5591
Kinetic Study of the Hydrolysis of (NH,) ,COCO,+ D. J. Francis and Robert B. Jordan Contribution from the Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada. Received April 4, 1967 Abstract:
The hydrolysis of (NH3)bCoC03+was found t o follow the rate law -d In [complex]/dt = kl'[OH-]-l = 1.0 ( N a N 0 3 ) between 45 and 5 5 " . The ks[OH-] path has been attributed t o the normal alkaline hydrolysis of (NH&CoC03+ with AH* = 30.0 kcal mole-', A S * = 18 eu, and kf = 3.3 x 10-6 M-1 sec-1 a t 25" (by extrapolation). The kl'[OH-]-' term is consistent with the uncatalyzed hyin which case kl' = klK,,./K1 where K I is the acid dissociation constant of the bicardrolysis of (NH3)5CoC03H2+, bonatocomplex. Byextrapolationto 25", k l / K l = 4.2 X IO6 M-' sec-l, AH*= 17.1 kcal mole-', and AS* = 30 eu. Further kinetic studies a t 25", p = 1.0 (NaC104), and p H 8.5 t o 9.5 in carbonate buffers have permitted a determination of K1 = 5.9 x 10-9 M and k l = 2.3 X lo-* sec-l. The equilibrium constant Kf for the reaction (NH3)sCoOH2+ HC03- % (NH3)5CoC03H2+ OH- has been determined as 3 X a t 25", p = 1.0 (NaC104).
+ ks[OH-] a t 0.02 to 1.00 M N a O H and
+
+
T analysis
he hydrolysis rate constant and pK, of bicarbonatopentaamminecobalt(II1) have been derived from of the variation of rate of carbonate exchange with pH.ls2 The present study reports a direct measurement of these values as well as the formation constant of the complex. The values found have led to a reinterpretation of the previous carbonate exchange data. Also the rate constant for the hydroxide ion catalyzed hydrolysis of carbonatopentaamminecobalt(II1) has been determined. The activation parameters for this process compared to those for hydrolysis of the bicarbonato complex indicate the differences to be expected for Co-0 and 0-C bond breaking.
optical densities were determined after at least eight half-times. These data gave good linear first-order plots for at least 95 reaction. The carbonate buffer concentration (about 0.020 M ) was sufficiently high relative to the carbonato complex concentration M ) so that the pH will remain constant during the (about hydrolysis reaction. The pH of the buffered reaction medium was measured with a Beckman Expandomatic pH meter with a 1 pH unit scale expansion. The measured pH was corrected for sodium ion error. This correction was negligible below pH 9 and was 0.024 pH unit at the highest pH used. From the known amounts of total carbonate and hydroxide added to the buffer solutions and the measured pH it is possible to calculate the acid dissociation constant of HC03in 1 M NaC104. Our calculated value of 2.75 + 0.10 X 10-lo is in good agreement with the value of 2.7 X 10-lO also in 1 M NaC104determined by Frydman, et aL6
Results Experimental Section Preparation and Analysis of Complex Salt. Carbonatopentaamminecobalt(II1) nitrate was prepared according to the method of Lamb and Mysels3 and stored over calcium sulfate. The analysis of the complex for cobalt4 and ammonia6 agreed with the formula ((NH&CoC03)(N03).1S H 2 0 reported by Lamb and Mysels. Anal. Calcd for ((NH3)jCoCO3)(N03). 1.5BO: Co, 20.1 ; "3, 29.07. Found: Co, 20.9; NH3, 29.1. The purity was also checked by comparing the spectrum of the acid hydrolysis product of the carbonato complex to the known spectrum of C o O H P . The results gave a calculated molecular weight of 287 z!