Forward and backward processes

In a number of reactions the point of equilibrium is not displaced predominantly in one direction or the other, and in such instances it is often found experimentally that the observed reaction rate may be 

Kistiakowsky s results show that the rate ma3 be expressed in the form 

The left-hand side of this equation has the correct form of the equilibrium constant expressed in terms of concentrations as in equation (4 34). Bodenstein] confirmed by experiment that the ratio kjk of the experimental velocity constants is equal to the measured equilibrium constant. It follows that the thermodynamic conditions mentioned above are entirely satisfied in this example. 

The restrictions on the permissible form of the kinetic equations are rather less stringent than is often supposed. The matter can best be discussed by considering a specific reaction whose stoichiometry is expressed by aA+bB=cC. 

Case a). Single reaction in a perfect gas mixture. In this instance the equilibrium constant, expressed in terms of concentrations, IS 

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Since the equilibrium probability Ed.s, t) contains the Boltzmann factor with an energy Tid.s, ), the condition (12) leads to the ratio of transition probabilities of the forward and backward processes as... 

The parameter G is the Gibbs energy of activation of the forward and backward process. The BV approximation assumes G to change linearly with changes in the thermodynamic driving force, that is, the overpotential ) = (E — E0), according to... 

Reverting to eqn. (1), the overall rate coefficient for the formation of products, providing that the concentration of the encounter pair (AB) is small and assuming a steady state, is kAka/(k-d + ka). When the reaction of the encounter pair to form products becomes fast compared with the diffusive forward and backward processes, the rate of formation of products is determined by the rate at which A and B can diffuse together to form the encounter pair (AB). The opposite situation is where the rate of reaction of the encounter pair is very slow compared with the backward diffusion (ka < fe d), and the products form at a rate... 

It can be shown that, for the reverse reaction, the same correction applies since zr = za n as is expected since the transition state and hence the reaction plane must be the same for both forward and backward processes. 

Most switching devices studied make use of light for interconverting a molecule between two different states. Both forward and backward processes may be photo-induced or one of them, usually the reverse transformation, may be thermal. 

The reaction rates of the shift reaction (10.20) are determined for the forward and backward processes ... 

The first exponential term in both equations is independent of the applied potential and is designated as k and A(L for the forward and backward processes, respectively. These represent the rate constants for the reaction at equilibrium, e.g. for a monolayer containing equal concentrations of both oxidized and reduced forms. However, the system is at equilibrium at E0/ and the products of the rate constant and the bulk concentration are equal for the forward and backward reactions, i.e. k must equal Therefore, the standard heterogeneous electron transfer rate constant is designated simply as k°. Substitution into Equations (2.19) and (2.20) then yields the Butler-Volmer equations as follows ... 

Dynamic equilibrium (8.5, 12.2) State achieved when the rates of the forward and backward processes in a chemical reaction become equal to one another. 

In general, for a system driven by a time symmetric process, the resulting nonequilibrium steady-state ensemble would be invariant under time reversal. This symmetry ensures that the forward and backward processes become indistinguishable and the entropy production is odd under a time reversal, the fluctuation theorem will be valid for any integer number of cycles ... 

At last, the fourth reason comes from the property of a chain to implement naturally the notion of composed properties in going along the chain from pole to pole. It means that when a transmission of entities occurs, each link depends on the behavior of the preceding one. This dependence does not work in only one direction but is truly bidirectional as an exchange is always based on forward and backward processes, even when one is dominating the other. The key notion here is the one of reversibility which is a property of an exchange that can be easily understood as a dipole property that must be composed with other dipole reversibilities for featuring the reversibility of the whole chain. In other words, the reversibility of a sequence of processes depends on the reversibility of each element. 

Equilibrium is dynamic. Equilibrium represents the most stable, lowest energy state for a system. However, in most systems this equilibrium point represents a dynamic balance between forward and backward processes that continue to occur with equal rates. Even small changes can upset this balance. The most common ways that we can shift the equilibrium point of a system are by changing temperature, pressure, or composition. 

The effect of the double layer on the kinetics is contained within the term xp[(oicn — ZQ)iFA(t>2lRT)], which is known as the Frumkin correction. It is the same for the forward and backward processes in compliance with transition state theory and the importance of the correction depends upon the magnitude and signs of olq, , Zq, and A02- If it is assumed that equilibrium prevails within the diffuse layer even when charge transfer occurs and that the diffusion layer is much thicker than the diffuse layer, then Gouy-Chapman theory can be used to calculate the dependence of 02 on the supporting electrolyte concentration (Equation (5.35)). The combination of these theoretical calculations with experimental o jE data allows the dependence of 02 on potential to be obtained, as shown in Fig. 5.9. The magnitude of A02 depends upon the position of the... 

If a reaction can proceed to an equilibrium in which reactants and products are present the reaction is said to be reversible. It has been found that the rate of such reactions must be expressed as the difference between two terms, each of which contains a velocity constant. Theory regards the positive and negative terms as the individual rates of the forward and backward processes respectively. For an elementary reaction ... 

Obviously, not only the paths but also the overall rates of forward and backward processes, S — P and P S, can be different. Under real experi-... 

The heterolytic H2-cleavage reaction of Eq. (1) is reversible. Hence, Cu(II) and Ru(III) can catalyze the isotopic exchange between hydrogen gas and water through forward and backward processes of Eq. (1) ... 

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