Entropy and the Absolute Rate of Chemical Reactions I. The Steric Factor of Bimolecular Associations

Abstract

The equilibrium constant for a bimolecular association may be expressed in terms of the energy change, ΔE, and standard entropy change, ΔS°, on association. On account of the well-known relation between the equilibrium constant, and the rate constants of the bimolecular association and its reverse, the corresponding unimolecular decomposition, the values of these rate constants could be determined separately, if one could divide each of the terms, ΔE and ΔS°, into two parts, in the proper way. The proper method of dividing ΔE is known; this paper is concerned with the division of ΔS°. Considered from a statistical point of view, the entropy of a system depends upon the volume in phase space available to the system under fixed thermodynamic conditions. The separate rate constants will depend upon the fraction of the phase space in which it is possible for the reaction under consideration to take place. Application of this principle leads to an interpretation of the collision number and the steric factor of bimolecular association reactions. The known bimolecular associations have been discussed from this point of view.

Unimolecular Reactions in a Spherically Symmetric Potential. 3. Lifetimes of Collision Complexes

“…(13) Note that the thermodynamic limit, described in eq 10, conforms to that relation. Thus the Rice-Gershinowitz assumption, which might have been expected to apply only to "tight", localized transition states, pertains also to at least one limit of those derived from spherically-symmetric potentials.…”

Some properties of microcanonical rate constants

“…To obtain the term a lnk(Tl)/aJ* in that equation, however, we will need to adopt a model. It will be assumed, following Rice and Gershinowitz [18], that angular Applications of this result in several contexts have been given [19,20]. It must be emphasized however that, despite a superficial similarity to (17), this relation is on a more tenuous footing.…”

“…Only for 'loose' transition states will these factors differ significantly, however [9]. The value reported above makes it clear that reaction (18) does not fall into this category. It thus offers a reliable measure of what to expect in a heat bath.…”

Transition State Theory and Beyond — A Constrained Phase Space Approach

“…The Lagrange multiplier p for the constraint (24) of detailed balance can be solved for by introducing (34) and (35) To solve for q it is necessary to insert (40) or (39) in (17). Using (1 1). or, for the probabilities / [ ( n ) -2a(la ) ] .…”