= 3 compared to the predicted value of 292. This deviation and the slight discrepancy in the other analysis are probably due to partial dehydration of the compound. Base-Hydrolysis Kinetics. Solutions containing sodium hydroxide and sodium nitrate (to adjust the ionic strength to 1.O M ) of known concentration were brought to temperature equilibrium. A weighed quantity of the carbonato complex was added to the reaction solution. Aliquots were taken at various times, filtered through a 0.45-p Millipore filter (Millipore Filter Corp., Bedford, Mass.) to remove any cobalt oxide formed, and diluted to volume. Optical densities of the diluted filtrate were determined at 328 mp on a Bausch and Lomb Spectronic 505 spectrophotometer. Solutions for the kinetic measurements at 25" and low pH were prepared by adding varying volumes of a solution of carbonato complex in sodium hydroxide to a known volume of sodium bicarbonate solution in a 5-cm cell. All solutions were adjusted to 1.0 M ionic strength with sodium perchlorate before mixing. The solution containing the complex ion was added from a syringe, and the change in optical density (295 mp) with time was recorded as soon as possible (usually about 15 sec) after mixing. Infinite time (1) (2) (3) (4) (5)
D. R. Stranks, Trans. Faraday SOC.,51, 505 (1955). G. Lapidus and G. M. Harris, J . Am. Chem. SOC.,85, 1223 (1963). A. B. Lamb and K. J. Mysels, ibid., 67, 468 (1945). R. E. Kitsen, Anal. Chem., 22, 664 (1950). H. A. Horan and H. J. Eppig, J . Am. Chem. SOC.,71, 581 (1949).
The variation of the rate of hydrolysis of (NH3)SCoco3+ with hydroxide ion concentration at 45-55" is consistent with the rate law
-
dt
+
= kl[(NH3)5C~C03H2+]
where [TI represents the concentration of total carbonato complex ( N H 3 ) b C o C 0 3 + plus ( N H 3 ) 5 C o C 0 3 H 2 + ; Kl is the acid dissociation constant of ( N H 3 ) 6 C o C 0 3 H 2 + and K, is the ion product of water. Under the conditions of our experiment the hydroxide ion concentration was always in large excess over the complex and K1 >> [H+]; therefore the rate law may be represented by d[T1 - kobsd[T] dt
=
The expression for kl' can be found by comparison with eq 1. The values of kobsd determined experi(6) M. Frydman, G . Nilsson, T. Rengemo, and L. G . SillCn, Acta Chem. Scand., 12, 878 (1958).
Francis, Jordan
Hydrolysis of (NH3)6CoC03+
5592
mentally at 50" and the values calculated from the best fit values of kl' and kz are given in Table I. These data are typical of the fitting obtained at 45 and 5 5 " . The values of kl' and k2 at the three temperatures are given in Table I1 along with values of kl/Kl. The latter were calculated from kl' using values of K, at the appropriate temperature estimated from the data of Harned and Hamer.' Values of AH* and A S * for k l / R and kz were determined in the standard way from transition-state theory. Table I. Variation in the Rate of Hydrolysis of (NH3),CoC03+ with [OH-] at 50", p = 1.0 (NaN08)
where Kz = [(NH3)5CoOH2+]/[(NH3)bCoOHz3+][OH-]. Let the total concentration of carbonato compiex at zero time be [TI,, at any time be [TI, and at equilibrium be [TI,. Then applying the equilibrium and stoichiometry conditions [(N H 3)
COCO aH 2+]
= -___ [H+l
Ki
+ [H+l [TI
(5)
where Kl is the acid dissociation constant of the bicarbonato complex as defined previously. Table 111. Hydrolysis of (NH&CoC03 + at 25", p = 1.0 (NaC104) kobsd X lo3 SeC-'
0.020 0,040 0.060 0.100 0.200 0.500 0.800 0.900 1.00 a
22.3 12.2 9.00 5.97 5.37 9.00 12.6 14.8 16.7
Calculated from kobsd = (0.44/[OH-]
22.3 11.6 8.26 6.01 5.42 8.93 13.4 14.9 16.5
+ 16.1[OH-]) X
Table 11. Hydrolysis Rates of (NH8)5CoC03f ki/Kia X ki' X lo5
Temp, "C
M sec-I
45 50 55
0.19 0.44 0.82
10-8 M-' sec-1
AH*, kcal mole-'
0.27 0.45 0.62 17.1 18
AS*, cal mole-' deg-1
k p x lo5 M-1
eo X 10-3
8.492 8.648 8.695 8.763 8.855 8,960 9.013 9.148 9,237 9.294 9.338
2.32 2.44 2.32 2.40 2.38 2.57 2.39 2.41 2.39 2.22 2.28
,E
X 10-3
Found
Calcdb
1.630 1.645 1,581 1,575 1 ,590 1.515 1.575 1.445 1,420 1.390 1.355
26.2 19.5 18.0 15.9 11.8 10.5 9.62 5.87 4.68 4 68 4.22
26.7 19.1 18.0 15.0 13.1 16.2 9.46 6.04 4.94 4.87 3.91
Corrected for sodium ion error. * Calculated from eq 7 using kl = 2.26 X lo-* sec-' and Kl = 5.94 X 10-9 M .
