464
WALTER
KRUSEAND
DARWIN
THUSIUS
Inorganic; Chemistry
COSTRIBUTION FROM
THE
MAX-PLANCK-INSTITUT FUR PHYSIKALISCHE CHEMIE, GOT~INGES, \%‘EST GERMASY
Kinetics of Thiocyanate Binding to Vanadium(I1) and - (111) BY WALTER KRUSE
ASD
DARWIN THUSIUS1nZ
Received August 4 , 1967 Formation and dissociation rate constants (kf and k d ) for the binding. of thiocyanate to 17(H20)6*L and I’(H20)1;3C have been determined by means of the temperature-jump method. In the case of V ( I I ) , kf = 15 i 2 sec-’ and k d = 1.4 ri: 0.2 sec-’ a t 24” and w = 1 M. The corresponding rate constants for V(II1) are 104 =t10 i W 1 sec-’ and 0.7 i 0.1 sec-l a t 23” and p = 1 d l . T h e results are discussed in terms of electronic effects on the substitution labilities of octahedral complexes. Also considered is the possibility of distinguishing between outer-sphere and inner-sphere reductions from an estimate of the vanadium(I1)-water exchange rate. Unlike substitution reactions of other trivalent hexaaquo complexes, no evidence was found for a catalytic path involving the hydroxy form of V(II1).
Introduction Although a great deal of data is now available on the kinetics of metal complex formation, little published work exists on vanadium species. Particularly needed are the rates of replacement of coordinated water in V(H20)a2+ and V(H20)63+.These complexes play an important role in electron-transfer studies and their labilities pertain directly to the problem of differentiating between “outer” and “inner-sphere” oxidationreduction reactions. A related subject is the effect of electron configuration on octahedral substitution rates. Comparing V(I1) and V(II1) anation rates with those of other (first row) bi- and tripositive aquo cations, respectively, mould be a means of assessing the importance of electronic effects in these two series. Using the temperature-jump method we have measured the formation and dissociation rate constants for the 1: 1 thiocyanate complexes of V(I1) and V(III).334 Thiocyanate was chosen as ligand because it forms fairly stable complexes with the vanadium species in question and is free of complications arising from hydrolysis. Also, since thiocyanate has often been employed in other anation studies, its binding rate leads directly to relative reactivities between a number of aquo complexes. Experimental Section VOSOl and S a S C N were reagent grade. NaSCS was recrystallized twice from water and its stock solutions were analyzed b y titration with AgN03. A11 other chemicals were analytical grade a n d were used without further purification. V(I1) a n d V(II1) are easily oxidized and must be handled in the absence of oxygen. In preparing a reaction solution, vanadium stock of known concentration was added t o a stoppered serum bottle containing a nitrogen-purged mixture of XaSCN, h7aC104, a n d HC101. Prior t o receiving t h e reaction solution, the temperature-jump cell was also purged with nitrogen. Solutions were transferred b y means of glass syringes equipped with stainless steel needles. Vanadium(I1) perchlorate was prepared b y electrolytic re-
(1) Xational Institutes of Health Postdoctoral Fellow, 1966-1967. (2) Author t o whom inquiries should be addressed a t the Laboratoire D’Enzymologie, Orsay, France. (3) T h e same systems have recently been t h e subject of a stopped-fiow Investigation. For a preliminary report see B. R. Baker, M. Orhanovic, and N. Sutin, J . A m . Ckem. SOL,89, 722 (1967). (4) T h e present results supersede the preliminary findings of W. K.la**r
duction of 1702+ in HC104, the vanadyl perchlorate being prepared by mixing equivalent amounts of Ba(C10& and VOSO4 solutions. The reduction was carried out under a n atmosphere of nitrogen. V ( I I ) solutions are unstable with respect t o the slow reduction of perchlorate, resulting in V(II1) accumulation.3 Since replacing perchlorate with chloride had no appreciable effect on the kinetics, most reaction mixtures were therefore made from vanadium(I1) chloride (even a t relatively low concentrations S-(III) could interfere spectrophotometrically with the V(I1) kinetic measurements and, in principle, could lead to catalytic aquation aia VSCS+-V(II1) electron transfer). The vanadium(11) chloride was prepared b y electrolyzing a known amount of NHdVOa in HC1 medium. T h e extent of reduction was estimated from the optical density at 400 mp. At this wavelength W ~ I I ) / W ( I I ) = 10 and the OD thus serves as a sensitive measure of [I.(III)].6 On this basis no more than 37, of the vanadium existed as V(111). T o prepare stock vanadium(II1) perchlorate, a slight excess (usually 5 mole yo)of vanadium(I1) perchlorate was added to a n acidic solution of vanadyl perchlorate. These solutions were used before any significant oxidation of TT(II1) could take place by perchlorate .5 The T(I1) and V(II1) spectra were in very good agreement with those reported in the literature.6 The temperature-jump apparatus was of double-beam design. Discharging a O.O5-,F capacitor loaded to 40,000 V effected a temperature rise of 6 2~ 1’. Since platinum catalyzes the evolution of hydrogen from V(I1) solutions, gold-plated electrodes were employed in the temperature-jump cell. The reciprocal relaxation time,g T - I , was calculated from a plot of -log AC us. time, where AC is proportional t o the deviation of (M-NCS) from its equilibrium position. A t least five oscillograms were averaged per run. The deviation from the mean was usually less than 57,.
