Reversible reaction vs. time

This result is usually simplified one more time in one of two ways Assume that either (1) the reverse of the second reaction does not occur (i.e., k 2 = 0) or (2) at the beginning of the reaction [P] is negligibly small in either case, one gets that the speed of the reaction v is given by 

Experimentally, values for V are determined at the start of a reaction and correspond to initial rates, V o or V at time 0. Testing in this manner ensures that [P] 0, and that the reverse reaction may be ignored. In many treatments of enzyme kinetics, the initial rates are explicitly labeled V0 instead of V. 

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. 

Another branch of the work was concerned with a reverse reaction, the interaction of mercury dichloride with organometallic compounds of Groups III, IV, or V. At that time, (1934), the literature on the reaction was surprisingly scarce. 

These results indicate a reversible reaction between electrogenerated Co(l) and C02-It is of particular interest to note that, depending on the time scale of the experiment, two different Co—CO2 complexes with reduction potentials —1.26 V and —1.53 V vs. see may be formed. Catalytic reduction of CO2 to CO and carbonate was observed with high selectivity and satisfactory current efficiency, when 1—2 mM Co(ll)L solutions saturated with CO2 were electrolyzed at potentials beyond —1.26 V. Note that sustained electrocatalysis was obtained indifferently whether the elctrolysis potential was beyond the reduction of the first or second CO2 complex. This result possibly 

Fig. 6.22. The 14 different qualitative forms for the stationary-state locus for cubic autocatalysis with reversible reactions and inflow of all species, with c0 < a0 the broken line represents the equilibrium composition which is approached at long residence times. (Reprinted with permission from Balakotaiah, V. (1987). Proc. R. Soc., A41J, 193.)

S A was also applied to the reversible reactions considered in Section XII.C.4. Since the results were not satisfactory, an extended superposition approach (ESA) was developed, then linearized, and later known as LESA [241]. Independently, a similar linearization over deviations from equilibrium was also made in Ref. 242. Although the asymptotic description of the quenching kinetics is improved, it was recognized [242] that LESA is not valid with a large equilibrium constant K because the superposition approach worsens when K increases [241]. This is especially true at earlier times when the deviations from equilibrium are not small. However, the authors who constructed LESA claimed that it is applicable at all times [241]. Therefore, it was taken for comparison with other approximations. In the irreversible limit (K —> oo), the kernels obtained in both works [241,242] coincide with that listed as LESA in Table V. 

During the reverse potential sweep in CV experiments on the other hand, the product of the initial oxidation or reduction of the electroactive species is complementary reduced or oxidized (Figure 2.5). In this context, and correspond to the anodic and cathodic potential peaks, respectively [1, 6, 7]. It is important to note that for reactions characterized by fast electron transfer events relative to the time-scale of the potential sweep rate (reversible reactions, where the difference pa - E is independent of v), the formal thermodynamic electrode potential E° can be readily estimated using Equation 2.2. 

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