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Reactions of the diaquatetraamminecobalt(III) ion in weakly alkaline solutions
J. inorg, nucl. Chem., 1973, Vol. 35, pp. 2407-2415.
Pergamon Press.
Printed in Great Britain
REACTIONS OF THE D I A Q U A T E T R A A M M I N E COBALT(III) ION IN WEAKLY A L K A L I N E SOLUTIONS S. BALT and P. M. KWANTES (in part) Chemical Laboratory Free University, De Lairessestraat 174, Amsterdam, The Netherlands
(Received 11 September 1972)
A b s t r a c t - Kinetic measurements are reported on the tetramerization and the isomerization reactions of the conjugate bases of the diaquatetraamminecobalt(lll) ion. A combination of stopped flow and pH-stat techniques has provided further support for a previously constructed reaction scheme, in which the tetramerization is preceded by a cis-trans isomerization. The general picture of the isomerization rates has been found to follow the pattern set by the analogous bis-ethylenediamine complexes.
INTRODUCTION
THE DIAQUATETaAAMMINECOBALT(III)cation in weakly alkaline aqueous solutions undergoes a tetramerization reaction [ 1]: 4 Co(NH3)4(H20)23+ + 6 O H [Co{(OH)2Co(NH3)4}:~] 6+ + 4 NH3 + 8 H20.
(l)
The T(H20)23+ ion (the symbol T will be used for the tetraammine moiety Co(NH3)4) behaves as a weak acid and on raising the pH forms the ions T(OH) (H20) 2+ and T(OH)2+; consequently the tetramerization reaction (1) will take an accordingly modified form. A kinetic study of reaction (1) has recently been started in our laboratory. At a fixed temperature (20-7°(2) the pH dependence of the observed rate constant could be explained from a reaction scheme in which the c i s - t r a n s isomerizations of the various tetraammine complexes play an important part [2]. Reaction (1) can be stopped by adding ammonia; in this way the c i s - t r a n s isomerizations referred to have been studied separately [3]. From this study it ensued that the c i s - t r a n s isomerization of the T(H20)23+ and the T(OH)._,+ ions goes mainly via the T(OH)(H20) 2+ species. In the study cited [3] direct measurements on the isomerization of this ion were not reported, as the relatively high rates presented a problem for the conventional spectrophotometric technique used. To fill this gap the present study reports stopped flow spectrophotometry on the reaction: cis-T(OH)(H20)
2+ (
, trans-T(OH)(H20)
1. A. G. Sykes and J. A. Weil, Prog. lnorg. Chem. 13, 1 (1970). 2. S. Bait and W. de Kieviet, lnorg. Chem. 11,2251 (1972). 3. S. Ball, R ecl. Tray. Chim. Pays-Bas 91, 1026 (1972). 2407
2+.
(2)
2408
S. BALT and P. M. KWANTES
The results obtained are used to further unravel the complicated pattern of the t e t r a m e r i z a t i o n r e a c t i o n (1). I n a d d i t i o n , f o r r e a c t i o n (1) t h e t e m p e r a t u r e d e p e n d e n c e o f t h e r a t e p a r a m e t e r s f r o m p H - s t a t m e a s u r e m e n t s is p r e s e n t e d to c o m p l e t e the picture. EXPERIMENTAL The chemicals and solutions used, together with details of pH-stat and pH calibration have been described fully elsewhere [2, 3]. pH-stat measurements [reaction (1)] Reaction (1) has been followed at different temperatures (accuracy 0.1 ~C) and constant concentration of the diaquatetraamminecobalt(III) perchlorate: 0.10M. The concentration of perchlorate has been kept constant at 1-00M. Constancy of the pH was assured within 0.03 pH units. Stopped flow measurements [reaction (2)] Construction of the instrument. The stopped flow Spectrophotometer has been built after the design of Gibson [4] in our laboratory by Musch and van Rooij. Here follows a short description of modifications introduced. Some more flexibility compared to the original design is attained by using quartz fibers in the optical connections between monochromator, observation chamber and photomultiplier, while the application of pneumatically driven valves facilitates the operation. The optical part comprises a Unicam SP 500 monochromator and a RCA IP28 Photomultiplier; the signal coming from this tube is fed into a logarithmic amplifier and then displayed on a Tektronix 564B Storage Oscilloscope. The electronic parts have been constructed by v.d. Linden and Kost. The mixing time is better than 2 msec, that is considerably smaller than the half-life of the reactions studied (see Tables 2 and 3). Kinetic measurements. The procedure followed was to mix rapidly equal volumes of 1) a slightly acidified (pH ca. 4) aqueous solution of diaquatetraamminecobalt(lll) perchlorate and ammonium perchlorate (1.00M) and 2) a buffer solution of 1.00M ammonium perchlorate and ammonia (0.100.40M). The constant ammonium perchlorate concentration assured Constant ionic strength. The rather high concentration of this salt was dictated by the minimum concentration of ammonia necessary to stop reaction (1); whether this was accomplished could be verified by studying the u.v. part of the absorbance spectrum of the mixed solutions [2, 5]. In all kinetic runs the total concentration of cobalt complex was kept at 10-2M; the temperature was adjusted by circulating thermostatted water around the mixing block, the observation chamber, and the syringes, of th~ stopped flow spectrophotometer. The temperature was constant within 0.1°12. The pH was measured immediately after mixing in a parallel experiment. The values reported could be reproduced within 0.02 pH units.
