Entropy and Chemical Change. II. Analysis of Product Energy Distributions: Temperature and Entropy Deficiency

Abstract

Detailed experimental and theoretical information on the distribution of product energy states resulting from reactive molecular collisions are characterized by their entropy deficiency and temperature. Explicit algorithms are developed both for the case of ultimate resolution (both angular and internal state distribution) which provides the intrinsic (i.e., maximal) entropy deficiency and for the more realistic situations (e.g., chemiluminescence, molecular beam velocity analysis) where only averaged distributions are available and the entropy deficiency is therefore smaller. Twelve ``known'' product distributions are analyzed. The largest values of the entropy deficiency are found for reactions where there is significant deviation from a simple equilibrium distribution of products. A temperature parameter is introduced as a measure of the deviation from equilibrium. Inverted populations are characterized by a negative value of this temperature. Consideration of a number of isotopic reactions indicate that this temperature is essentially invariant under isotopic substitution. The new temperature parameter introduced in this work is the one appropriate for a finite system and differs from the more familiar (but special) form appropriate for a system coupled to an infinite heat bath. Two new tools are thus proposed for characterizing the deviation of an observed product state distribution (or a computational simulation thereof) from an equilibrium, microcanonical one. These are the temperature parameter (a differential measure) and the entropy deficiency (an integral one). They measure, respectively, the local and the average deviation between observed and equilibrium distributions.