High Pressure Solution Kinetics of Metal Complexes Surapong Suvachittanont Faculty of Science, Prince of Songkla University, Haad-Yai, Thailand In ascertaining the nature of the activated complex to elucidate reaction mechanism, a n u d e r of techniques have been commonly employed by inorganic chemists including competition between nucleophiles, linear free energy relationships, isotopic labelling, and various activation parameters. Activation enthalov (AH') andin narticular entronv are ."(AS+) , well known for their application in aiding mechanistic interoretation. The use of activation volumes f 4 V i )derived from the pressure effect on reaction rates, although less familiar, has become more popular in recent years (1-4). The latter activation parameter is thought to be more readily visualized than the former two. Inorganic chemistry has lagged behind organic chemistry in the elucidation of reaction mechanisms. This is also the case for interpretation by means of activation volumes. An article dealing with activation volumes for organic reactions appeared in 1967 (5).At that time a large,numher of in THIS JOURNAL AV" values had been reported for organic systems while only A
-
.
-. ,, .
.
.,,..
system where X = C1- or Br- ( 6 , 7 ) .Advances in high pressure techniaues and e a u i ~ m e n during t the ~ a s ten t vears have
Figure 1. Typical graphs of In k versus pressure ( P ) : (a) negative AV' with non-linear increase of In k with P. (b) positive AV+ with non-linear decrease of In k with P. (c) positive AV+ with linear increase of In k with P.
"
basic principles and arguments behind the mechanistic interpretation of 4V' which have been applied to a variety of inorganic reactions in solution. Determination of Activation Volumes The effect pressure on the rate constant of a reaction at constant temperature is given by the expression (8)
(-1a
in h :
ap
= T
AVt RT
(1)
lnh,=Inho+ bP+cPZ
which can he easily derived with the application of the transition state theory and some thermodynamic relationships. The activation volume is defined as the difference in partial molar volumes between the transition and the reactant states, that is, say, for the generalized reaction A
+ B +. . . * X + -products
AV+=vx+-&-vB-.
~~
~
Journal of Chemical Education
(3)
where b and c are coefficients. By convention, in the nonlinear case, only the activation volume at zero pressure (AVHo) is quoted. This value is indistinguishable from the value at atmospheric pressure for all practical purposes. The activation volume at zero pressure is described by A V g = -bRT
(2)
rate constant of a reaction has been determined at various pressures, usually up to 2 or 3 kbar, the activation volume can be evaluated. Activation volumes can be positive, negative, or even zero value. For a positive AV' value, the rate observed would decrease with applied pressure while for a negative AVi value, the rate increases with pressure. If the rate does not change with pressure, then a zero AV* value is expected. Generally, a graph of in h , or in (k,lho) versus P plots falls into one or the other of two categories (Fig. 1).In one, such a plot yields a linear graph while in the other, a non-linear graph is observed. This non-linear graph always curves toward the pressure axis independent i f whether-AV' is positive or negative. Such a graph implies that 4 V i is pressure-depen150
dent in contrast to 4 V + of the first category in which i t does not depend on pressure. For the case where linearity of the graph is obtained AV' can be evaluated from the slope of the graph of ink, versus P plots as indicated hy eqn. (1).For the non-linear case there are no exact relationships which can he used to fit the experimental data, and thus, the solution is empirical in nature. Among the many relationships proposed, the most popular one is the quadratic form of the type (9)
(4)
where the coefficient b represents the limiting slope at zero pressure. The evaluation of AVC is usually carried out via a computer program once the data of In h, versus P plots have been found to be non-linear. The activation volume has also been found to be temperature-dependent hut within small temperature ranges this effect i8 not too serious to necessitate a comparison of activation volumes at the same temperature. Another useful thermodynamic quantity often used together with AV* is the reaction volume, symbolized by 4Vn. This quantity describes the difference in the partial molar volumes hetween the product and the reactant states, that is AVO = VproductP- VA- VB - . . .
(5)
Reaction volumes can he measured dilatometrically or evaluated from the effect of pressure on the equilibrium constant ( K )of the reaction via the equation
,
Sealing plug
Solution container Pressure compartment
. .
Figure 3. A high pressure optical cell for incorporating into a spectrophotomster.
polarimeter ( 1 0 , l l ) . Other types of high pressure cell for in situ experiments such as high pressure T-jump (12-14), high pressure NMR (15) and, most recently, high pressure stopped-flow have also been constructed (16,17). These latter types of cells have proved to be valuable in ohtaining AV# data for many fast inorganic reactions in solution including reactions of biochemical interest (18,19). Interpretation of Activation Volumes
Figure 2. Details of components of a high pressure sampling vessel.
T o extract mechanistic information from the experimental activation volume (AVf.?..). ..,. it is common in ~ r a c t i c eto I .,n.;idc.r ,I.; :I first qq~ruximnricm that 1\1',,,!, .wises irtm two en intrimit. t)nrl