RESULTS Tetramerization I n a l k a l i n e s o l u t i o n s t h e t e t r a m e r i z a t i o n o f t h e T ( O H ) ( H 2 0 ) z+ a n d T ( O H ) 2 ÷ i o n s p r o d u c e s h y d r o x y l ions. I n t h e p H - s t a t m e t h o d p e r c h l o r i c a c i d is a d d e d d u r i n g t h e r e a c t i o n to k e e p c o n s t a n t p H . T h e a m o u n t o f a c i d u s e d a s a f u n c t i o n o f t i m e o b e y s a first o r d e r r a t e l a w a s w o r k e d o u t p r e v i o u s l y [2]. T h e p s e u d o first o r d e r r a t e c o n s t a n t [ h e r e a f t e r c a l l e d k l ( o b s d ) ] is a f u n c t i o n o f p H a n d t e m p e r a t u r e ( T a b l e 1). T h e a c c u r a c y o f t h e e x p e r i m e n t a l c o n s t a n t s is ca. 4 p e r c e n t , e x c e p t at 33.7°C, w h e r e t h e l i m i t s o f t h e m e t h o d h a v e b e e n r e a c h e d , t o t h e e x t e n t t h a t t h e m a x i m u m o f t h e k l - p H g r a p h [2] c o u l d n o t b e m e a s u r e d . F o r this t e m p e r a t u r e t h e a c c u r a c y is e s t i m a t e d at 7 p e r cent. I s o m e r i z a t i o n o f the T ( O H ) ( H 2 0 ) 2+ ion T h e i s o m e r i z a t i o n r e a c t i o n (2) h a s b e e n f o l l o w e d at different w a v e n u m b e r s ,
4. R. H. Gibson and L. Milnes, Biochem. J. 91, 161 (1964). 5. A. B. Hofman and H. Taube, lnorg. Chem. 7, 903 (1968).
Diaquatetraaminecobalt(lII) ion reactions
2409
temperatures, and pH. The observed stopped flow trace in all cases obeyed a first order rate law. The actual values of the rate constants [called k2(obsd)] were taken from a least squares analysis of the measured (between 0 and 80 per cent reaction) absorbance as a function of time (,4 t) by using the formula:
[At --A~] In [ ~ ] = - k,~(obsd),t
(3)
in an iterative fit for the constants k2(obsd), A0 and A~, A0 and A ~ are the absorbances at zero time and at equilibrium respectively [6]. This procedure was chosen because no exact value for A ~ can be measured directly, reaction (2) being followed by a much slower uptake of ammonia to form the pentaammine complex. From Table 2 it is evident that k2(obsd) is independent of wave number. Consequently the entries of Table 3, spreading over a much larger range of conditions, have been obtained from measurements at a single wave number: 19.200 cm -1, lying between the visible maximum of T(OH)2 + and that of T(H20)23+. it must be stressed here that a high accuracy in k2(obsd) is not possible as a result of the small changes in absorbance between the cis complexes and the cis-trans equilibrium mixture. The experimental value for k2(obsd) could be reproduced within 10 per cent. DISCUSSION
The pH dependence of the rate constants pertaining to the reactions under study are consistent with the following reaction scheme [2, 3]: cis-T(HzO)23+ ,
kss
cis-T(OH)(H~O) 2+ ,
, trans-T(H20)23+
k~
, trans-T(OH)(H20) 2+ ~
~ Co(NH3).~(NH2)(OH)(H20) ÷
® cis-T(OH)£ ~
q)
trans-T(OH)~ ÷
@
k,=
> intermediate leading to tetramer.
The indexing of the rate constants parallels the numbering of the complex ions. The acid-base reactions are instantaneous [7]; for these reactions the equilibrium constants are:
K,m --- A n" [H +] Am (this notation slightly differs from the one previously used [2, 3]). A,, is the concentration of the complex@; the activity [H +] follows from pH 6. D. F. Deter, Editor, Computer Programs for Chemistry, p. 117. Benjamin, N e w York (1968) 7. G. Schwarzenbach, J. Boesch and H. Egli, J. inorg, nucl. Chem. 33, 2141 (1971 ).
2410
S. BALT and P. M. KWANTES
measurements. Expressions for the observed rate constants k~ and k2 may now be derived.
Reaction (1) As explained elsewhere[2], the rate determining step of the tetramerization reaction is a dissociative reaction of either complex ® or complex ®, forming a reactive intermediate ® that rapidly combines with three tetraammine species to form the tetramer. The constant kl(obsd) is given by: a J [ H +] kl(obsd) = { 1 + Cl[[H+]}. { 1 + cd[H+]}
with al =
4 . k28. K24. k34, k2s. K24 " c1 = K13; c2 = k43 k43
(4)
if the mechanism is operative via complex ®. If the reaction goes via ®, the product k2s • K24 in the equations (4) must be substituted by krs • K47. It has been shown [2], that the k~(obsd) values at 20.7°(2 can be fitted with Eqn (4). This was done by using a steepest descend computer program on a IBM 1 130 computer applying a least squares criterium. Exactly the same procedure has been applied to the present k~(obsd) values. The parameter values are in Table 4, while Table 1 contains a comparison between observed and calculated rate constants. Table 4 Table 1. Results* of pH-stat experiments as a function of pH and temperature pH
103 • kl
pH
lOS.k1
(sec-1)
(sec-1) obsd calc.
7"50 8.00 8"30 8"70 9.00 9.30
14'9°C 0'27 0"52 0-80 0"92 0.90 0.69
7.00 8.00 8.30 8.50 8"70 9"10 9-30 9.50 9'70
20.7~'J" 0.07 0.16 1 . 0 8 1"23 1 " 9 3 1"92 2.43 2"37 2"80 2"68 2 " 5 5 2'60 2"10 2"22 1 " 6 0 1"75 1"33 1"28
0.24 0.56 0"78 0"94 0.88 0.69
obsd calc.
7-00 7.50 8.00 8"50 9.00 9"35
25.2°C 0.80 2.50 4.08 6.00 4.83 3.07
7"25 7"35 7-50 7"61 8.86 8.90
33"7°C 6.7 8"2 8'8 9.9 13"5 12"8 16"2 15"2 17"7 17 "5 16.2 16"5
*At ionic strength I = 1.00M. TFrom reference [2].
