KOTRAV. KRISHNAWRTY AND GORDON M. HARRIS
346
for the heat of formation of Tho(&, AHOm (form) = -8.0 kcal./mole. Combining this value with the dissociation energy of oxygen and our heat of sublimation of thorium metal yields a dissociation heat a t 1883°K.for ThO(g) of +200.0 kcal./mole corresponding to Doo(ThO) = 196.1 kcal./mole. This is to be compared with Brewer'sfo estimated value of 200 :i= 20 kcal./mole. Further work on the reaction of thorium with thorium dioxide and with oxygen is in progress.
Acknowledgment.-The
VOl. 64 authors wish to thank
Dr. S. J. Yosim and Dr. D. E. McKenzie for many enlightening discussions and Romuald Zalubas of the National Bureau of Standards for providing us with his preliminary data on the spectra of thorium. (30) L. Brewer, "Dissociation Energies of Gaseous Oxidea," Univeraity of California Radiation Laboratory, U. 9. Atomic Energy Report UCRL-8356, 1958.
SUBSTITUTION REACTIONS OF OXALATO COMPLEX IONS. 11. KINETICS OF AQUATION OF TRISOXALATOCHROMIUM(III) IONSOLVENT DEUTERIUM ISOTOPE EFFECT BYK ~ T RV. A KRISHNAMURTY AND GORDON M. HARRIS Department of Chemistry, University of Bufllo, Buflab, N . Y. Received Ssptambm SO, 196s
The kinetics of aquation of the ion Cr(G0,h-a have been studied as a function of complex ion concentration, acidity, added oxalic acid, tem rature and heavy water solvent composition, wing a spectrophotometric method. The total reaction in strong1 acitf%lution is cr(G04)J-a 2&0+ + Cr(C204)dHzO)*- HICs04. The following rate law is co~ik''(&0+)~Cr(C~O,)r-~). The &tent with the oiserved kinetic data -d(Cr(GO4)~-~)/dt = k'(&0+)(Cr(cd?4),-J) mixed order with respect to (H+) is interpreted in terms of a rapid pre-equdibration of complex with one proton, followed by @el ratedetermining reaction paths involving either non-catalyzed or acid-catalyzed displacement of oxalate. Expenmenta in H*O/D,O solvent mixtures show that the rate of aquation increaaes aa a function of deuterium atom fraction in agreement with the Grosa-Butler equation. This finding is consistent with the proton pre-equilibration postulate made here, and in an earlier study of the oxalate exchange reaction of Cr(CZO4h-*ion. Some exchange experiments using carbon-14 labelled feeoxalate-Cr(G04MHtO~-ion mixtures indicate that oxalate exchange with the latter ion occurs a t a negligible rate, even under conditions where exchange with Cr(CzO4)a-8 ion is quite rapid.
+
+
I n the first communication in this Series' a study of the kinetics of oxalate exchange of the trisoxalato chromium(II1) ion was reported. A mechanism waa proposed which waa consistent with the rate data, and part of which consisted of the acid-catalyzed aquation of the tris-oxalato ion to produce a m a l l equilibrium concentration of bisoxalatodiaquochromium(II1) ion. It was thus deemed worthwhile to supplement this exchange investigation with cognate work along two linesfirstly, an attempt to study the rate of the oxalate exchange reaction of the bis-oxalatodiaquo ion, and secondly, an attempt to determine the kinetics of the acid-catalyzed aquation of the trisoxalato ion. The first of these aims has been only partially accomplished, due to complications discussed below. The aquation reaction has proved amenable to detailed study, and a report on it forms the major part of this paper. Four previous studies involving the Cr(C20,),(H20)%-ion are of significance to the present work. H a m and Perkins2 investigated the kinetics of the reaction Cr(Chh(H:,Oh-
+ Ch- +Cr(Ch)i-' + 2H20
where Ch = oxalate or malonate. The rates were first order in the diaquo-chromium species and independent of added anion concentration. They were also independent of pH over the range on each aide of the neutral point within which acidic (1) F. D. Gradano and G . M. Harris. THISJOVBNAL. a,330 (1969). (2) R. E. Hamm m d (1966).
