suggested A2 mechanism without cleavage of rhodium-oxygen bonds. The slower formation of a pentacoordinated intermediate permits the interchange of inner a n d outer oxygens, hence accommodating inner-oxygen exchange as well as allowing for the possibility of inversion which may receive assistance through additional protonation. Addition of a water molecule to the pentacoordinated intermediate, t o form a hexacoordinate intermediate with a monodentate oxalate, provides the path toward aquation.
+
F
or r e s o l v a b l e c o m p l e x e s t h e possibility of relation-
s h i p s b e t w e e n r a c e m i z a t i o n a n d related r e a c t i o n s has l o n g b e e n a m a t t e r of ~ o n c e r n . ~ O* u~r special interest in this m a t t e r d e v e l o p e d while w e were e x a m i n i n g acid-catalyzed e x c h a n g e of o x y g e n b e t w e e n Rh(C2o4),,- a n d s o l v e n t w a t e r , w h e r e m a r k e d differences between rates f o r outer- a n d inner-oxygen exchange w e r e o b ~ e r v e d . ~In particular, t h e r a t e s of oxygen e x c h a n g e b e t w e e n i n n e r o x y g e n s a n d s o l v e n t w a t e r at -56" w e r e f o u n d to b e very similar t o the r a t e s of r a c e m i z a t i o n c a l c u l a t e d f r o m the d a t a of Odell, et nl., for s i m i l a r c o n d i t i o n s of acidity and i o n i c strength.6 H o w e v e r , a c t i v a t i o n p a r a m e t e r s m e a s u r e d f o r i n n e r - o x y g e n e x c h a n g e 5 and t h o s e r e p o r t e d f o r r a c e m i z a t i o n 6 w e r e not i n particularly c l o s e a g r e e m e n t . Because of t h e possible mechanistic implications, we decided to investigate the r a c e m i z a t i o n reaction f u r t h e r , and a l s o to r e e x a m i n e the p r e v i o u s l y s t u d i e d a q u a t i o n reaction.' We h a v e earlier given s u m m a r y a c c o u n t s of our finding^;^^^ we n o w p r e s e n t t h e results i n detail.
Experimental Section Materials. Reagent grade materials were used except where otherwise specified. Normal water was obtained from ordinary (1) Supported by the National Science Foundation. (2) Presented at the 12th International Conference on Coordination Chemistry, Sydney, Australia, Aug 1969; Proc. Int. Conf. Coord. Chem., 1969, 12,38(1969). (3) A . Werner, Justus Liebigs Ann. Chem., 386, 1 (1912); Ber., 45, 1228, 3061 (1912). (4) F. Basolo and R. G. Pearson, "Mechanisms of Inorganic Reac1967, Chapter 4. tions," 2nd ed, Wiley, New York, N. Y., (5) L. Damrauer and R. M. Milburn, J . Amer. Chem. Soc., 90, 3884 (1968). (6) A. L. Odell, R. W. Olliff, and F. B. Seaton J . Chem. SOC.,2280 (1965). (7) (a) D. Barton and G. M. Harris, Inorg. Chem., 1, 251 (1962); (b) K. V .Krishnamurty, ibid., 1,422 (1962).
distilled water which was refluxed with potassium permanganate and sodium hydroxide in a Barnstead S-1 water still, redistilled, and finally passed through the distillation apparatus a second time. Water enriched in ' 8 0 was obtained from Yeda Research and Development Co., Inc., Rehovot, Israel. Perchloric acid and sodium perchlorate solutions were used to control acidity and ionic strength. A stock perchloric acid solution was prepared from about 60% acid and was standardized against dried sodium carbonate. A stock sodium perchlorate solution was prepared from perchloric acid and anhydrous sodium carbonate. The preparation, analysis, and storage of unresolved K3Rhhave been described.8 Solutions of this complex (C204)a. 1.5H20 salt were prepared by dissolving weighed amounts in water. In some cases these solutions were used directly for the preparation of reaction solutions (the complex salt being the only source of potassium ion). In other cases potassium ion was exchanged for sodium ion. Potassium tris(oxalato)rhodate(III) was resolved following the procedure of Werner.8 A solution of K3Rh(CZ04)3. 1.5H20 (0.905 g in 50 ml of water at 50") was added to a solution of strychnine nitrate(2.10 gin 100 ml of water at 85"). After standing for 1 hr, the yellow precipitate of the strychnine salt of Rh(C204)3awas separated from solution by suction filtration. Further precipitation continued as water from the solution evaporated at room temperature, and, in all, five fractions were collected. A fivefold weight excess of potassium iodide, dissolved in the minimum amount of water at room temperature, was added to each fraction. Each mixture was ground thoroughly and filtered, and the white solid strychnine iodide was washed with -2 ml of water. Ethanol (95%) was added to the filtrates to precipitate the yellow potassium tris(oxalato)rhodate(III). The solid was collected by filtration, washed with -2 ml of ether, dried by pulling air through the funnel, and stored. Solutions of ( -)j46-potassium tris(oxa1ato)rhodate(111) were prepared as necessary. The optical rotation of solutions measured at 365, 436, 546, and 578 nm with a Perkin-Elmer 141 spectropolarimeter agreed very well with published ORD curves. lo (8) M. W. Hsu, H. G. Kruszyna, and R. M. Milburn, ibid., 8 , 2201 (1969). (9) A. Werner, Ber., 47,1954 (1914).