0.82 2.17 4.41 5"86 4.78 3"15
Diaquatetraaminecobalt(III) ion reactions
2411
Table 2. Pseudo first order rate constant for the isomerization reaction (2) as a function of wave number* Wave number (cm-')
102. k2 (sec-q
18.200 19.200 26.300 27.800
1.07 1.20 1.00 0.92
*t = 25.55°C; pH = 9.28; (NH3) = 0.25M; 1 = 1.00M. Table 3. Pseudo first order isomerization rate constant as a function of pH and temperature (stopped flow results)
pH*
(NH3)* M
10 2 . k2 (sec-') obsd. calc.~
k,13/k34
8-89 9-11 9"11 9'24
0' 10 0'15 0'15 0.20
22-60°C 1"00 0-94 0"63 0.67 0-66 0'67 0"55 0.53
5"5 4"8 4.3 4"0
8"42 8"77 8-99 9"13
0"05 0-10 0-15 0.20
25 "60°C 2"76 2'53 1.59 1"77 1'36 1.30 1.04 1.04
5" 1 4-9 5-2 4-9
8"37 8-37 8-93 9.06
0.05 0.05 0.15 0.20
28-30°C 4-72 4-28 4.08 4-28 2.00 2.09 1'72 1.68
6"0 5.7 6-7 6' 1
* After mixing the reagent solutions. tLeast squares analysis with Eqn (7).
also contains K13 from extrapolating the pH-stat graphs to zero time in the usual way [2]. Reaction (2) A relation expressing k2(obsd) as a function of pH can be deduced as follows. The pH region for the stopped flow experiments has been chosen in such a way t h a t t h e T ( O H ) ( H 2 0 ) 2+ c o m p l e x e s c o m p r i s e a n o n - n e g l i g e n t p r o p o r t i o n o f t h e
2412
S. BALT and P. M. KWANTES Table 4. Rate and equilibrium constants from fitting the tetramerization results* Temp. (°C)
1011. a l f (M. see -~)
109 • c2f (M)
14"9 20.7 25"2 33"7
0.90 1"73 8.90 54.9
5.40 2.52 8.50 4'76
10 TM. C2t (M) 5"80 8.15 9"50 57.2
109. K13' (M) 6'3 3"2 5"9 2"2
*1 = 1.00M ?Estimated accuracy in al is 5 per cent; in c~ and c2 20 per cent. ;tDetermined directly.
total amount of cobalt complex present. This means that the isomerizations via the T(OH)2 + ions (as given by the rate constants ka2 and k21) can be neglected, as the sum k~2+ kzl is much smaller than the sum kz4 + k4313], k2(obsd) may then be expressed as: k2(obsd) = ka4. [H +] k43. [H +] (5) [H +] + K13 + [H +] + K2~ Relation (5) may be simplified by observing that K13 and K24 refer to connected equilibria, so that:
Kz4 Kxa
k43[ka4 k21/k12"
(6)
In an earlier paper[3] the ratio k21/k12 has been estimated from the assumption that the molar absorbance coefficient of the trans-T(OH)2 + ion is half that of the corresponding cis compound. This assumption is based on the similarity in chemistry and absorption spectra between the tetraammine complexes under investigation and the analogous bis-ethylenediamine complexes, for which this relation holds. The identical assumption for the T(OH)(H20) 2+ ions enables us to calculate the gross equilibrium constant (cis[trans) for the mixture of T(OH) (H20) z+ and T(OH)2 + isomers from the stopped flow results. If the ratio k43/k34 differs considerably from the value of k21/k12, the gross equilibrium constant calculated in the way indicated above, will show a pH dependence, as the amount of the tetraammine present as T(OH)(H20) 2+ is a function of pH. Now the values obtained for the gross equilibrium constant cisltrans (last column of Table 3) not only are independent of pH at a fixed temperature, but also change very little on changing the temperature. The actual value calculated is very nearly equal to k2~/ka2: this constant has been found [3] to be nearly constant at the value 4 from 20 to 35°C. All this means that k43/k34 may be put equal to k2~]k12(therefore the last column of Table 3 has already been headed k43/kz4) and consequently K~3 = Kz4. After rearranging relation (5) transforms to (7): 1
1
1
k 2 ( o b s d ) = (k34 -[- k43) "[" [H+~
KI~ "(k34"-[-k43)"
(7)
Diaquatetraaminecobalt(Ill) ion reactions
2413
Table 5. Parameters used to fit the stopped flow results Temp. (~)
102.(k34+k43) (sec -1)
22.6 25.6 28-3
2.5±0-4 3.8±0.6 7.1±1.0
10~.K,z (M) 2.1±0.4 2.0±0-4 2.8±0.5
A least squares analysis of the values in Table 3 using the relation (7) gives the parameter values of Table 5. In passing it may be noted that we are now in the possession of three sets of values for the equilibrium constant K,3: the set of directly determined values and the ones obtained from the fitting procedure of Eqn (5) (both in Table 4) and the values of Table 5. Unfortunately no value for K,3 has been published for conditions that resemble the present ones. From the three sets obtained in the present work Table 5 has the smallest values for K,3. This might signify that the assumptions involved are not one hundred percent justified. All the same we may state that in view of the many assumptions and fitting analyses involved, agreement between the three sets of Ka3 is quite satisfactory. We are now in a position to calculate the individual constants k:~4and k43 at the three experimental temperatures and subsequently to apply a least squares activation analysis [8] to the resulting values, from which: k34
AH # ----24.1 _ 2.2 AS# = 12.3±4-0
k43
33.1 _ 2-2 kcal. mol-' 45.7_4-0e.u.
Table 4 compares the initial k values with the ones calculated from the activation parameters.