R. H. Perkina, J .
A n . Cbm. Bocc.,W , 2083
+
or basic decomposition reactions of Cr(Ch)3-3 are negligibly slow. For the oxalate, this range was from 4.0 to 9.3, and within these limits the association appeared to be completely unidirectional as written, with a half-time of 26 minutes a t 50". Dutt and SurS attempted to determine the stepwise instability constants of Cr(C204)3-3,and found that only the first step is observable even with acid concentration as high as 0.16 M , clearly indicating the great stability of the diaquo ion. Studies of the truns-cis isomerization of Cr(Cz04)2(HzO)z-ion have been made independently by Hamm4 and by Cunningham, Burley and Friend.6 The trans to cis reaction goes essentially to completion in aqueous solution, is first order in complex, independent of pH, and only slightly affected by ionic strength. The reaction half-time is less than 3 minutes a t 50". Experimental Materials.-Crystalline &Cr(C204)l.3Hz0 and cisKCr(G04)2(H*0.)l.2Hz0were prepared accordingto ublished procedureaeJ uslng reagent grade chemicals. TEe purity of each salt was checked by analysis. Oxalate waa determined permanganometrically after decomposing the complex with hot KOH, filtering off the Cr(OH)r, and acidifying the filtratewith HW4. The Cr(OH), precipitate, after washing free of alkali, was ignited to Cr201 and weighed to determine the chromium. The found oxalate-chromium ratios were 2.96 and 1.99,respectively, for the tris and bis complexes. a.
(3) N. K. Dutt and B. Sur, 2.onorp. allgem. Cham.. 491, 195 (1957). (4) R. E. Hamm, J . Am. Chum. Soc., 76, 609 (1953). (5) 0. E. Cunningham, R. W. Burley and M. T. Friend, Nafurs. 166, 1103 (1962). ( 6 ) H. Croft, Phil. Mog., S l , 197 (1842). (7) A. Werner, Ann., 406,261 (1914).
March, 1960
THEKINETICSOF A Q U A T I O N OF TRISOXALATOCHROMIUM(III) 347
Absorption spectra of the two oxalato complexes were run in l-cm. Corex cells in a Beckman Model DK-2 Spectrophotometer. The observed peak wave lengths and correspondin molar absorption coefficients were: tris-oxalato. 420 an 573 mp, 137.5 and 68.9, respectively; cis-bis-oxalato, 416 and 562 mp,. 67.3 and 52.0, respectively. Baker C.P. perchlonc acid and G. F. Smith anhydrous sodium perchlorate were used without further purification. All other standard chemicals were of reagent grade. Commercial carbon-14 labelled oxalic acid solution of high specific activity waa diluted with inactive potassium oxalate to give a stock solution such that when precipitated aa Cac&* HzO the counting rate by conventional thin solid-sample counting technique waa about 600 counta/mg./min. C?free water from an ion-exchange purifier waa used in makmg all solutions. 99.5% heavy water waa obtained from the Stuart Oxygen Company. b. Exchange Studies.-Calculated volumes of 0.05 M KCr(Cs04MHsOb and of standardized solutions of HClO4 and/or-NaClO, were mixed in 40-ml. glass-stoppered centrifuge tubes and theimostated, as also waa the stock solution of labelled oxalate. Reaction waa commenced by pipetting aliquots together with rapid mixing. Three-ml. samples were withdrawn at intervals and quenched by adding 4 ml. of solution 0.25 Mr in each of CaCL, NH4Cl and HOAc. The precipitated CrrCz04.H10waa separated immediately by centrifugation, washed and counted according to established procedure.' A check of the separation method showed that recovery of the fre'e oxalate was not quantitative a t higher acidities due to the solubility of the precipitate in acid. However, specific activity determinations of the sampleswere generally reproducible within *lye. At the lower acidities, oxalate recovery was complete, but the experiments were complicated by the ra id reaction between Cr(CZH4)t(H*O)2and free oxalate ion azeady mentioned. c. Aquation Studies.