Rate forward, reverse

Fig. 1. Effect of rf chuck power on forward reverse voltages (top) and etch rate and surface roughness (bottom).

Our present topic is the relationship between permeability and lipophilicity (kinetics), whereas we just considered a concentration and lipophilicity model (thermodynamics). Kubinyi demonstrated, using numerous examples taken from the literature, that the kinetics model, where the thermodynamic partition coefficient is treated as a ratio of two reaction rates (forward and reverse), is equivalent to the equilibrium model [23], The liposome curve shape in Fig. 7.20 (dashed-dotted line) can also be the shape of a permeability-lipophilicity relation, as in Fig. 7.19d. 

One advantage of the initial rate method is that complex rate functions that may be extremely difficult to integrate can be handled in a convenient manner. Moreover, if one uses initial reaction rates, the reverse reactions can be neglected and attention can be focused solely on the reaction rate function for the forward reaction. More complex rate functions may be tested by the choice of appropriate coordinates for plotting the initial rate data. For example, a reaction rate function of the form... 

Much fundamental work yet remains in the study of intramolecular donor-acceptor molecules to find out what structural parameters of the donor, acceptor and particularly the linkage enhance the efficiency of forward electron transfer while at the same time inhibiting the rate of reverse electron transfer. Progress so far is very promising. 

At equilibrium, the rates of the forward and the reverse reactions are equal. Therefore, to drive the reaction rate forward in the direction of the ester linkages, represented by z, then reaction by-products, EG and water must be removed. Both reactions are affected by one or more of the following ... 

It must be however underlined that, in measuring the peak-to-peak separation, a departure of 10-20 mV from the theoretical value (especially at relatively high scan rates) does not compromise the criterion of reversibility, in that the eventual presence of solution resistances not adequately compensated by the electrochemical instrumentation (see Chapter 3, Section 2) tends to lay down the forward/ reverse peaks system, thus increasing the relative Aisp value. 

Many, if not most, step polymerizations involve equilibrium reactions, and it becomes important to analyze how the equilibrium affects the extent of conversion and, more importantly, the polymer molecular weight. A polymerization in which the monomer(s) and polymer are in equilibrium is referred to as an equilibrium polymerization or reversible polymerization. A first consideration is whether an equilibrium polymerization will yield high-molecular-weight polymer if carried out in a closed system. By a closed system is meant one where none of the products of the forward reaction are removed. Nothing is done to push or drive the equilibrium point for the reaction system toward the polymer side. Under these conditions the concentrations of products (polymer and usually a small molecule such as water) build up until the rate of the reverse reaction becomes equal to the polymerization rate. The reverse reaction is referred to generally as a depolymerization reaction other terms such as hydrolysis or glycolysis may be used as applicable in specific systems. The polymer molecular weight is determined by the extent to which the forward reaction has proceeded when equilibrium is established. 

I. The rate of forward reaction is equal to the rate of reverse reaction. 

Type Structure Size Reverse Leakage Forward/Reverse Flow Rate... 

Check Valve Rverse Leakage (Pressure) Forward/ Reverse Flow Rate Dynamic Response... 

Consider the mineral AB (Reaction 7.1), where A denotes any cation (A+) and B denotes any anion (B ). Upon introducing H20, the mineral undergoes solubilization (forward reaction) until precipitation (reverse reaction) becomes significant enough so that the two rates (forward and reverse) are equal ... 

Obviously, therefore there must be an intermediate case in which the kinetics of both the forward and reverse electron-transfer processes have to be taken account of. Such systems are described as being quasi-reversible and as would be expected, the scan rate can have a considerable effect on the nature of the cyclic voltammetry. At sufficiently slow scan rates, quasi-reversible processes appear to be fully reversible. However, as the scan rate is increased, the kinetics of the electron transfer are not fast enough to maintain (Nernstian) equilibrium. In the scan-rate region when the process is quasi-reversible, the following observations are made. 

As = surface area of a semiconductor contact [A ] = concentration of the reduced form of a redox couple in solution [A] = concentration of the oxidized form of a redox couple in solution A" = effective Richardson constant (A/A ) = electrochemical potential of a solution cb = energy of the conduction band edge Ep = Fermi level EF,m = Fermi level of a metal f,sc = Fermi level of a semiconductor SjA/A") = redox potential of a solution ° (A/A ) = formal redox potential of a solution = electric field max = maximum electric field at a semiconductor interface e = number of electrons transferred per molecule oxidized or reduced F = Faraday constant / = current /o = exchange current k = Boltzmann constant = intrinsic rate constant for electron transfer at a semiconductor/liquid interface k = forward electron transfer rate constant = reverse electron transfer rate constant = concentration of donor atoms in an n-type semiconductor NHE = normal hydrogen electrode n = electron concentration b = electron concentration in the bulk of a semiconductor ... 

It is easy to see from Equation (2.2.5) that if ( 2 i) > 0 then the reaction is exothermic and likewise if ( 2 — 1) < 0 it is endothermic (refer to Appendix A for temperature dependence of A c). In a typical situation, the highest yields of products are desired. That is, the ratio (CsCw/C CB%q will be as large as possible. If the reaction is endothermic. Equation (2.2.5) suggests that in order to maximize the product yield, the reaction should be accomplished at the highest possible temperature. To do so, it is necessary to make exp[( 2 — i)/(/ T)] as large as possible by maximizing (RgT), since ( 2 — 1) is negative. Note that as the temperature increases, so do both the rates (forward and reverse). Thus, for endothermic reactions, the rate and yield must both increase with temperature. For exothermic reactions, there is always a trade-off between the equilibrium yield of products and the reaction rate. Therefore, a balance between rate and yield is used and the T chosen is dependent upon the situation. 

Briefly comment on the effect of a catalyst on each of the following (a) activation energy, (b) reaction mechanism, (c) enthalpy of reaction, (d) rate of forward step, (e) rate of reverse step. 

---