Reverse rate, defined

If kj and kj denote tlie forward and reverse rate constants respectively, die general rate of disappearance (-r ) for any type of reaction is defined as ... 

We have noted previously that the forward and reverse rates are equal at equilibrium. It seems, then, that one could use this equality to deduce the form of the rate law for the reverse reactions (by which is meant the concentration dependences), seeing that the form of the equilibrium constant is defined by the condition for thermodynamic equilibrium. By and large, this method works, but it is not rigorously correct, since the coefficients in the equilibrium condition are only relative, whereas those in the rate law are absolute.19 Thus, if we have this net reaction and rate law for the forward direction,... 

Because association is reversed by the dissociation reaction, one does not ever achieve complete conversion of free E and I to the El complex. Rather, the system approaches an equilibrium with respect to the concentrations of E, /, and EL We can define an equilibrium association constant as the ratio of products to reactants, or as the ratio of the forward to reverse rate constants ... 

CHEMRev The Comparison of Detailed Chemical Kinetic Mechanisms Forward Versus Reverse Rates with CHEMRev, Rolland, S. and Simmie, J. M. Int. J. Chem. Kinet. 37(3), 119-125 (2005). This program makes use of CHEMKIN input files and computes the reverse rate constant, kit), from the forward rate constant and the equilibrium constant at a specific temperature and the corresponding Arrhenius equation is statistically fitted, either over a user-supplied temperature range or, else over temperatures defined by the range of temperatures in the thermodynamic database for the relevant species. Refer to the website http //www.nuigalway.ie/chem/c3/software.htm for more information. 

The difference between the potential applied and the reversible potential for a reaction is known as the overpotential. It represents the driving force for the kinetics of the reaction. Anodic overpotentials are associated with oxidation reactions, and cathodic overpotentials are associated with reduction reactions. The relationship between the overpotential and the reaction rate defines the kinetics. Mathematical relationships exist for many instances, but in corrosion situations, the data are generally experimentally derived. 

The equilibrium constant (based on volumetric concentrations) is defined as the ratio of the forward and reverse rate constants and is related to the composition at equilibrium as follows ... 

On the more theoretical level, once the system is sufficiently defined to determine the forward- and reverse-rate coefficients, thermodynamic quantities can be calculated. If the reaction is first-order, the ratio of rate coefficients is the thermodynamic equilibrium constant, from which the change in Gibbs free energy can be obtained. By using multiple equilibration temperatures, enthalpy change can be calculated (Harter and Smith, 1981). 

For NarGH, rapid and reversible inter-conversion of kineticaUy distinct enzyme forms occurs on sweeping across the electrochemical potential domain. Raising the pH has two effects, both of which are fully reversed on returning the film to solutions of pH 6. First, there is an overall decrease in activity of the film at both high and low nitrate concentrations. Second, the peak in activity at low nitrate concentrations becomes more pronounced. Thus, variation of pH has distinct effects on the rate-defining events of enzyme- and nitrate-limited turnover. 

The rate-determining step is often defined as the slowest of a series of steps that occur. In catalysis, adsorption of reactant, surface reaction, and desorption all occur in series. Because all of these occur at steady state, they should all proceed at the same rate. Therefore, the word slowest is a misnomer. The controlling step is really the step that consumes most of the driving force. Even in the case where all of the steps are fast enough to have reached equilibrium, i.e., the steady overall rate = (ratef rward reverse) there will be a controlling step. This is the step for which the ratio of the two rates is significantly different from 1. For all other steps, the forward and reverse rates are both so high that the ratio tends to be almost unity. 

The presteady-state burst will be followed by steady-state turnover at a rate given by cat The presteady-state burst of product formation will occur at a rate defined by the sum of the rates of the chemical reaction and product release. The amplitude is also a function of both rate constants, k2 and kj. Thus, the amplitude of the burst can be predicted from the rate of the burst and the rate of steady-state turnover. Although this model can account for burst kinetics, it is often inadequate due to the assumed irreversibility of the chemical reaction. The internal equilibrium arising from the reverse of the chemical reaction k-2) reduces the amplitude of the burst to less than predicted by Eq. (26). 