Combination of reaction (1) and reaction (2) The results of the stopped flow and the pH-stat experiments may be brought together by substituting the quotient k43/k34 from the stopped flow experiments (after a proper temperature extrapolation from the activation parameters given above) into the fitting constant a, of Table 4 to give k2s [equation (4)]: this is the entry kz8 (a) of Table 7. A combination of al and c2 from Table 4 gives k.~4,also housed in Table 7. It is satisfactory that both sets of k34 obtained so far (in Tables 6 and 7) are in very good agreement. Except at 25°C the values calculated from the stopped flow activation parameters are very close to the ones independently deduced from the pH-stat experiments [see Table 7, entries (c) and (d)]. To kz8 a least squares activation analysis has been applied: AH # = 57.2 ± 1"0 kcal. mo1-1 AS # = 125.8__+2-2e.u.
1 = 1.00M
8. A. A. Frost and R. G. Pearson, Kinetics and Mechanism, 2nd Edn. John Wiley, New York (1961).
2414
S. BALT and P. M. KWANTES Table 6. Isomerization rate constants for the T(OH)(H20) 2+complexes Temp. (°C) 22.60 25-60 28.30
102 • k34 (see-5 0.44* 0.63* 1.00"
0"43t 0.67t 0"97t
1 0 2 • k4z
(sec-q 2"1" TOt 3"2* 3.5t 6.1" 5.8t
*Calculated from k34+ k43 in Table 5 and the ratio k43/k34of Table 3. tCalculated from the least squares activation parameters. Table 7. Rate constants from a combination of pH-stat and stopped flow results Temp. (°C) 14.9 20.7 25.2 33"7
kzs (sec -1)
10 2 .
0.10" 0"6* 1.9* 48*
0.08t 0'6t 2"7t 40t
10 2 - k34
(sec -~) 0 . 4 5 0.2§ 0.5~: 0.3§ 2.3:~ 0-7§ 2"55 2.1§
*Calculated as worked out in the text. tFrom activation parameters (see text). tCalculated from the pH-stat parameters. §From stopped flow activation parameters. AS # is c o n s p i c u o u s l y high. T h e r e f o r e t h e a l t e r n a t i v e m e c h a n i s m f o r t h e t e t r a m e r i z a t i o n v i a t h e a m m i n e c o n j u g a t e b a s e o f t h e trans-T(OH)(H20) 2+ion h a s a l s o b e e n a p p l i e d . I n this c a s e t h e a c t i v a t i o n a n a l y s i s g i v e s f o r t h e i n s e p a r a b l e p r o d u c t k78. K4r t h e f o l l o w i n g p s e u d o a c t i v a t i o n p a r a m e t e r s : A H # = 49-0___ 1.0 kcal. mo1-1. AS # = 60.0___3.1 e.u.
I = 1.00M
T h e s e v a l u e s in o r d e r o f m a g n i t u d e r e s e m b l e t h e o n e s f o u n d f o r a g e n e r a l S N 1CB m e c h a n i s m [9]. T h i s c o u l d b e a n i n d i c a t i o n f o r this k i n d o f m e c h a n i s m , b u t it c e r t a i n l y is n o p r o o f .
Consequence for acidic solutions The picture of the isomerizations worked out above for alkaline solutions may b e e x t e n d e d to a c i d i c s o l u t i o n s , f o r w h i c h t h e a c i d - b a s e e q u i l i b r i a a r e d o m i n a t e d 9. F. Basolo and R. G. Pearson, Mechanisms of Inorganic Reactions, 2nd Edn. John Wiley, New York (1967).
Diaquatetraaminecobalt(l 11) ion reactions
2415
by the constants K35 and K46. Only at 20°C an unambiguous value for the first step of acid dissociation of the d i a q u a t e t r a a m m i n e c o b a l t ( I I I ) ion is available: K35 determined by S c h w a r z e n b a c h et al.[7] with a stopped flow technique for p H m e a s u r e m e n t , at the ionic strength of 0.10M. F r o m a previous p a p e r by one of us [3] it follows that: k:~4 . K:~z-l-k43. K46 = 3.2. 10-7
M. s e c - '
(8)
(extrapolated to 20°C; 1 = 0-20M). K35 at 1 = 0.20M m a y be calculated from the value at 1 = 0.10M in the way indicated by Bjerrum[ 10]. T h e present study did not allow experiments at a lower ionic strength than 1M. T h e isomerization rate constants m a y h o w e v e r be e x p e c t e d [8] and indeed have been shown [2, 3] not to be influenced much by the ionic strength, so the values f r o m the present work extrapolated to 20°C m a y be substituted into equation (8). Then: K46 = 2-7
.
10-SM
(I = 0.20M; 20°C)
(K:~5 = 0.14.10-SM)
and, with a relation analogous to (6): k6.~/k,~ = 75.
This result is substantiated by the fact that acidified solutions of the c i s - T ( H 2 0 ) 2 :~ ion show no isomerization [3]. T h e difference between K35 and K46 together with the r e s e m b l a n c e b e t w e e n K24 and K,.~ reported here for the t e t r a a m m i n e c o b a l t ( I I I) c o m p l e x e s has also been o b s e r v e d for the corresponding b i s - e t h y l e n e d i a m i n e complexes [ 1 1]. CONCLUSION T h e present study has provided a consistent picture of the isomerization and tetramerization reactions of the t e t r a a m m i n e c o b a l t ( I I I ) ions. At the m o m e n t it is too early to say m o r e about the activation p a r a m e t e r s involved or to try to outline details of the p r o p o s e d mechanism. W e intend to shortly publish a study about the reactions of the t e t r a a m m i n e ions with a m m o n i a ; it is hoped that a link can then be made with the present work. Acknowledgements-Construction of the stopped flow spectrophotometer and the pH-stat by the
technicians mentioned in the text is gratefully acknowledged. The authors also wish to thank Professor Dr. J. M. Los for computer facilities. 10. J. Bjerrum, Metal Ammine Formation in Aqueous Solution P. Haase and Son, Copenhagen, (1941). I 1. J. Bjerrum and S. E. Rasmussen,Acta chem. stand. 6, 1265 (1952).