-Kinetic runs were made in a Beckman Model :DU Spectrophotometer, using a thermostated cell compartment capable of temperature control 10.2'. Calculated volumes of standardized solutions of HC104 and NaClO,, diluted with the necessary amount of water, were mixed in a 25-ml. volumetric flask and brought to tem erature equilibrium in the bath used to thermostat the c e i compartment. The required volume of 0.05 M I(pCr(CaO4)a stock solution, similarly thermostated, was pipetted into the reaction flask with thorough mixing. A portion of the react8ionmixture waa immediately transferred to the spectrophotometer cell and the run commenced. These preliminary o erations were completed within 45 seconds. The opticafdensity of the reaction mixture a t 420 mp waa determined a t frequent intervals. Since the zero time optical density Do is entirely due to the pure tris complex, and that at infinite time, D,, that of pure cis-bis complex,* the fraction of reaction F in any given run where Dt is the optical density at time t is given by the equation F := (Do- Dt)/(Do D m ) Series of experiments were carried out to determine the effects of variation of the concentration of complex ion, hydrogen ion and oxalate ion, and of temperature and ionic strength, all in noimal water solvent. Deuterium solvent effect experiments were done using a 0.05 M stock solution of com lex made by diasolvin the required quantity of solid &Cr(8&)~3H@ in.pure D$, and a stock solution of deuterated perchlonc s.cid made by diluting 11.6 M HC104 with pure DtO. Reaction mixtures containing aa much aa 91% D could be prepared in this way, and runs were made with several such mixtures in the manner already described.
26 hours, although nearly half of the free oxalate was used up by the association reaction to form Cr(C20&-3 under these conditions.2 At 50°,with pH 1.0,ionic strength = 0.5, (complex) = (free oxalate) = 0.05 M , no exchange was detected during a 6 hour period. Finally, a more detailed experiment was carried out under conditions closely comparable to those of the Cr(C204)3-3-oxalate exchange study,' yielding the results recorded in Table I.
(8) Proven by the fact that the speotra of the reaction mixturas became indistinouishalble after nevera reaction half-times from thore of pure cicKCr(Ct0a)dHtO)t n o l u t i o ~of the same oonoentration. No trow-isomer a p w i among the produotr. ~ i exmted a from the inerbUty d tha krter form under the prwent oonditionr (m.toref,4).
librium concentrations of bi-oxdato, tris-oxalato and total free oxalate ions am estimated to be 0.035 M. 0.015 bf and 0.005 M , respectively. The Mtud (Ctoa-) b obtained from the total oxalate fimm by uno of the d u e of 8 X 10-8 for the Mcond ionisation oonstant of o u l i o d d , e x t r w d ~ t dfrom the detr of Earned and Fallonal*
8
TABLE I EXCHANGE OF F'BEE OXAJATE WITH BOUND OXALATEOF THE Cr(c%)s(H&)1- ION Temp., 75'; (complex) = 0.05 M ; (free oxalate) = 0.02 pH Time, mu.
Wt. of CaC,Od.HtO, mg.
Specific activity.a counts/min./mg.
1.5 9.2 303* 15 6.4 322 30 5.1 325 120 2.8 276 360 2.2 128 720 2.2 108 Corrected for self-absorption and self-scattering.l * Large sample, subject to greater counting errom than the others.
