TY - JOUR
T1 - Thermodynamically consistent forward and reverse degrees of rate control in reversible reactions
AU - Foley, Brandon L.
AU - Bhan, Aditya
N1 - Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/9
Y1 - 2020/9
N2 - The net rate of a composite reaction is the difference between the forward and reverse reaction rates, which are kinetically distinct despite sharing elementary reaction steps and therefore have different rate-controlling transition states and species. Thus, degrees of rate control defined to identify rate-controlling transition states and species for the net rate confound contributions from the forward and reverse reactions. Herein, the forward and reverse degrees of rate control are defined to independently quantify the extent that species and transition states control the forward and reverse rates in reversible reactions. These degrees of rate control are defined as the relative change in the forward and reverse reaction rates per kBT decrease in the standard-state molecular free energies of transition states and species, and they are related to experimentally measurable quantities such as steady-state fractional coverages, reaction orders, and energies and entropies of activation of the forward and reverse reaction rates. The forward/reverse degrees of rate control represent stoichiometric coefficients for species and transition states in an equilibrium between the initial states and transition states of the apparent rate-controlling steps of forward and reverse overall reactions. At equilibrium, the apparent transition states for the forward reaction and reverse reaction converge, and thus the forward and reverse rate-controlling steps combine to form a single apparent rate-controlling step. This apparent rate-controlling step is comprised of an apparent initial state, transition state, and final state, where the apparent final state of the forward reaction is the apparent initial state of the reverse reaction. The apparent rate-controlling step behaves identically to an elementary step reaction at equilibrium with a pseudo-mass-action rate function given by the transition-state-theory (TST) form rate function (Foley and Bhan, 2020) with a stoichiometric number equal to the affinity-averaged stoichiometric number, σ¯. The ratio of the forward and reverse TST-form rate functions is identical to the overall thermodynamic equilibrium relation, consistent with the principles of microscopic reversibility and detailed balance at equilibrium.
AB - The net rate of a composite reaction is the difference between the forward and reverse reaction rates, which are kinetically distinct despite sharing elementary reaction steps and therefore have different rate-controlling transition states and species. Thus, degrees of rate control defined to identify rate-controlling transition states and species for the net rate confound contributions from the forward and reverse reactions. Herein, the forward and reverse degrees of rate control are defined to independently quantify the extent that species and transition states control the forward and reverse rates in reversible reactions. These degrees of rate control are defined as the relative change in the forward and reverse reaction rates per kBT decrease in the standard-state molecular free energies of transition states and species, and they are related to experimentally measurable quantities such as steady-state fractional coverages, reaction orders, and energies and entropies of activation of the forward and reverse reaction rates. The forward/reverse degrees of rate control represent stoichiometric coefficients for species and transition states in an equilibrium between the initial states and transition states of the apparent rate-controlling steps of forward and reverse overall reactions. At equilibrium, the apparent transition states for the forward reaction and reverse reaction converge, and thus the forward and reverse rate-controlling steps combine to form a single apparent rate-controlling step. This apparent rate-controlling step is comprised of an apparent initial state, transition state, and final state, where the apparent final state of the forward reaction is the apparent initial state of the reverse reaction. The apparent rate-controlling step behaves identically to an elementary step reaction at equilibrium with a pseudo-mass-action rate function given by the transition-state-theory (TST) form rate function (Foley and Bhan, 2020) with a stoichiometric number equal to the affinity-averaged stoichiometric number, σ¯. The ratio of the forward and reverse TST-form rate functions is identical to the overall thermodynamic equilibrium relation, consistent with the principles of microscopic reversibility and detailed balance at equilibrium.
KW - Degree of rate control
KW - Detailed balance
KW - Forward rate
KW - Microscopic reversibility
KW - Rate-controlling step
KW - Reverse rate
KW - Reversibility
KW - Sensitivity
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U2 - 10.1016/j.jcat.2020.06.013
DO - 10.1016/j.jcat.2020.06.013
M3 - Article
AN - SCOPUS:85088123596
SN - 0021-9517
VL - 389
SP - 566
EP - 577
JO - Journal of Catalysis
JF - Journal of Catalysis
ER -