(10) A . M. Sargeson in "Chelating Agents and Metal Chelates," F. P. Dwyer and D. P. Mellor, Ed., Academic Press, New York, N. Y . , 1964, p 221.
Damrauer, Milburn
/ Tris(oxalato)rhodate(III)Ion
6482 Table I. Pseudo-First-Order Rate Constants for the Exchange of Outer Oxygens
z
Expt no.
[H+] X lo2, M
[Complex], X loz, M
Ionic strength
Temp, "C
k X 108, sec-10
deviationb
01 02 03 04 05 06 07 08 09 010 011
0.978 4.89 9.78 9.78 9.78 20.4 9.78 9.78 20.4 20.4 0.978
1 .oo 1 .oo 1 .oo 1.00 1.oo 1.00 2.00 0.500 1.00 1.00 1.00
0.54 0.54 0.54 0.54 0.54 0.54 0.60 0.51 0.54 0.54 0.070
25.1 25.1 25.1 25.1 25.1 25.1 25.1 25.1 45.0 56.3 25.2
0.795 (7) 4.20 (4) 7.17 (3) 7.88 (4) 9.05 (8) 20.2 (4) 8.23 (6) 9.27 ( 5 ) 127 (3) 302 (3) 2.28 ( 5 )
0.4 0.6 2.6 1.3 1 .o 1.8 0.2 1.4 1.7 0.4 0.8 ~~
Rate constants calculated from least-squares slopes for plot of eq 1, on the assumption that six oxygens exchange at the same rate and six oxygens do not exchange. Numbers in parentheses give number of points used to compute the least-squares slope. Equal to the standard deviation for the least-squares slope X 100, divided by the least-squares slope. a
Table II. Pseudo-First-Order Rate Constants for Exchange of Inner Oxygens
Expt no.
[H+l X IO2, M
[WCzOa)a '-1 X lo2, M
Ionic strength
Temp, "C
012 013 014 015 016 017 018 019
20.4 20.4 4.83 20.3 20.3 40.6 20.2 20.8
0.993 0.993 0.988 0.988 0,988 0.988 0.982 0.494
0.54 0.54 0.53 0.53 0.53 0.53 0.53 0.24
45.0 45.0 56.3 56.3 56.3 56.3 67.0 56.3
k
x
108, sec-1
z
deviationb
a
3.78 (7) 4.15 ( 5 ) 3.02 ( 5 ) 16.6 (6) 14.7 ( 5 ) 36.0 ( 5 ) 45.3 ( 5 ) 23.8 ( 5 )
1.9 1.4 4.1 2.0 3.2 3.3 3.4 7.6
~~~
~~
Rate constants calculated from least-squares slopes for plot of eq 1, using as the initial atom fraction the point when one-half of the oxygens had equilibrated with solvent (in most cases equilibrated at 25"). Thus NO for inner-oxygen = N , for outer-oxygen exchange, In fact, the No value is unimportant in determining the least-squares slope, because a plot of log [ ( N , - No)/(" - Nt)] against t gives the same slope as a plot of -log ( N , - N t ) against t , since NOis a constant. Equal to the standard deviation for the least-squares slope X 100, divided by the least-squares slope. a
Table 111. Activation Parametersa 7
Process
Symbol
Outer-oxygen exchange Inner-oxygen exchange Racemization
k 02
Rate constant Value at 56.3"
1.48 X M-l sec-l 8.5 X M-l sec-l M-1 sec-1 4.2 X 2 . 4 x 10-4 M-2 ~a-1 1.67 X M-l sec-l 1.16 X M-2 sec-l
kiz
krz kr3
Aquation
--
kaz ka3
AH*, kcal mol-'
16.9 + 2 . 0 23.4 ?C 2 . 0 23.3 ?C 1 . 5 26.8 f 1 . 5 25.5 f 2 . 0 25.9 i 2 . 0
AS*, eub
-20.0 -6.3 -8.2 +5.8 -7.8 -2.9
f 6.0 f 6.0 4~ 4 . 0 f4.0
i6.0 f 6.0
Values of AH* and AS* are quoted t o one-tenth of a unit (although the uncertainties are larger) e All values are for ionic strength 0.54. to enable calculation for various temperatures of the more precise values of the rate constants. The uv and visible spectra also matched spectra of the unresolved starting material. Oxygen-Exchange Studies. The procedures used to study the exchange of oxygen between Rh(Cz04)33-and solvent water were similar t o those described earlier for the Pt(Ct04)22- ion." The essential details of these studies have already been presentedS6 For each kinetic run values of N , the atom fraction of oxygen-18 [lsO])),were obtained as a function of (=[1801/([180] ["O] time from the standard expression N = R/(R 2), where R is the isotope ratio for carbon dioxide ( = [Cl6>1802]/( [Cl6>1 6 0 2 1 [C18,1702]]). The left side of eq 1 could then be plotted against time. Values of N , were calculated without inclusion of per-
