STEADY-STATE THEORY OF ADSORPTION PSEUDOCAPACITANCE IN ELECTROCHEMICAL RADICAL-ION REACTIONS

1964 ◽  
Vol 42 (1) ◽  
pp. 90-106 ◽  
Author(s):  
B. E. Conway ◽  
E. Gileadi
Keyword(s):  
Steady State ◽  
Adsorption Isotherms ◽  
Rate Constants ◽  
State Theory ◽  
Electrochemical Reactions ◽  
Recombination Reaction ◽  
Quasi Equilibrium ◽  
Adsorbed Species ◽  
Heterogeneity Parameter ◽  
State Case

The theory of adsorption pseudocapacity behavior is developed for a sequence of electrochemical reactions involving an ion discharge step which produces an adsorbed radical, followed by an "ion–atom" recombination reaction with or without desorption of the product of this step. The adsorption pseudocapacity behavior is deduced analytically particularly for the steady-state case and distinguished from the results obtained for assumed quasi-equilibrium in the ion discharge step when the succeeding step is rate-controlling. The effect of variation of the relative values of the rate constants of the discharge and of succeeding steps is investigated. It is shown that the capacity-potential behavior is sensitively dependent on the ratio of these rate constants, particularly for the case of adsorption isotherms involving a large value for the "heterogeneity parameter", r, defining the variation of energy of adsorption of the intermediates with coverage. Under the latter conditions, limiting coverages of the electrode by the adsorbed species are reached with increasing potential, depending on the relative values of the rate constants and the value of r.

scholarly journals Reversible enzyme-catalysed reactions: the quasi steady state as a a quasi-equilibrium, and a correction to Haldane's kinetic constants and to secondary relationships involving kinetic constants.

2021 ◽  
Author(s):  
Eric A Barnsley
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Rate Of Change ◽  
Kinetic Constants ◽  
Rate Equations ◽  
Quasi Equilibrium ◽  
Quasi Steady State ◽  
Enzyme Substrate ◽  
State Approximation ◽  
Specificity Constant

For reversible enzyme-catalysed reactions obeying Henri-Michaelis-Menten kinetics, theoretical solution of the rate equations for the enzyme-substrate intermediate are generally incorrect when the quasi-steady state approximation, equating the rate of change of the concentration of the enzyme-substrate intermediate to zero, is used.  For the simplest kinetic model used by Haldane, such a procedure does not reveal that in one direction, that starting with the reactant having the lower binding constant, the quasi-steady state is one of quasi-equilibrium, and Haldane’s structure of the Km written in terms of rate constants is incorrect. This is probably also true of more complex mechanisms in which the structure of kcat may also be in error.  Modern methods of numerical integration for the solution of rate equations, if applied to reversible reactions to obtain rate constants from measured catalytic constants, will require the correct expressions for kcat and Km. Furthermore, the (now called) Haldane relationship, relating the kinetic constants kcat and Km for the forward and reverse reactions to the equilibrium constant of a reaction, is now seen to be generally incorrect, and in addition another exception for a the theoretical validation of kcat /Km as a specificity constant arises.

scholarly journals Simplifications of the derivations and forms of steady-state equations for non-equilibrium random substrate-modifier and allosteric enzyme mechanisms

1976 ◽  
Vol 159 (3) ◽  
pp. 449-456 ◽  
Author(s):  
E P Whitehead
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Dissociation Rate ◽  
Partial Ordering ◽  
British Library ◽  
Quasi Equilibrium ◽  
State Equations ◽  
Allosteric Enzyme ◽  
Dissociation Rate Constants ◽  
Alternative Routes

The steady-state equations for “random” enzymic mechanisms (ones with alternative routes for substrate and enzyme to form enzyme-substrate complexes) are non-Michaelian and very complicated when a quasi-equilibrium approximation cannot be used. General methods for simplifying their forms and derivations are given and applied to several single-substrate mechanisms of general or topical interest. The special simplifications resulting from partial ordering of reaction mechanism, from gross inequalities of rate constants, and from special relationships between catalytic and dissociation rate constants, are considered with reference to allosteric mechanisms. Some equations mentioned, but not given here, and more detailed working out of some of those given, have been deposited as Supplementary Publication SUP 50069 (18 pages) at the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms given in Biochem. J. (1976) 153, 5.