Results The V(1I) reaction was followed at 520 mp. At this wavelength only negligible absorption is expected from trace amounts of V(II1) and VNCS2f.6-8 T - ~ , plotted as a function of the equilibrium concentrations (Figure 1), conforms to the behavior expected for a substitution process first order in ligand and metalg (eq 1-3). (6) W. R. King and C. S.Garner, J . Phys. Chenz., 58, 29 (1954). (6) G. Gordon and P. H. Texvvari, ibid., 7 0 , 200 (1966). (7) ~ V N C S ’ -2:3 and E V N C S ~ +-13 a t 520 mg. Taken together with ~ v ( I I )W, < I I I ) ,and the stability constants for SCN- binding, we calculate t h a t trivalent vanadium contributes no more than 6 % t o t h e total OD of any reaction solution. (8) For reasons presented elsenheres i t is assumed t h a t S C N - is bound t o vanadium through the nitrogen atom. (9) M. Eigen arid L. de Maeyer in “Technique of Organic Chemistry,” A. Weissberger, Ed., Val. 1’111, part 2, 2nd ed, Interscience Publishei-s, Inc., New York, N. Y . , 1963.
THIOCYANATE BINDINGTO VANADIUM(I1) AND -(III) 465
Vol. 7 , No. 3, March 1968
TABLE I FORMATION AND DISSOCIATION OF THE VrlNCS AND VIIINCS COMPLEXES AND ESTIMATED RATESOF CATION-SOLVENT WATEREXCHANGE RATES OF
I
V
0,
ln
.
M
v
P
kf, M -1 sec-1
kd. sec-1
K,"
kex?
M -1
sec-1
1 . 4 1 0.2 11 -75 0.7 f 0 . 1 153 (-3 X 103) a K = kf/kd. The rate of exchange of a particular water At 24' and p = 1 M (mixed C1-in the hexaaquo complex. At 23' and p = 1 M (c104-medium). c104- medium). V(1I)C V(II1)d
c
3
15zt 2 104 zt 10
spectrum (we find the spectrum in 1 M C1- identical with that in 1 M ClOh-) or the substitution kinetics (see Figure 1). I n addition, trace amounts of trivalent vanadium can be tolerated; a t ([V(II) I [SCN-I) = 0.084 M the total concentration of trivalent vanadium was made 0.01 M , but no significant change occurred in 7. The kinetics were also independent of [H+] in the range 0.1-0.4 M . The V(II1) reaction was followed a t 400 mp. Ratios of [V(III) ]total/ [SCN-]t0t,~were always greater than 3 and equilibrium concentrations varied from 2.9 X to 5.0 X M for [V(III) ] and from 3.0 X to 6.5 X M for [SCN-1. I n addition to the relatively slow complex formation, a very fast ( T < 15 psec) reaction was observed, the amplitude of the relaxation effect increasing as the acidity was decreased. From a consideration of relative extinction c ~ e f f i c i e n t s ,concentrations, ~*~f~~ and AH values,11012 the effect can be attributed to the hydrolysis equilibrium V O H ~ ~ +V O H ~ + H+. Using 100 M-' as a first approximation to the stability constant,12an initial plot of 7-l vs. ([V(III)] [SCN-I) was made. The s1ope:intercept ratio of the resulting straight line gave a second approximation (150 M-l) and this new value was used to plot the graph appearing in Figure 2. The two plots gave essentially the same rate constants. Varying [H+] from 0.04 to 0.5 M had no appreciable effect on 7. A t the lower acidity, [VOH2+]/[VOH23++l = 0.05.