It is obvious that oxalate exchange of the Cr(CZO~)((H~O)Zion is a negligibly slow process both under conditions where addition of C204- ion to the complex goes essentially to completion (at 25' and pH 6, half-time for association reaction is 9 hours2), and under conditions where the reverse process, aquation of Cr(&O4),9w3 ion, is completely predominant (at 50" and pH 1, half-time for aquation is also 9 hours--see Table 111). The data of Table I enable three significant qualitative deductions: (i) aa shown by the second column, the association reaction Cr(GO4MH2O)t-
+ GO4- = Cr(GOA-* + 2H10
(1)
proceeds rapidly a t 75" and pH 3 to an equilibrium, with a half-time of the order of magnitude of 25 minutes. An extrapolation of the data of Hamm and Perkins* leads to a value of 1.6 minutes for this quantity at the same temperature and pH 6. The reaction clearly becomes pHdependent outside the range studied by these authors. Further work is necesssry to determine the exact nature of this dependence. (ii) The equilibrium constant for the dissociation of Cr(C204)3-s(reverse of reaction 1) a t 75" may be estimated9 to be K = (bis-oxalato)(GOr)/ (tris-oxalato) = 3.5 x 10-4. The only comparable a t 32". figure in the literatures is K = 3.4 X Results and Discussion Our value is consistent with this if the heat of the a. Exchange Studies.-Several experiments reaction has the reasonable magnitude of 20 kcal./ were carried out,in which the specific activity of the mole. free oxalate was determined as a function of dura(iii) The half-time of exchange obtained from tion of mingling with the bis-oxalato complex the conventional linear plot of the h(1 - fraction compound. At 25", with pH 6, (complex) = exchange) us. time is close to 4 hours. It is unlikely 0.01 M , (free oxalate) = 0.02 M , there was no (9) The p d p i t a t e weight figures show that about */a of the free significant change in free oxalate activity during oxalate is wed up by reaction with b w x a l a t o ion. Thus the equi-
-
KOTRAV. KRISHNAMURTY AND GORDON M. HARRIS
348
Vol. 64
The dependence of the rate on the concentration of hydrogen ion is shown in Table 111. The values for kexp = 0.693/tl/, were obtained from straight line plots such as illustrated in Fig. 1. The calculated over-all rate constants were determined by the assumption that JCcalcd = k'(H30+) k"(HsO+)2, where k' and k" have the values 1.7 X Lmole-' sec.-l and 5.0 x IO-' 1.2mole-2. sec.-l, respectively, a t 50".
II)
+
05 0.
w
I4 2
Q
TABLE I11 DEPENDENCE OF AQUATION RATEON CONCENTRATION OF
2
0
V I-
HYDROQEN ION Temp., 50.0"; (complex) = 5.0 X 10-8 M; ionic strength = 1.00 (adjusted with NaC104)
a
U .
-I ai
(HM+L
hXP, ge~.-1
0.01 .02 .05 .10 .20 .40
0.05
0
200
4 00
600
.w
x
kaSlCd.
sec.-1
101
0.03 .04 .ll .23 .57 1.31
Fig. 1.-Ty ical aquation rune-conditions: 50.0", M d!r(C204)8-a,15 X 10-aM K+, 0.97 M C104-, 5.0 X ionic strength adjusted to 1.00 by addition of NaC104except in run F: curve A, 0.10 M H+, t l / z 530 min.; B, 0.20 M H +, t*/z202min.; C~,0.40MH+,t1/r88,min.; D,O.NMH+, tl/* 63 min.; E, 0.65 M H +,tl/* 35 min.; F, 0.97 M H +,tl/l 17 m n .
a
10'
.03 .09 .22 .54 1 48
1.83
2 10
.65
TIME, MlN.
x
0 02
3.30 -80 4.45 * 97 6.48" Meen value from Table 11.
