5. H. Laurie
City of Leicester Polytechnic , Leicester, LEI ~ B H England
I
I
Kinetic Stability versus ~hermod~natni;Stability
It is stated or inferred in many inorganic textbooks that no correlation exists between kinetic stability and thermodynamic stability (inertness). This statement generally arises in discussions of the reactions, p&cicularly, those of complex formation, of the transition metal ions, where many complexes are observed to be thermodynamically stable and yet kinetically labile, and vice-versa. The explanation of this phenomenon is usually given in terms of the potential energy profile of a reaction, in which the kinetic stability is dependent on the activation energy (E.) and the thermodynamic stability on the so-called reaction energy (AE) (see figure). This lack of correlation between the kinetic and thermodynamic stabilities is often puzzling to students who have learnt that reversible reactions (which includes the vast majority of complex formation reactions) obey the law of mass action. That is, a t equilibrium the number of forward reactions equals the number of reverse reactions; so that for a typical complex formation involving an unidentate ligand Lm[M(H,O).I"+
+ Lm- s [M(H,O),-,Lln-- + H,O
~ J [ M ( H ~ O L I[Hz01 L I = krlM(H~O)sl [LI
and K
=
kjlk,
(1)
i.e., the thennodynamic equilibrium constant is equal to the ratio of two kinetic rate constants. It is obvious from eqn. (1) that the two reaction rates can both be labile or both inert and yet have the same ratio, and hence the samevalue for K. Over the last few years, with the advent of fast reaction techniques developed mainly by Eigen and his school ( I ) , a considerable number of k, and k, values have been obtained over a wide range of rates, and an examination of the simple expression in eqn. (1) can often give useful insight into reaction mechanisms as well as reveal properties not always directly reflected in the thermodynamic equilibrium constants (8). Furthermore, eqn. (1) can be used as a basis for dividing metal-ion complexes into four classes. For this purpose, use shall be made of a suggestion by Taube (5) that labile be arbitrarily taken to mean those reactions which are complete within the time of mixing (1 min a t room temperature and 0.1 M reactants), so that, for a bimolecular reaction, we have k (labile) > (approx) 0.1 M-I see-'
< k (inert)
and, correspondingly, for aunimolecular reaction k (labile) > (approx) 0.01 see-' < k (inert) 746
/
Journal o f Chemical Education
Potential energy profile of a reaction.
Class I: Thermodynamically Stable and Kinetically Labile
I n t,his class, K > 1, k, > k,, forward and reverse reactions labile. This is the predominant class, covering the known stable complexes of the group I metal ions and the divalent metal ions of the periodic table, excluding Pd(I1) and Pt(I1). Frequently, for these metal ions k, is a t the limit of 10"10'0 M-I sec-I corresponding to the rate of diffusion of ions; under these conditions variation in the formation constant K is then a function of the rate constant lc,. Also included in this class are the metal-ion activated-state complexes present in many metal-ion catalyzed reactions. The greater thermodynamic stabilit,y of the 1: 1 and 1:2 complexes (I) of the amino acid a-alanine with metal ions compared to the corresponding complexes of palanine (11) is u-ell known and in line with the general observation that five-membered chelate rings are thermodynamically more stable than sixmembered rings. The reasons for this difference are attributed to both (4) enthalpy (steric constraints) and entropy effects (chelate effect).
Quite recentjy the kinetics of formation of thcse com= Co(II), Ki(I1) and Cu(I1)) have been plexes (&!I measured (6),with the interesting observation, that for a-alanine, as vith other strong chelating agents, the rate determining step in complex formation is ligand penctration. For palanine, however, the sub-
stantially lower rates of complex formation (as rcflect,ed in t,he lower magnitude of K) are att,ribut,ed to ringclosure being more difficult and hence the ratcdetermining skp. This provides an excellent example of how rate data can providc additional insight. into complcx
for which t,he thermodynamic equilibrium constant increases markedly with increase of ionic strength. I 1, k , > k,, forward and reverse reactions inert. These conditions are typical of the many complexes of cobalt(III), chromium(III), and some of t,he 4d and 5d transition metals, e.g., Pt(II), Pd(I1). A familiar example is that of the chromium(111)-EDTA complcx for ~vhicht b r formation constant has the value of loz3.',and yet, a t room t,emperature, t,he addition of EDTA t,o an aqueous solut,ion of chromium(II1) produces no observable complex formation! Complex formation does proceed on warming or on addition of zinc which acts as a cat,alyst. It is typical of cobalt(II1) and chromium(II1) chemist,ry that catalysts, such as zinc metal, or charcoal, are invariably needed to cat,alyze the formation of their complexes. The function of t,hese catalysts is to overcome their kinetic inertness by forming catalytic amounts of t,he divalent metal ions-the complexes of which belong to Class I. The complexes of rhodium(II1) and iridium(II1) are known to be even more inert than their cobalt(II1) analogs which makes their complex formation more difficult to carry out practically. In the case of rbodium(III), a suit,able catalyst has been found to be et,hanol (7) which is t,honght to act by formation of rhodium(1) species-which again belong to Class I. Class Ill: Thermodynamically Unstable and Kinetically Inert
In Class I11 K < 1, k , < k , forward and reverse reactions inert. Some cobalt(II1) and chromium(II1) complexes come under this category, and although thermodynamically unstable, t,hey ca.n be isolated because of their kinetic inert,ness. One of the more familiar is [Co(NH&I3+, which under acidic conditions undergoes t,he reaction
+ 6 H s 0 + S 4[Co(H10)sl'++ 6NH4+
[Co(NH,)a18+
the equilibrium constant of this reaction is approximately loz3 and yet, the hexaamminecobalt(III) ion is stable for several days in acid solutions. It is becausc some of the cobalt(II1) complexes come under Class 111, that they have been so thoroughly studied; their ratcs of reaction being convenient to follow by the more conventional techniques. One of the more thoroughly studied reactions is t,he aquation of the complex ions [ C O ( N H ~ ) ~ X ](X ~ + ,= F-, C1-, Br-, I-, NOa-, H2POn-). Langford (8) has found that a linear relationship exist,s betveen the thermodynamic equilibrium constants for the aquation of these complexes and the forward rate constants of the aquation reaction (linear free-energy relationship) and applied this as a test of proposed mechanisms. Many of the rhodium(II1) and iridium(II1) complexes, particularly the haloammine complexes, also fall within this class; their extreme inertness, however, has prevented as thorough a study as that of their cobalt(II1) analogs. Class IV: Thermodynamically Unstable and Kinetically Labile
I n Class IV K < 1, k , < k,, fomard and reverse reactions labile. This may seem, a t first glanc?, a hypothetical class, and certainly a t t,he extreme (K