+
2
1
I
I
I
#
I
0.10
0.05
([VCIIn
+
I
0.15
-
+
[SCNl)
Figure 1.-Concentration dependence of t h e reciprocal relaxation times of t h e vanadium(I1) reaction a t 24' and in Cl--C104medium of p = 1 M: 0 , 0 . 2 M H+; A, Clod- medium, 0.2 M H + ; 0, 0.1 M H+;0 , 0.4 M HC. kr
M + L e M L
(1)
kd
7-l
= k f ( [ M l f [LI) -k
K =
kr/kd
kd
( 2) (3 )
Equilibrium concentrations were calculated using 14 M-l for the stability constant, K . This figure was obtained by spectrophotometric titration (23" and 1.1 E= 0.4 M ) but, owing to the formation of more than one complex a t high [SCN-1, can only be considered a first approximation.lo T o prevent higher complexes from interfering in the kinetic runs, the total vanadium concentration was always kept a t least threefold larger than the total thiocyanate concentration. Equilibrium concentrations ranged from 0.13 to 0.023 M in the case of V(I1) and from 0.014 to 0.0040 M in the case of SCN-. Considering the differences in temperature and ionic strength, the formation and dissociation rate constants calculated from the slope and intercept of Figure 1 give a stability constant (Table I) in satisfactory agreement with the one estimated spectrophotometrically. Although C1- was present in most V(I1) reaction mixtures, it had no appreciable effect on either the V(I1) (10) I n the kinetic studies, the condition [V(II)] >> [SCN-I was always satisfied. Therefore the calculated coacentfstion sum of eq 2 is relatively insensitive t o errOrS in K. T h e same holds fot the V(II1) reaction.
+
Discussion The V(I1) Reaction,-The wealth of experimental evidence to date indicates that the bipositive aquo ions of the first transition series undergo ligand substitution via rapid ion-pair formation followed by rate-determining loss of coordinated waterl39l4 Ko
M (Hz0)~'+
ki
+ Ln )JM (Hz0)~' L n k
M (H20)sL +$
+*
'-n
+ HzO
-I
(4)
Kok,,
kf = Koki kd
=
k-1
(5) (6)
For a particular metal, formation rate constants, kf, are generally independent of the nature of the ligand. (11) S. C. Furman and C. S. Garner, J . Am. Chcm. Soc., 73, 1785 (1950). (12) S. C. Furman and C. S. Garner, ibid., 73, 4528 (1951). (13) M . Eigen and R. G. Wilkins in "Mechanisms of Inorganic Reactions," R. K. Murmann, Ed., Advances in Chemistry Series, No. 49, American Chemical Society, Washington, D. C., 1965, p 55. (14) N. Sutin,?Ann. Rev. Phys. Chem., 17, 119 (1966).
I norgrinic Chemistry
/
i/
/ T
2-
/”
i’
I-/@
0 1 0
I
0 01
I 0 02
I
0.03
-
-
Figure 2.-Concentration dependence of the reciprocal relaxation times of the vanadium(II1) reaction at 23” and in perchlorate medium o f p = 1 M: 0 , 0.5 X H + ; 0,0.04 M H + ; 0,0.1 M H + .