3.22 4.58 6.35
Some other experiments were done a t 50°, with (complex) = 0.005 M and (HsO+) = 0.97 M ,and other conditions set as follows: (i) solution also 0.005 M in oxalic acid, ionic strength adjusted to 1.00 with NaC104, (ii) ionic strength made up to 1.50; (iii) ionic strength made up to 2.00. In none of these experiments was the rate of aquation significantly different from the mean value of Table 11. The temperature dependence of the rate was as shown in Fig. 2, which presents the results of experiments at two acidities carried out at temperatures of 40, 50, 60 and 75, respectively. The lines have the same slopes within experimental error, and the over-all activation energy calculated from this slope is 22.1 & 0.2 kcal./mole. The rate of aquation data can be interpreted by the reaction mechanism
to be sheer coincidence that this figure agrees well with the expected value of 3.9 hours calculated from the data of Graaiano and Harris for Cr( C Z O ~ ) Boxalate -~ exchange under the same conditions. The logical conclusion is that only the Cr(C20&-a formed in the system provides a path spefor oxalate exchange. The Cr(C204)2(H20)2cies is so stable that direct oxalate substitution is negligibly slow under the present conditions. Similar behavior previously has been inferred for the corresponding:cobalt(I1) complex ion. l1 b. Aquation Studies.-For individual runs, plots of In(1 .- F ) against time give good straight lines, as seen in Fig. 1. This seeming first-order dependence on tris-oxala to complex ion concentration was confirmed by a series of runs where all Cr(C204)r-' + H80+ Cr(CPOl)20Cz09HH20' K 2 (2) factors were fixed except the initial (complex ion), C~(CZO~)*OGO,H.H*O+ HnO+ as &own in Trtble 11. TABLE I1 DEPENDENCE 01F AQUATION R A OF~ CONCENTRATION
-
+
OF
cr(GOd)*-' ION Tamp., 50.0"; (H+) 0.97 M . ionic strength = 1.00 (adJusted with kaC10,) (Complex), M X 103
2.5 4.0 5.0 6.0 7.5 25.0
lU?,
min.
17.0 f 0 . 3 17.5 .3 17.0 f . 3 19.0 f 1 . 0 22.0 f 2 . 0 18.0 f 0 . 7
0.693/L1/:, aeo.-l X 10'
6.80 6.60 6.80 5.99 5.26' 6.41b Mean 6.48 f 0.26" ' Optical denuity data inaccurate due to high abeo tion in 1 cm. cell. * 1 mm.path-length cell used. Excluxng 5th run in eeriee.
*
+ +
Cr(GO4h(H&XHGOd- k4 (3) Cr(CnO&OGO8H.HS0' HIO+ -+ cr(G04MH~0)- HZC~O,k7 (4)
This leads to the rate law -d(Cr(GO~h-~)/dt= K,kr(H~0)(HIO+)(Cr(G04)r-a)
+
f&h(HsO+)YCdGWa-9
where the symbols Kn, kr and k7 are consistent with those used in the &t paper of this series,' and the mme assumptions concerning equilibrium reaction 2 are made as before. The last column of Table I11 illustrates that this law fits the data well with previously defined constants k' and k" equated to &h(I-&O) and hk7, respectively. The absence of ionic strength effects in the present study is probably without real significance, since the values used were 80 high as to be outside the range of
March, 1960
THE
KINETICS OF AQUATION OF
349
TRISOXAI~A'l~oC~iiloMlUh~(III)
