506
10 The Statistical Basis of Bioenergetics
λ ij = λ ji ,
(10.266)
which constitutes Onsager’s proof of his reciprocity relation. 67
10.11 Kinetic Theories for Chemical Reactions
Thermodynamics and statistical mechanics focus on equilibrium states of thermal
systems. Time considerations for a process enters principally in discriminating
between reactions that actually reach quasi-equilibrium in the system in times
comparable to or shorter than the typical times needed for given processes. Catalysts
and other mechanisms can dramatically change these time scales.
Kinetic theory attempts to develop models and understandings for the detailed
time evolution of a system, including the effect of catalysts and intermediate states.
The models may be empirical or based on the known kinetics and interactions of
the molecules and structures involved. A detailed biomolecular kinetic theory of
reactions follows the time evolution of biomolecular interactions in solutions and
with surfaces, including the dispersive effects of thermal motion. Quantum theory,
described in the next chapter, provides a successful framework for these details, all
within the subject of ‘chemical kinematics’.
10.11.1 Conversion Reactions with Reverse Rates
Because of atom conservation, the rate of change of the concentration of molecules
of any given molecule will depend on the change in concentration of other molecules
taking part in a reaction. If the proximity of reactants is statically based, then rates
depend on the participating concentrations raised to a power. These powers need not
be the stoichiometric coefficients, but rather depend on details on how the molecules
come together in a reaction. For the reaction rates in one direction, the sum of the
powers of the concentrations is called the ‘order’ of the reaction. The order need not
be an integer.
To see what’s involved in an empirical model, take an example of the time
evolution of a reaction that converts a molecule from type A to type B:
A B.
A phase change is of this category, as is an isomeric transformation.
67 For more on Onsager’s reciprocity relations, see Sect. 9.23.2.
10 The Statistical Basis of Bioenergetics
λ ij = λ ji ,
(10.266)
which constitutes Onsager’s proof of his reciprocity relation. 67
10.11 Kinetic Theories for Chemical Reactions
Thermodynamics and statistical mechanics focus on equilibrium states of thermal
systems. Time considerations for a process enters principally in discriminating
between reactions that actually reach quasi-equilibrium in the system in times
comparable to or shorter than the typical times needed for given processes. Catalysts
and other mechanisms can dramatically change these time scales.
Kinetic theory attempts to develop models and understandings for the detailed
time evolution of a system, including the effect of catalysts and intermediate states.
The models may be empirical or based on the known kinetics and interactions of
the molecules and structures involved. A detailed biomolecular kinetic theory of
reactions follows the time evolution of biomolecular interactions in solutions and
with surfaces, including the dispersive effects of thermal motion. Quantum theory,
described in the next chapter, provides a successful framework for these details, all
within the subject of ‘chemical kinematics’.
10.11.1 Conversion Reactions with Reverse Rates
Because of atom conservation, the rate of change of the concentration of molecules
of any given molecule will depend on the change in concentration of other molecules
taking part in a reaction. If the proximity of reactants is statically based, then rates
depend on the participating concentrations raised to a power. These powers need not
be the stoichiometric coefficients, but rather depend on details on how the molecules
come together in a reaction. For the reaction rates in one direction, the sum of the
powers of the concentrations is called the ‘order’ of the reaction. The order need not
be an integer.
To see what’s involved in an empirical model, take an example of the time
evolution of a reaction that converts a molecule from type A to type B:
A B.
A phase change is of this category, as is an isomeric transformation.
67 For more on Onsager’s reciprocity relations, see Sect. 9.23.2.