Pergamon Press.
Printed in Great Britain
REACTIONS OF THE D I A Q U A T E T R A A M M I N E COBALT(III) ION IN WEAKLY A L K A L I N E SOLUTIONS S. BALT and P. M. KWANTES (in part) Chemical Laboratory Free University, De Lairessestraat 174, Amsterdam, The Netherlands
(Received 11 September 1972)
A b s t r a c t - Kinetic measurements are reported on the tetramerization and the isomerization reactions of the conjugate bases of the diaquatetraamminecobalt(lll) ion. A combination of stopped flow and pH-stat techniques has provided further support for a previously constructed reaction scheme, in which the tetramerization is preceded by a cis-trans isomerization. The general picture of the isomerization rates has been found to follow the pattern set by the analogous bis-ethylenediamine complexes.
INTRODUCTION
THE DIAQUATETaAAMMINECOBALT(III)cation in weakly alkaline aqueous solutions undergoes a tetramerization reaction [ 1]: 4 Co(NH3)4(H20)23+ + 6 O H [Co{(OH)2Co(NH3)4}:~] 6+ + 4 NH3 + 8 H20.
(l)
The T(H20)23+ ion (the symbol T will be used for the tetraammine moiety Co(NH3)4) behaves as a weak acid and on raising the pH forms the ions T(OH) (H20) 2+ and T(OH)2+; consequently the tetramerization reaction (1) will take an accordingly modified form. A kinetic study of reaction (1) has recently been started in our laboratory. At a fixed temperature (20-7°(2) the pH dependence of the observed rate constant could be explained from a reaction scheme in which the c i s - t r a n s isomerizations of the various tetraammine complexes play an important part [2]. Reaction (1) can be stopped by adding ammonia; in this way the c i s - t r a n s isomerizations referred to have been studied separately [3]. From this study it ensued that the c i s - t r a n s isomerization of the T(H20)23+ and the T(OH)._,+ ions goes mainly via the T(OH)(H20) 2+ species. In the study cited [3] direct measurements on the isomerization of this ion were not reported, as the relatively high rates presented a problem for the conventional spectrophotometric technique used. To fill this gap the present study reports stopped flow spectrophotometry on the reaction: cis-T(OH)(H20)
2+ (
, trans-T(OH)(H20)
1. A. G. Sykes and J. A. Weil, Prog. lnorg. Chem. 13, 1 (1970). 2. S. Bait and W. de Kieviet, lnorg. Chem. 11,2251 (1972). 3. S. Ball, R ecl. Tray. Chim. Pays-Bas 91, 1026 (1972). 2407
2+.
(2)
2408
S. BALT and P. M. KWANTES
The results obtained are used to further unravel the complicated pattern of the t e t r a m e r i z a t i o n r e a c t i o n (1). I n a d d i t i o n , f o r r e a c t i o n (1) t h e t e m p e r a t u r e d e p e n d e n c e o f t h e r a t e p a r a m e t e r s f r o m p H - s t a t m e a s u r e m e n t s is p r e s e n t e d to c o m p l e t e the picture. EXPERIMENTAL The chemicals and solutions used, together with details of pH-stat and pH calibration have been described fully elsewhere [2, 3]. pH-stat measurements [reaction (1)] Reaction (1) has been followed at different temperatures (accuracy 0.1 ~C) and constant concentration of the diaquatetraamminecobalt(III) perchlorate: 0.10M. The concentration of perchlorate has been kept constant at 1-00M. Constancy of the pH was assured within 0.03 pH units. Stopped flow measurements [reaction (2)] Construction of the instrument. The stopped flow Spectrophotometer has been built after the design of Gibson [4] in our laboratory by Musch and van Rooij. Here follows a short description of modifications introduced. Some more flexibility compared to the original design is attained by using quartz fibers in the optical connections between monochromator, observation chamber and photomultiplier, while the application of pneumatically driven valves facilitates the operation. The optical part comprises a Unicam SP 500 monochromator and a RCA IP28 Photomultiplier; the signal coming from this tube is fed into a logarithmic amplifier and then displayed on a Tektronix 564B Storage Oscilloscope. The electronic parts have been constructed by v.d. Linden and Kost. The mixing time is better than 2 msec, that is considerably smaller than the half-life of the reactions studied (see Tables 2 and 3). Kinetic measurements. The procedure followed was to mix rapidly equal volumes of 1) a slightly acidified (pH ca. 4) aqueous solution of diaquatetraamminecobalt(lll) perchlorate and ammonium perchlorate (1.00M) and 2) a buffer solution of 1.00M ammonium perchlorate and ammonia (0.100.40M). The constant ammonium perchlorate concentration assured Constant ionic strength. The rather high concentration of this salt was dictated by the minimum concentration of ammonia necessary to stop reaction (1); whether this was accomplished could be verified by studying the u.v. part of the absorbance spectrum of the mixed solutions [2, 5]. In all kinetic runs the total concentration of cobalt complex was kept at 10-2M; the temperature was adjusted by circulating thermostatted water around the mixing block, the observation chamber, and the syringes, of th~ stopped flow spectrophotometer. The temperature was constant within 0.1°12. The pH was measured immediately after mixing in a parallel experiment. The values reported could be reproduced within 0.02 pH units.
