Toward a unified master-equation theory of thermal decompositon reactions. Analytic solution for diatomic dissociation

Journal Article · Thu Jan 11 04:00:00 EST 1979 · J. Phys. Chem.; (United States)

DOI:https://doi.org/10.1021/j100464a021· OSTI ID:6486981

Yau, A W; Pritchard, H O

The master equation is formulated and solved analytically for a ladder-climbing model of the dissociation of a diatomic molecule diluted in a heat bath. The dissociation rate is explicitly related to the normal modes of relaxation of the internal degrees of freedom of the molecule giving, in closed form, an expression for the pseudo-second-order dissociation rate in terms of the energy-level structure and collisional transition probabilities. This form of the rate constant shows clearly the criteria for the occurrence of ''bottleneck'' and ''network'' effects. The dissociation of H/sub 2/ in Ar is studied in detail between 2000 and 6000/sup 0/K. The principal qualitative conclusions in respect of the rate of dissociation are that (a) nonequilibrium effects are significant even at 2000/sup 0/K; (b) rotation enhances the reaction rate, although it is only at very high temperatures (above 6000/sup 0/K) that rotational energy contributes equally with vibrational energy in causing dissociation; (c) the presence of tunneling gives only a very modest enhancement in the rate. The relative contributions to the Arrhenius temperature coefficient of the rate of the following theoretical constructs are delineated. A parallel set of calculations on the dissociation of D/sub 2/ in Ar also gives results in good agreement with experiment. The principal determinants of the kinetic isotope effect are the differences between H/sub 2/ and D/sub 2/ in the internal relaxation rates and in the energy-level densities. 7 figures, 83 references, 7 tables.

• Research Organization: York Univ., Downsview, Ontario
• OSTI ID: 6486981
• Journal Information: J. Phys. Chem.; (United States), Journal Name: J. Phys. Chem.; (United States) Vol. 83:1; ISSN JPCHA
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400201 -- Chemical & Physicochemical Properties
400202* -- Isotope Effects
Isotope Exchange
& Isotope Separation
ARGON
CHEMICAL REACTION KINETICS
CHEMICAL REACTIONS
COMPARATIVE EVALUATIONS
CRYOGENIC FLUIDS
DEACTIVATION
DEUTERIUM
DISSOCIATION
ELEMENTS
ENERGY LEVELS
EXCITED STATES
FLUIDS
HYDROGEN
HYDROGEN ISOTOPES
ISOTOPE EFFECTS
ISOTOPES
KINETICS
LIGHT NUCLEI
MATHEMATICAL MODELS
NONMETALS
NUCLEAR MODELS
NUCLEI
NUMERICAL SOLUTION
ODD-ODD NUCLEI
PRESSURE DEPENDENCE
RARE GASES
REACTION KINETICS
RECOMBINATION
ROTATIONAL STATES
STABLE ISOTOPES
TEMPERATURE DEPENDENCE
TUNNELING
ULTRAHIGH TEMPERATURE
UNIFIED MODEL
VERY HIGH TEMPERATURE