+
+
+
+
chlorate oxygen, which is not considered to exchange under the reaction conditions used.I2 In using eq 1 , linear first-order rate plots are obtained for the early stages of reaction only if N , values are calculated on the (1 1) J. E. Teggins and R. M . Milburn, Inorg. Chem., 4,793 (1965). (12) (a) N. F. Hall and 0. R. Alexander, J . Amer. Chem. Soc., 6 2 , 3455 (1940); (b) E. R. S. Winter, M. Carlton, and H. V. A. Briscoe, J . Chem. Soc., 131 (1940); (c) A. I. Brodskii and N. A. Vysotskaya, Dokl. AkadNauk S S S R , 101,869 (1955).
Journal of the American Chemical Society
1 93:24
basis that very close to one-half of the 12 oxygens have equilibrated with solvent (ref 5 , Figure 1A). Plots made on the basis that just one-half of the oxygens are exchanging provide pseudo-first-order rate constants which we associate with exchange of the outer oxygens. The data obtained is summarized in Table I. After the outer oxygens have equilibrated with solvent, inneroxygen exchange can be followed. Linear first-order rate plots are obtained now if one takes as the initial time the point when onehalf of all oxygens have equilibrated. Thus, No for inner-oxygen exchange is equal to N , for outer-oxygen exchange.13 A representative rate plot for inner-oxygen exchange has already been presented (ref 5, Figure 1B). Data obtained for inner-oxygen exchange are summarized in Table 11. If a modified McKay equation is used for the case where one-half of the atoms exchange at one rate and one-half at a different rate,14,15linearity is obtained for exchange of 90% of all oxygens. (13) Because the activation energy for outer-oxygen exchange was found to be less than that for inner-oxygen exchange, the usual procedure was to equilibrate the outer oxygens with solvent at 25" before following inner exchanges at higher temperatures. At 25" outer OXYgens exchange -60 times more rapidly than inner oxygens; at 56" the difference is -20-fold. (14) C. A. Bunton, J. H. Carter, D. R. Llewellyn, C . O'Connor, A. L. Odell, and S. Y. Yih, J . Chem. Soc., 4615 (1964).
December I , 1971
6483 Table IV. Pseudo-First-Order Rate Constants for Racemization" Expt no. R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 R17 R18 R19 R20 R21 R22 R23 R 24 R25
[H+] 0.104 0.209 0.398 0.104 0.208 0.397 0.104
0.208 0.397 0.0519 0.104 0.208 0.415 0.502 0.207 0.208 0.209 0,208 0.208 0.207 0.589 0.592 0.591 0.589 0.587
Ionic strength Temp, "C 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.53 0.54 0.54 0.53 0.54 0.53 0.53 0.24 0.71 0.71 0.71 0.70 1.81 2.98 2.97 2.96 2.95
45.0 45.0 45.0 50.0 50.0 50.0 53.2 53.2 53.2 56.4 56.4 56.4 56.4 56.4 63.9 56.. 4 42.9 48.1 56.4 63.9 56.4 45.0 50.0 56.4 63.9
kobsd 106, sec-1 *
deviationc
0.175 0.490 1.31 0.318 0.892 2.55 0.485 1.38 3.90 0.272 0.698 1.97 5.97 8.17 5.22 3.27 0.343 0.625 1.63 4.38 7.35 2.20 4.25 9.53 23.7
0.91 0.74 0.68 0.46 0.34 0.15 0.33 0.50 1.2 0.62 0.60 0.35 0.23 0.23 0.61 0.30 0.63 0.63 0.37 0.25 0.29 0.30 0.57 0.25 0.38
x
*I
z
M for all exa Complex concentration equal to -5.2 X periments. b Rate constant calculated from least-squares slope for plot of log (degrees) against time. c Equal to the standard deviation for the least-squares slope X 100, divided by the leastsquares slope.
7