RESULTS Tetramerization I n a l k a l i n e s o l u t i o n s t h e t e t r a m e r i z a t i o n o f t h e T ( O H ) ( H 2 0 ) z+ a n d T ( O H ) 2 ÷ i o n s p r o d u c e s h y d r o x y l ions. I n t h e p H - s t a t m e t h o d p e r c h l o r i c a c i d is a d d e d d u r i n g t h e r e a c t i o n to k e e p c o n s t a n t p H . T h e a m o u n t o f a c i d u s e d a s a f u n c t i o n o f t i m e o b e y s a first o r d e r r a t e l a w a s w o r k e d o u t p r e v i o u s l y [2]. T h e p s e u d o first o r d e r r a t e c o n s t a n t [ h e r e a f t e r c a l l e d k l ( o b s d ) ] is a f u n c t i o n o f p H a n d t e m p e r a t u r e ( T a b l e 1). T h e a c c u r a c y o f t h e e x p e r i m e n t a l c o n s t a n t s is ca. 4 p e r c e n t , e x c e p t at 33.7°C, w h e r e t h e l i m i t s o f t h e m e t h o d h a v e b e e n r e a c h e d , t o t h e e x t e n t t h a t t h e m a x i m u m o f t h e k l - p H g r a p h [2] c o u l d n o t b e m e a s u r e d . F o r this t e m p e r a t u r e t h e a c c u r a c y is e s t i m a t e d at 7 p e r cent. I s o m e r i z a t i o n o f the T ( O H ) ( H 2 0 ) 2+ ion T h e i s o m e r i z a t i o n r e a c t i o n (2) h a s b e e n f o l l o w e d at different w a v e n u m b e r s ,
4. R. H. Gibson and L. Milnes, Biochem. J. 91, 161 (1964). 5. A. B. Hofman and H. Taube, lnorg. Chem. 7, 903 (1968).
Diaquatetraaminecobalt(lII) ion reactions
2409
temperatures, and pH. The observed stopped flow trace in all cases obeyed a first order rate law. The actual values of the rate constants [called k2(obsd)] were taken from a least squares analysis of the measured (between 0 and 80 per cent reaction) absorbance as a function of time (,4 t) by using the formula:
[At --A~] In [ ~ ] = - k,~(obsd),t
(3)
in an iterative fit for the constants k2(obsd), A0 and A~, A0 and A ~ are the absorbances at zero time and at equilibrium respectively [6]. This procedure was chosen because no exact value for A ~ can be measured directly, reaction (2) being followed by a much slower uptake of ammonia to form the pentaammine complex. From Table 2 it is evident that k2(obsd) is independent of wave number. Consequently the entries of Table 3, spreading over a much larger range of conditions, have been obtained from measurements at a single wave number: 19.200 cm -1, lying between the visible maximum of T(OH)2 + and that of T(H20)23+. it must be stressed here that a high accuracy in k2(obsd) is not possible as a result of the small changes in absorbance between the cis complexes and the cis-trans equilibrium mixture. The experimental value for k2(obsd) could be reproduced within 10 per cent. DISCUSSION
The pH dependence of the rate constants pertaining to the reactions under study are consistent with the following reaction scheme [2, 3]: cis-T(HzO)23+ ,
kss
cis-T(OH)(H~O) 2+ ,
, trans-T(H20)23+
k~
, trans-T(OH)(H20) 2+ ~
~ Co(NH3).~(NH2)(OH)(H20) ÷
® cis-T(OH)£ ~
q)
trans-T(OH)~ ÷
@
k,=
> intermediate leading to tetramer.
The indexing of the rate constants parallels the numbering of the complex ions. The acid-base reactions are instantaneous [7]; for these reactions the equilibrium constants are:
K,m --- A n" [H +] Am (this notation slightly differs from the one previously used [2, 3]). A,, is the concentration of the complex@; the activity [H +] follows from pH 6. D. F. Deter, Editor, Computer Programs for Chemistry, p. 117. Benjamin, N e w York (1968) 7. G. Schwarzenbach, J. Boesch and H. Egli, J. inorg, nucl. Chem. 33, 2141 (1971 ).
2410
S. BALT and P. M. KWANTES
measurements. Expressions for the observed rate constants k~ and k2 may now be derived.
Reaction (1) As explained elsewhere[2], the rate determining step of the tetramerization reaction is a dissociative reaction of either complex ® or complex ®, forming a reactive intermediate ® that rapidly combines with three tetraammine species to form the tetramer. The constant kl(obsd) is given by: a J [ H +] kl(obsd) = { 1 + Cl[[H+]}. { 1 + cd[H+]}
with al =
4 . k28. K24. k34, k2s. K24 " c1 = K13; c2 = k43 k43
(4)
if the mechanism is operative via complex ®. If the reaction goes via ®, the product k2s • K24 in the equations (4) must be substituted by krs • K47. It has been shown [2], that the k~(obsd) values at 20.7°(2 can be fitted with Eqn (4). This was done by using a steepest descend computer program on a IBM 1 130 computer applying a least squares criterium. Exactly the same procedure has been applied to the present k~(obsd) values. The parameter values are in Table 4, while Table 1 contains a comparison between observed and calculated rate constants. Table 4 Table 1. Results* of pH-stat experiments as a function of pH and temperature pH
103 • kl
pH
lOS.k1
(sec-1)
(sec-1) obsd calc.
7"50 8.00 8"30 8"70 9.00 9.30
14'9°C 0'27 0"52 0-80 0"92 0.90 0.69
7.00 8.00 8.30 8.50 8"70 9"10 9-30 9.50 9'70
20.7~'J" 0.07 0.16 1 . 0 8 1"23 1 " 9 3 1"92 2.43 2"37 2"80 2"68 2 " 5 5 2'60 2"10 2"22 1 " 6 0 1"75 1"33 1"28
0.24 0.56 0"78 0"94 0.88 0.69
obsd calc.
7-00 7.50 8.00 8"50 9.00 9"35
25.2°C 0.80 2.50 4.08 6.00 4.83 3.07
7"25 7"35 7-50 7"61 8.86 8.90
33"7°C 6.7 8"2 8'8 9.9 13"5 12"8 16"2 15"2 17"7 17 "5 16.2 16"5
*At ionic strength I = 1.00M. TFrom reference [2].