Additional insights into the resonance effect on the stabilization of 72 comes from a consideration of the rate constants ki and k-i, or, more precisely, the intrinsic rate constants. The general definition of the intrinsic rate constant, ko, of a reaction with forward and reverse rate constants k and k-i, respectively, is ko = k = k-i when = 1 if dealing with free energies, one can define an intrinsic barrier, AGq, as AGq = AGj = AgIj when AG° = q H9,i20 significance of ko or AGq is that they are purely kinetic measures of chemical reactivity because they separate out thermodynamic effects from kinetic effects and hence they allow meaningful comparisons of reactivity between different reactions. 

Equation 5,38 cannot be set to zero to define the equilibrium concentration, nor is the ratio of the forward and reverse rate constants equal to the equilibrium constant for the elementary reaction. The equilibrium... 

Reversibility, so defined, actually depends on the relative rates of the electrode process and of the rapidity of the electrochemical measurement a particular system may behave reversibly when measurements are made slowly, but irreversibly if the measurement involves short times (pulses of current or voltage, or high frequencies of an alternating electrical signal). Consequently, in modern usage, one prefers to talk about electrode processes as being fast or slow, and as behaving reversibly or... 

The futnre market price of a zero-coupon bond in this framework can be found by defining the reversion rate, P, the volatility, and the... 

Some models assume that a system reaches a steady state rather than equilibrium. Equilibrium is defined by the principle of detailed balance, which requires that the forward and reverse rates are equal and that each step along the reaction path is reversible. The forward and reverse rates of steady-state processes are equal but the process steps that produce the forward rate are different from those that produce the reverse rate. At steady state, the state variables of an open system remain constant even though there is mass and/or energy flow through the system. The steady-state assumption is especially useful for processes that occur in a series, because the concentrations of intermediates that are formed and subsequently destroyed are constant. Perturbation of a steady-state system produces a transient state where the state variables evolve over time and approach a new steady state asymptotically. 

This is quite a complex integrated rate equation. However, if we study the kinetics of the reaction at points in time near the establishment of equilibrium, we make the assumption that the forward and reverse rates are becoming equal (as when equilibrium is really established). At equilibrium we define [x] as [x]e, where the extent of reaction is as far as it is going to go, which leads to W[ A]o - [x]c) = fcr([B]o + [x]e). Solving this equality for fcf[ A] - A r[B] , and substituting the result into Eq. 7.41, leads to Eq. 7.42. This tells us that as one approaches equilibrium, the rate appears first order with an effective rate constant that is the sum of the forward and reverse rate constants. This is an approximation because we defined [.v] as [. ]e to obtain this answer, but it is a very common way to analyze equilibrium kinetics. Chemists qualitatively estimate that the rate to equilibrium is the sum of the rates of the forward and reverse reactions. 

Klinger and Kochi have introduced a quantitative measure of reversibility in electrochemistry as the deviation of the surface concentrations from the values that would exist under Nernstian conditions. Reversibility thus defined is a function of position along the cyclic voltammogram (i.e., potential). This is because the heterogeneous rates are modulated several orders of magnitude... 

The models developed here account for unmeasurable intermediates such as adsorbed ions or free radicals. Microkinetic analysis, pioneered by Dumesic and cowokers"", is an example of this approach. It quantifies catalytic reactions in terms of the kinetics of elementary surface reactions. This is done by estimating the gas-phase rate constants from transition state theory and adjusting these constants for surface reactions. For instance, isobutane cracking over zeolite Y-based FCC catalysts has 21 reversible steps defined by 60 kinetic parameters." The rate constants are estimated from transition state theory... 

Not only have we defined forward rate constants fcj and k2, but we also define reverse rate constants and k 2- According to the previous section, we can also define equilibrium constants for each reaction, Ki and K2, as... 

Newton s law is formulated so that the rate of shear (duy/dz) plays the role of a driving force while the force per unit area plays the role of a rate variable. This seems like a role reversal, but defining Newton s law in this way corresponds to a viscosity coefficient that is larger for more viscous fluids. Newton s law is valid only for laminar flow, which means flow in layers. Flow that is not laminar is called turbulent flow, and Newton s law does not hold for turbulent flow. There are some liquids, such as blood and polymer solutions, that do not obey Newton s law even for laminar flow. These fluids are called non-Newtonian fluids or thixotropic fluids and can be described by a viscosity coefficient that depends on the rate of shear. 

The potential of an electrode in an electrolytic solution when the forward rate of a given reaction is exactly equal to the reverse rate. The equilibrium potential can only be defined with respect to a specific electrochemical reaction. 

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