Differences are observed for ligands of different charge, but these can be attributed to variations in KO, the outer-sphere association constants. Values of KOhave been obtained both e~perimentally’~ and estimated from the Bjerrum formulation for ion pairs.16 They indicate that k l is not far from Re,, the rate constant for metal-solvent water exchange.” Apparently V(I1) is no exception t o this general behavior. Although no anation rate constants are available for comparison with the SCN- results, some recent electron-transfer studies by Price and Taubel* suggest that V(I1) substitution rates are relatively independent of the nature of the ligand. It seems significant that recently published values for the V(I1) inner-sphere reductions of CrSCN2+ and ~is-Co(en)~(N~ are ) ~ +c ~ m p a r a b l eto~ ~what ~ ~ ~Price and Taube found for C O ( N H ~ ) ~ O & C O Xand ~ + Co(NH3)&04+, respectively. Therefore, in common with so many other bivalent cations, V(I1) appears to undergo substitution a t a rate primarily controlled by the loss of a coordinated water. (15) M. Eigen and K. Tamm, 2. Elektrochem., 66, 107 (1962). (16) See, e.g.: (a) G. G. Hammes and J. I. Steinfeld, J . A m . Chem. Soc., 84, 4629 (1962); (b) F. P. Cavisino, J. P h g s . Chem., 69, 4380 (1965); (c) R. G. Wilkins, Inovg. Chern., 3, 520 (1964); (d) D. B. Rorabacher, kbid., 5, 1891 (1966). (17) T. J. Swift and R. E. Connick, J . Chem. Phys., 57, 307 (1962). (18) H. Price and H. Taube, to be published. (IS) The V(I1) inner-sphere reduction of Cr(H20)aSCX2+ has a rate const3nt:of 7.1 M-’ sec-‘ a t 2 5 O and p = 1 (20) The V(I1) inner-sphere reduction of cis-Co(en)2(Na)2+ has a rate constant of 33 iM-1 sec-1 a t 25’ and p = 1 M : J. H. Espenson, J . A m . Chem.. SOG.,89, 1276 (1967).
From eq 5 it is seen that an estimate of the V(I1) water-exchange rate constant can be made from the relation14 (7)
where k e x , ~ i ( 1 1refers ) to the known rate of mater exchange“ of Ni(I1) and ~ E , N ~ ( I is I ) the rate constant for formation of S i N C S .21 Judging from the existing agreement between water-exchange and ligand-substitution data,I3 k e r , ~ ( 1 1 )obtained in this way (Table I) is probably valid to within a factor of 3. When comparing the labilities of aquo complexes and when considering rates of substitution os. rates of electron transfer for a particular metal, one is often dealing with rate constants differing by more than an order of magnitude; in these cases the error in the present estimate is of little consequence, Compared to other bipositive aquo complexes, V(I1) is strikingly inert. Even Ni(I1) is considerably more reactive, indicating a wider range of exchange rates than found previously. In the transition series, k,, varies from -73 sec-I (V(I1)) to 2 x IO8 sec-’ (Cu(11))at 25”. The inertness of V(I1) can be rationalized in terms of either valence bondz2 or crystal field23 theory applied to a d3 electron configuration. The latter approach is an attempt to quantitatively predict relative rates from estimated “crystal field activation energies” (CFAE) and finds experimental support in an apparent relationship between aquo ion labilities and crystal field stabilization energies (CFSE) . 2 4 A comparison of the SCX- anation rates of Ni(I1) and V(I1) should be a particularly straightforward application of the theory. The hexaaquo cations are identical in charge and very similar in size and thermodynamic affinity for SCN-. Furthermore, they both possess the large CFSE of 12Dq23 and, for an Sxl mechanism, would be assigned identical crystal field activation energies of 2.0Dq.23 Any difference in rates should then be accounted for solely by the difference in Dp between Ni(I1) and V(I1). Using spectroscopic Dg valuesz5and a CFAE of 2.0Dg, we calculate k f , ~ i ( 1 1 1 / R ~ , v ( I I ) = 40 (25’). However, it can be argued that the mechanism is better described as a “ligand-assisted diss~ciation.”~ In~ ~this ~ ~ case the CFAE of 2.ODq would be replaced by l.8Dq*6~28 giving kr,Ni(II,/kf,vcII, = 25. These ratios are to be compared with the experimental ratio of 300. The theory predicts correctly that Ni(I1) is the more reactive complex and is of value in making a semiquantitative estimate of the relative rates. At the same time the results indicate that either a refinement of the theory or a consideration of parameters other than crystal field stabilization energies is (21) A . G. Davies and a’. 11. Smith, Pi.0~.Chem. Soc., 380 (1961). ( 2 2 ) H. Taube, Chem. Rev., 60, 69 (1952). (23) F. Basolo and R. G. Pearson, “hlechanisms of Inorganic Reactions,” John Wiley and Sons, Inc., iiew York, S . Y., 1958, Chapter 3. (24) Wf. Eigen, Pure A p p l . Chent., 6, 97 (1963). ( 2 5 ) See ref 23, p 44. (26) I