0.82 2.17 4.41 5"86 4.78 3"15
Diaquatetraaminecobalt(III) ion reactions
2411
Table 2. Pseudo first order rate constant for the isomerization reaction (2) as a function of wave number* Wave number (cm-')
102. k2 (sec-q
18.200 19.200 26.300 27.800
1.07 1.20 1.00 0.92
*t = 25.55°C; pH = 9.28; (NH3) = 0.25M; 1 = 1.00M. Table 3. Pseudo first order isomerization rate constant as a function of pH and temperature (stopped flow results)
pH*
(NH3)* M
10 2 . k2 (sec-') obsd. calc.~
k,13/k34
8-89 9-11 9"11 9'24
0' 10 0'15 0'15 0.20
22-60°C 1"00 0-94 0"63 0.67 0-66 0'67 0"55 0.53
5"5 4"8 4.3 4"0
8"42 8"77 8-99 9"13
0"05 0-10 0-15 0.20
25 "60°C 2"76 2'53 1.59 1"77 1'36 1.30 1.04 1.04
5" 1 4-9 5-2 4-9
8"37 8-37 8-93 9.06
0.05 0.05 0.15 0.20
28-30°C 4-72 4-28 4.08 4-28 2.00 2.09 1'72 1.68
6"0 5.7 6-7 6' 1
* After mixing the reagent solutions. tLeast squares analysis with Eqn (7).
also contains K13 from extrapolating the pH-stat graphs to zero time in the usual way [2]. Reaction (2) A relation expressing k2(obsd) as a function of pH can be deduced as follows. The pH region for the stopped flow experiments has been chosen in such a way t h a t t h e T ( O H ) ( H 2 0 ) 2+ c o m p l e x e s c o m p r i s e a n o n - n e g l i g e n t p r o p o r t i o n o f t h e
2412
S. BALT and P. M. KWANTES Table 4. Rate and equilibrium constants from fitting the tetramerization results* Temp. (°C)
1011. a l f (M. see -~)
109 • c2f (M)
14"9 20.7 25"2 33"7
0.90 1"73 8.90 54.9
5.40 2.52 8.50 4'76
10 TM. C2t (M) 5"80 8.15 9"50 57.2
109. K13' (M) 6'3 3"2 5"9 2"2
*1 = 1.00M ?Estimated accuracy in al is 5 per cent; in c~ and c2 20 per cent. ;tDetermined directly.
total amount of cobalt complex present. This means that the isomerizations via the T(OH)2 + ions (as given by the rate constants ka2 and k21) can be neglected, as the sum k~2+ kzl is much smaller than the sum kz4 + k4313], k2(obsd) may then be expressed as: k2(obsd) = ka4. [H +] k43. [H +] (5) [H +] + K13 + [H +] + K2~ Relation (5) may be simplified by observing that K13 and K24 refer to connected equilibria, so that:
Kz4 Kxa
k43[ka4 k21/k12"
(6)
In an earlier paper[3] the ratio k21/k12 has been estimated from the assumption that the molar absorbance coefficient of the trans-T(OH)2 + ion is half that of the corresponding cis compound. This assumption is based on the similarity in chemistry and absorption spectra between the tetraammine complexes under investigation and the analogous bis-ethylenediamine complexes, for which this relation holds. The identical assumption for the T(OH)(H20) 2+ ions enables us to calculate the gross equilibrium constant (cis[trans) for the mixture of T(OH) (H20) z+ and T(OH)2 + isomers from the stopped flow results. If the ratio k43/k34 differs considerably from the value of k21/k12, the gross equilibrium constant calculated in the way indicated above, will show a pH dependence, as the amount of the tetraammine present as T(OH)(H20) 2+ is a function of pH. Now the values obtained for the gross equilibrium constant cisltrans (last column of Table 3) not only are independent of pH at a fixed temperature, but also change very little on changing the temperature. The actual value calculated is very nearly equal to k2~/ka2: this constant has been found [3] to be nearly constant at the value 4 from 20 to 35°C. All this means that k43/k34 may be put equal to k2~]k12(therefore the last column of Table 3 has already been headed k43/kz4) and consequently K~3 = Kz4. After rearranging relation (5) transforms to (7): 1
1
1
k 2 ( o b s d ) = (k34 -[- k43) "[" [H+~
KI~ "(k34"-[-k43)"
(7)
Diaquatetraaminecobalt(Ill) ion reactions
2413
Table 5. Parameters used to fit the stopped flow results Temp. (~)
102.(k34+k43) (sec -1)
22.6 25.6 28-3
2.5±0-4 3.8±0.6 7.1±1.0
10~.K,z (M) 2.1±0.4 2.0±0-4 2.8±0.5
A least squares analysis of the values in Table 3 using the relation (7) gives the parameter values of Table 5. In passing it may be noted that we are now in the possession of three sets of values for the equilibrium constant K,3: the set of directly determined values and the ones obtained from the fitting procedure of Eqn (5) (both in Table 4) and the values of Table 5. Unfortunately no value for K,3 has been published for conditions that resemble the present ones. From the three sets obtained in the present work Table 5 has the smallest values for K,3. This might signify that the assumptions involved are not one hundred percent justified. All the same we may state that in view of the many assumptions and fitting analyses involved, agreement between the three sets of Ka3 is quite satisfactory. We are now in a position to calculate the individual constants k:~4and k43 at the three experimental temperatures and subsequently to apply a least squares activation analysis [8] to the resulting values, from which: k34
AH # ----24.1 _ 2.2 AS# = 12.3±4-0
k43
33.1 _ 2-2 kcal. mol-' 45.7_4-0e.u.
Table 4 compares the initial k values with the ones calculated from the activation parameters.