sec-1
At equilibrium the forward and reverse rates are equal, so that
8.1 16.1 35.2 30.0 30
a kl' = k l K , / K , . Values of K , used are for 1.01 M KCI as calculated from ref 7. Ionic strength 1.0 adjusted with NaN03.
The results of the experiments at low pH and 25" are presented in Table 111. The value eo is the optical density at zero time (obtained by extrapolation) divided by the total cobalt(II1) complex concentration, E, is the optical density at infinite time also divided by the total complex concentration. The observed rate constants kobsd were determined from plots of log ( e t ern)against time. Extrapolation of the high-temperature results to 25 O shows that only the first term in the rate law will be important in the pH range 8.5 to 9.5 studied here. Therefore the rate data have been interpreted in terms of the reaction ki
(NH;)jCoC03H2+
PHa
+ Jr (NH3)jCoOHp3+ + HCO3-
(3)
Substituting from ( 5 ) and ( 6 ) into (4) and collecting terms gives the observed rate constant
The concentration ratio [T]o/([T]o - [TI,) can easily be expressed in terms of the apparent extinction coefficients (e) defined previously. Then (7)
The optical density due to (NH3)bCoOH2+was neglected because its measured extinction coefficient was only 1 of that of the carbonato complexes. Rearrangement of (7) gives
k- 1
The rate of decomposition is given by d'T1 - kl[(NH3)5CoC03H2+]dt
(7) H. S . Harned and W. J. Hamer, J . A m . Chem. SOC.,55, 2194 (1933).
JournaI of the American Chemical Society
89:22
Using the data in Table I11 a plot of EO/[kobsd(EO - E,)] against [H+]-l was found to be linear as shown in Figure 1. Values of kl-l and kl/Kl were derived from a least-squares fit of the data to a straight line. From this treatment Kl = 5.94 x 10-9 M and kl = 2.26 X l e 2 sec-' at 25" in 1 M NaC104. These results give kl/Kl = 3.9 X 106 M-l sec-1 at 25" in good agreement
1 October 25, 1967
5593
Figure 1. Plot of t O ( ( t O- t,)kobrd]}-l gives K i l and the slope equals kllK1.
DS.
[H+]-l. The intercept
with the value 4.2 X lo6 obtained by extrapolation of the high-temperature results. It is also possible to calculate the formation constant Kf for the bicarbonato complex
Kf =
[(NH~)~COCO~H~+][~H-] (9) [(NH3)sCo0H2+][HCO3-]
+
Figure 2. Plot of ( k e l - e,(Kl H+)}[H+]-’ DS. e,Kw([H+l. [HC03-])-1. The intercept equals €2, the extinction coefficient of Co(NH&COaHZ+, and the slope equals Kf-l.