Identification of Adsorbed Species during Steady-State Photocatalytic Oxidation of Ethanol on TiO2

1998 ◽  
Vol 180 (2) ◽  
pp. 111-122 ◽  
Author(s):  
Darrin S. Muggli ◽  
Kelley H. Lowery ◽  
John L. Falconer
Keyword(s):  
Steady State ◽  
Photocatalytic Oxidation ◽  
Adsorbed Species ◽  
Oxidation Of Ethanol

Insensitivity of steady-state distributions of generalized semi-Markov processes by speeds

1978 ◽  
Vol 10 (04) ◽  
pp. 836-851 ◽  
Author(s):  
R. Schassberger
Keyword(s):  
Steady State ◽  
General System ◽  
State Distribution ◽  
Lifetime Distributions ◽  
State Dependent ◽  
Semi Markov Process ◽  
Semi Markov Processes ◽  
Infinite State ◽  
State Case ◽  
Residual Lifetimes

A generalized semi-Markov process with speeds describes the fluctuation, in time, of the state of a certain general system involving, at any given time, one or more living components, whose residual lifetimes are being reduced at state-dependent speeds. Conditions are given for the stationary state distribution, when it exists, to depend only on the means of some of the lifetime distributions, not their exact shapes. This generalizes results of König and Jansen, particularly to the infinite-state case.

scholarly journals Reaction mechanism of the magnesium ion-dependent adenosine triphosphatase of frog muscle myosin and subfragment 1

1978 ◽  
Vol 171 (1) ◽  
pp. 165-175 ◽  
Author(s):  
M A Ferenczi ◽  
E Homsher ◽  
R M Simmons ◽  
D R Trentham
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Myosin Atpase ◽  
Forward Rate ◽  
Magnesium Ion ◽  
Skeletal Muscle Myosin ◽  
General Terms ◽  
Predominant Component ◽  
Main Components ◽  
Muscle Myosin

The Mg2+-dependent ATPase (adenosine 5′-triphosphatase) mechanism of myosin and subfragment 1 prepared from frog leg muscle was investigated by transient kinetic technique. The results show that in general terms the mechanism is similar to that of the rabbit skeletal-muscle myosin ATPase. During subfragment-1 ATPase activity at 0-5 degrees C pH 7.0 and I0.15, the predominant component of the steady-state intermediate is a subfragment-1-products complex (E.ADP.Pi). Binary subfragment-1-ATP (E.ATP) and subfragment-1-ADP (E.ADP) complexes are the other main components of the steady-state intermediate, the relative concentrations of the three components E.ATP, E.ADP.Pi and E.ADP being 5.5:92.5:2.0 respectively. The frog myosin ATPase mechanism is distinguished from that of the rabbit at 0-5 degrees C by the low steady-state concentrations of E.ATP and E.ADP relative to that of E.ADP.Pi and can be described by: E + ATP k' + 1 in equilibrium k' − 1 E.ATP k' + 2 in equilibrium k' − 2 E.ADP.Pi k' + 3 in equilibrium k' − 3 E.ADP + Pi k' + 4 in equilibrium k' − 4 E + ADP. In the above conditions successive forward rate constants have values: k' + 1, 1.1 × 10(5)M-1.S-1; k' + 2 greater than 5s-1; k' + 3, 0.011 s-1; k' + 4, 0.5 s-1; k'-1 is probably less than 0.006s-1. The observed second-order rate constants of the association of actin to subfragment 1 and of ATP-induced dissociation of the actin-subfragment-1 complex are 5.5 × 10(4) M-1.S-1 and 7.4 × 10(5) M-1.S-1 respectively at 2-5 degrees C and pH 7.0. The physiological implications of these results are discussed.

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