Combination of reaction (1) and reaction (2) The results of the stopped flow and the pH-stat experiments may be brought together by substituting the quotient k43/k34 from the stopped flow experiments (after a proper temperature extrapolation from the activation parameters given above) into the fitting constant a, of Table 4 to give k2s [equation (4)]: this is the entry kz8 (a) of Table 7. A combination of al and c2 from Table 4 gives k.~4,also housed in Table 7. It is satisfactory that both sets of k34 obtained so far (in Tables 6 and 7) are in very good agreement. Except at 25°C the values calculated from the stopped flow activation parameters are very close to the ones independently deduced from the pH-stat experiments [see Table 7, entries (c) and (d)]. To kz8 a least squares activation analysis has been applied: AH # = 57.2 ± 1"0 kcal. mo1-1 AS # = 125.8__+2-2e.u.
1 = 1.00M
8. A. A. Frost and R. G. Pearson, Kinetics and Mechanism, 2nd Edn. John Wiley, New York (1961).
2414
S. BALT and P. M. KWANTES Table 6. Isomerization rate constants for the T(OH)(H20) 2+complexes Temp. (°C) 22.60 25-60 28.30
102 • k34 (see-5 0.44* 0.63* 1.00"
0"43t 0.67t 0"97t
1 0 2 • k4z
(sec-q 2"1" TOt 3"2* 3.5t 6.1" 5.8t
*Calculated from k34+ k43 in Table 5 and the ratio k43/k34of Table 3. tCalculated from the least squares activation parameters. Table 7. Rate constants from a combination of pH-stat and stopped flow results Temp. (°C) 14.9 20.7 25.2 33"7
kzs (sec -1)
10 2 .
0.10" 0"6* 1.9* 48*
0.08t 0'6t 2"7t 40t
10 2 - k34
(sec -~) 0 . 4 5 0.2§ 0.5~: 0.3§ 2.3:~ 0-7§ 2"55 2.1§
*Calculated as worked out in the text. tFrom activation parameters (see text). tCalculated from the pH-stat parameters. §From stopped flow activation parameters. AS # is c o n s p i c u o u s l y high. T h e r e f o r e t h e a l t e r n a t i v e m e c h a n i s m f o r t h e t e t r a m e r i z a t i o n v i a t h e a m m i n e c o n j u g a t e b a s e o f t h e trans-T(OH)(H20) 2+ion h a s a l s o b e e n a p p l i e d . I n this c a s e t h e a c t i v a t i o n a n a l y s i s g i v e s f o r t h e i n s e p a r a b l e p r o d u c t k78. K4r t h e f o l l o w i n g p s e u d o a c t i v a t i o n p a r a m e t e r s : A H # = 49-0___ 1.0 kcal. mo1-1. AS # = 60.0___3.1 e.u.
I = 1.00M
T h e s e v a l u e s in o r d e r o f m a g n i t u d e r e s e m b l e t h e o n e s f o u n d f o r a g e n e r a l S N 1CB m e c h a n i s m [9]. T h i s c o u l d b e a n i n d i c a t i o n f o r this k i n d o f m e c h a n i s m , b u t it c e r t a i n l y is n o p r o o f .
Consequence for acidic solutions The picture of the isomerizations worked out above for alkaline solutions may b e e x t e n d e d to a c i d i c s o l u t i o n s , f o r w h i c h t h e a c i d - b a s e e q u i l i b r i a a r e d o m i n a t e d 9. F. Basolo and R. G. Pearson, Mechanisms of Inorganic Reactions, 2nd Edn. John Wiley, New York (1967).
Diaquatetraaminecobalt(l 11) ion reactions
2415
by the constants K35 and K46. Only at 20°C an unambiguous value for the first step of acid dissociation of the d i a q u a t e t r a a m m i n e c o b a l t ( I I I ) ion is available: K35 determined by S c h w a r z e n b a c h et al.[7] with a stopped flow technique for p H m e a s u r e m e n t , at the ionic strength of 0.10M. F r o m a previous p a p e r by one of us [3] it follows that: k:~4 . K:~z-l-k43. K46 = 3.2. 10-7
M. s e c - '
(8)
(extrapolated to 20°C; 1 = 0-20M). K35 at 1 = 0.20M m a y be calculated from the value at 1 = 0.10M in the way indicated by Bjerrum[ 10]. T h e present study did not allow experiments at a lower ionic strength than 1M. T h e isomerization rate constants m a y h o w e v e r be e x p e c t e d [8] and indeed have been shown [2, 3] not to be influenced much by the ionic strength, so the values f r o m the present work extrapolated to 20°C m a y be substituted into equation (8). Then: K46 = 2-7
.
10-SM
(I = 0.20M; 20°C)
(K:~5 = 0.14.10-SM)
and, with a relation analogous to (6): k6.~/k,~ = 75.
This result is substantiated by the fact that acidified solutions of the c i s - T ( H 2 0 ) 2 :~ ion show no isomerization [3]. T h e difference between K35 and K46 together with the r e s e m b l a n c e b e t w e e n K24 and K,.~ reported here for the t e t r a a m m i n e c o b a l t ( I I I) c o m p l e x e s has also been o b s e r v e d for the corresponding b i s - e t h y l e n e d i a m i n e complexes [ 1 1]. CONCLUSION T h e present study has provided a consistent picture of the isomerization and tetramerization reactions of the t e t r a a m m i n e c o b a l t ( I I I ) ions. At the m o m e n t it is too early to say m o r e about the activation p a r a m e t e r s involved or to try to outline details of the p r o p o s e d mechanism. W e intend to shortly publish a study about the reactions of the t e t r a a m m i n e ions with a m m o n i a ; it is hoped that a link can then be made with the present work. Acknowledgements-Construction of the stopped flow spectrophotometer and the pH-stat by the
technicians mentioned in the text is gratefully acknowledged. The authors also wish to thank Professor Dr. J. M. Los for computer facilities. 10. J. Bjerrum, Metal Ammine Formation in Aqueous Solution P. Haase and Son, Copenhagen, (1941). I 1. J. Bjerrum and S. E. Rasmussen,Acta chem. stand. 6, 1265 (1952).