It can be shown that
where Kl is the acid dissociation constant of (NH3)6CoC03H2+defined previously, and el and e2 are the molar extinction coefficients of the carbonato and bicarbonato complexes, respectively. The value of Kl was determined as described and el was measured at various hydroxide ion concentrations greater than 0.05 M where hydrolysis is slow and the only species present is (NH3)5CoC03+. However the value of e2 could not be measured directly because the hydrolysis is too fast at low pH where (NH3)6CoC03H2+ would be the predominant species. In principle, knowing el and Kl it should be possible t o calculate e2 from the eo values, since at zero time the only absorbing species are the carbonato and bicarbonato complexes. However the eo values in Table I11 do not show a smooth trend with pH. This randomness is most probably due to the error in extrapolating back to the zero time of mixing. In fact, as shown in the subsequent treatment where a value of e2 is derived, very little variation is expected in eo, and the observed values are generally within 10 % of the expected value. The values of €2 and Kf have been obtained by fitting the em values to a rearranged form of eq 10
The values used for €1, KI, and K, are 2180, 5.94 X 10-9, and 1.7 X 10-14,8respectively. The bicarbonate
ion concentration was calculated from the pH and bicarbonate acid dissociation constant, 2.75 X 10-l0, calculated from the pH of various carbonate buffers in 1 M NaC104. The resulting plot was found to be linear as shown in Figure 2. A least-squares fit of the data to a straight line gave Kf = 2.97 X l e 4 and e2 = 2134.
Conclusions The rate law for the hydrolysis of (NH3)5CoC03+ is -d In [complexlldt = kl’[OH-]-l k2[0H-1. The second term is consistent with the normal hydroxide ion catalyzed hydrolysis of pentaamminecobalt(II1) complexes. Other evidencela indicates that these reactions proceed by an S N ~ C Bmechanism. The present results are consistent with such a mechanism but do not substantiate it further. The first term, kl’[OH-]-’, in the rate law has been interpreted as due to the aquation of (NH&CoC03H2+. Previous tracer studies“ have shown that this aquation proceeds with 0-C bond breaking. The hydrolyses of the analogous protonated oxalate and phosphate’3 complexes indicate that the activation enthalpy for the hydrolysis of the protonated species is close to that
+
(8) R. Nasanen and P. Merilainen, Suomen Kemisfilehti, 33B, 149 (1960), as quoted in ref 9. (9) “Stability Constants,” Special Publication No. 17, The Chemical Society, London, 1964. (10) C. H. Langford and H. B. Gray, “Ligand Substitution Process,” W. A. Benjamin, Inc., New York, N. Y.,1965, pp 67. (11) J. P. Hunt, A. C. Rutenberg, and H. Taube, J. Am. Chem. SOC., 74, 268 (1952). (12) C. Andrade and H. Taube, Inorg. Chem., 5, 1087 (1966). (13) W.Schmidt and H. Taube, ibid., 2, 698 (1963).
Francis, Jordan / Hydrolysis of (NH3)6CoC03+
5594
for the unprotonated form. Therefore the difference of rate = (1'9 10-3)[Hf1 [ ( N H & C O C O ~ + ] ~(12) ~~,~ 13 kcal mole-' in this case is consistent with the breaking (6 X [H+l of a different bond in the hydrolysis of (NH3)jC03H2+. The value of 13 kcal mole-' is based on the assumption The fact that the rates calculated from eq 12 agree that the AH for Kl is small compared to the AH* for k1. within =t6x with the exchange rates implies that the The temperature dependence of the acid dissociation carbonate ion exchange rate can be explained adeconstant of the bicarbonate ion and of oxalatopentaquately by a hydrolysis mechanism without involving amminecobalt(II1) are consistent with this assumpcarbonate ion attack on the carbonato complex, tion. However the kl value is still about a factor of 10 It is possible that the rate law could contain a third smaller than the directly measured value. At least term which would be independent of acid and might part of the difference can be attributed to the differences correspond to either uncatalyzed aquation of (NH3)5- in ionic strength, which was about 0.08 M for the C o c o 3 + or the hydroxide ion catalyzed hydrolysis of exchange and 1.00 M in this work. Based on studies (NH3)jCoC03H2+. The results are consistent with of analogous complexes 1 4 , 1 5 the activity coefficient is such a term, but if such a term exists it must have an expected to decrease