applicability of the Debye-IIiickel theory in any case. Also, added oralate should have no effect on the rate if reactions 3 and 4 are essentially uriidirectional, as is the case under present couditions.8 The experimeiita1 activation energy is apparently independent of (H30+), indicating that the activation energies for reactions 4 and 3 , (E7 and 1i4), are equal. Assu.ming that AH for reaction 2 is not very different from that for protonation of a free oxalate (C20a-) ion (calculated t~obe 2.8 kca1.l mole from data in the literature'"), it follows t,hat E4 = 8 7 == 19.3 kcal./molc. This value for It4 is in reasonable agreenient with an approximate figure of 20 kcal./mole derivable from the exchange data." Other comparable data are those of Schliifer and co-work(:rsL2who report values of 21.6 and 19.5 kcal./mole for the activation energies of hydrolytic displacement of en from C r ( ~ n ) ~and +~ Cr(C204)zen-,respectively. It is also of intercst that the activation energy for the process Co(tn)&ol+ 4-2H20 = Co(tn)~(H~O)n+~ + CO1" is 24.8 kcal./mc~le.'~ Finally, one notes that the value for &k4(E[20) a t 75" deduced from the data 1. mole-' sec.-l, in good of this paper is 1.7 X 260 2.80 3.00 3.20 3.40 agreement with the figure 1.8 X 10-3 obtained for 1000/1. the same constant in the oxalate exchange study.' 2.--Tcmperaturc dependencc of rstc-conciitiwts: The runs mad.e in H20-D& solvent mixtures of 5.0Fig. M K+, 0.97 M Clod-, x 10-3 M Cr(C20&-3, 15 X several compositions resulted in the data shown ionic strength adjusted to 1.00 by addition of NaC104. in Table IV. Also tabulated are the various I c , / k ~ values calculated according to l'urlce's recapitulaTABLE IV t,ion of the Gross-Butler e q ~ a t i o n , 'utilizing ~ t,he SOLVENT DEUTERIUM ISOTOPEEFFECT ON THE: AQUATIUN liD/icI~ value obtained by graphical extrapolation RATEOF Cr( C2O4)3-a from our data. The good agreement betwcm t'he Tcmp., 50.0°, (complex) = 0.005 M ; (acid) = 0.07 ,If; obscrved and calculated values for kn/kH can be ionic strength = 1.00 It = (D)/ kexp. kn/kir kn/k~r taken as strong :support for the g e i i e r a l acid cst,nly(11 + D) S C C . - I x 104 (utr~c~.) (calcd.) sis mechanism: 13 H + e SH+; 8 H + --+ products, 0.00 6.8 1.00 1.00 with the second step rate-determiriiiig hut not 1 . 1 3 1.24 .26 7 . 7 sulijcct to isotope effect.16 This is exactly the type
+
(IO) €I. 9. 1Iarned and I,. D. E'dIo11, J . A m . Chem. Soc., 61, 81 11 (1039). ( 1 1 ) See ref. 1, p. 332. (12) 11. L. Schliifer and 0. liling. is. phlisrk. Ckem. (Yrankfuil), 16, 14 (1958); El. L. Scliliifer, Abstracts of l'apcrs, Int. Conf. Co-ord. Chein.. London, April, 195'3. ( 1 3 ) -1. E. Boyle and G. hf. IIarris, J . A m . Clrem. Soc.. 80, 782 (1958). (14) E. L. Purlce, ibid.. 81, 2(i3 (I!l59).
A modified Gross-Ilutler equation was used in obtaining the k J k H calculated value
shcrc k r l , k,,, and k D me the r:rte constants in pure 11~0,1ltO I h O and DrO. allt,) a n d a w ,ire the aetivitics of 1 1 ~ 0and l h 0 , and arc givcn, in terms of inole fractions. by ( 1 - n)* and 7 1 2 , rcspcctivcly. Valurs for the Q ' ( t r ) function and the equilibrium constant L at 50' were taken from Purlcc's tabulated data. (15) K. B. Wiberg, Chem. Revs., 66, 713 (1955).
.49 10.1 1.49 2.35 .91 16.0 2.G2 1 .OO 17.8" Gmp1iic:ally cstrapolatcd valuc.
1 58 2.38
(2.6%)
of mechanism proposcd in thc present study, with our k D / k H ratio of the same order of magnitude as observed in reactions of this type involving organic compounds. l 4 S 1 6 Absence of hydrogcn isotope effect in either reaction 3 or 4 is to be expected, since the rate-dctcrmining process in these reactions is almost certain to be cithcr Cr-0 or C--0 bond breakage, as appears to 1)c the case for acid-catalysed aquatioil of the Co(NH3)&03+ i0n.l6~l7 (16) F. A. l'osey and 11. Taube. J . A m . Chem. Soc., 7 6 , 409'3 (1953). (17) I). It. Stranks and G . hI. Harris, TIUSJ O W n N A L , . 66, 9OG (1952).