by about a factor of 5 with an apparent rate constant not larger than the value for increase in ionic strength from 0.08 to 1.0 M . It is kl' and it never contributes more than 10% to the not possible to predict quantitatively the effect of carover-all rate. Therefore it cannot be determined bonate ion pairing but it is expected to be small beaccurately and inclusion of such a term does not imcause of the large size and low charge of the ions inprove the fit between experimental and calculated obvolved. served rate constants. The above analysis, indicating that there may not be The acid dissociation constant of (NH3)jCoC03H2+ a carbonate ion dependent term in the exchange rate is approximately 20 times greater than that of the free of (NH3);CoC03+, might be questioned on the basis bicarbonate ion, both in 1 M NaC104. Previous results that there is such a term in the rate law for carbonate on complexed H02C202- and H2P04-l 3 indicate that exchange of chelated carbonatoamminecobalt(II1) comthe complexed ligand has a K, about 40 and 100 times plexesU2 This term is too significant in the rate law larger, respectively, than that of the free ion. Thus for the latter complexes to be eliminated by a simple the acid dissociation constant is in agreement with juggling of rate and equilibrium constants. However, estimates which can be made from values for other the results of Scheidegger and Schwarzenbach16 on ligands complexed to cobalt(II1). carbonatobisethylenediaminecobalt(II1) indicate that Previous work on the rate of 14C032-exchange on the chelate C03*- ring opens rapidly and the complex carbonatopentaamminecobalt(II1) has given a value of exists largely in the monodendate form below pH 10. 3.8 X M for Kl and 7.8 X sec-' for k l . The If this result is assumed to apply generally to other Kl value is in reasonable agreement with that reported carbonato chelates, then these complexes may undergo here; however, our hydrolysis rate constant is about carbonate exchange through a dicarbonato complex a factor of 30 larger (Table IV). as outlined for (en)2CoC03+.
+
Table IV. Hydrolysis and 14C03z-Exchange Rates of (NH3)5C~C03+ at 25'
, OHC
~~
PH" 9.31 8.75 9.10 8.80
Exchange rateb x M sec-' 5 3 10 6 8 8 16.8
Hydrolysis ratec x 10-6 M sec5 5 11.3 8.9 15.8
-~ a The pH, complex concentration, and carbonate ion concentrations used are those given in Table 2 of ref 1. * Calculated from the rate law of Lapidus and Harris2using concentrations as noted in footnote N . c Calculated from eq 12 assuming only a hydrolysis mechanism.
In attempting to determine the reason for the discrepancy in the values of the hydrolysis rate constant, we have tried to fit the exchange rate data to a simple hydrolysis mechanism, using the value of K1 determined in the present work. The exchange rates were calculated for solution concentrations given by Stranks (Table 2 of ref I), taking these concentrations as representative experimental conditions. The rates were calculated from the rate law of Harris and Lapidus. These rates are compared to those calculated from eq 12, which assumes only a hydrolysis mechanism for exchange.
(en)*Co 'OC0,H
+ HI4CO3-
d0W
(en)
c
,O-l4COZH O\O-CO2H
+ OH-
This mechanism is only open to the chelated carbonate complexes, and a carbonate ion dependent exchange rate is to be expected for these complexes but not for (NH3);CoC03+. It should also be noted that the formation of the dicarbonato complex may proceed with 0-C bond making since the aquation of these complexes is known to involve 0-C bond This possibility is consistent with the fact that the carbonate ion dependent exchange rate has the same activation energy for all the chelate systems studied2 except the trimethylenediamine, where steric factors may be important. Oxygen-18 tracer experiments currently in progress should establish if this mechanism is correct. Acknowledgment. The authors wish to acknowledge the financial support of the National Research Council of Canada. (14) W. L. Masterson and J. A. Scola, J . P h j , ~Chem., . 68,14 (1964). (15) C. H. Brubaker and T. E. Haass, ibid., 65,866 (1961), and refer-
ences quoted therein. (16) H. Scheidegger and G. Schwarzenbach, Chimia, 19, 166 (1965). (17) F. A. Posey and H. Taube, J . A m . Chem. Soc., 75, 4099 (1953).
Journal of the American Chemical Society / 89.22 J October 25, 1967
