Rate-determining step in reaction

Example 5.4.2.2b. Rate-determining step in reaction of Example 5.5.2.2a... 

The rate-determinating step in reaction (45) is second order, illustrating that Lewis acid-base interactions are involved in this process. Eqs. (43)-(45) are similar to reactions (36) and (37) since the tin(II) compounds formed are highly associated (tin(II) chloride and tin(II) sulfide can be isolated as pure and large crystals), the equilibrium is shifted to the right side. 

Here, Ais the free energy change of Reaction 17.3 (kJ mol 1), R is the gas constant (8.3143 J K-1 mol-1), and 7k is absolute temperature (K). Factor co is the reciprocal of the average stoichiometric number, which can be taken as the number of times the rate determining step in Reaction 17.3 occurs per turnover of the reaction (Jin and Bethke, 2005). 

The rates of many chemical reactions does not appear to depend on the solvent. This is because the activation energy for the process of diffusion in a liquid is nearly 20 kJ mol1 whereas for chemical reactions it is quite large. Thus, step (i) is usually not rate determining step in reactions in solutions. When the reaction takes place in solution, it is step (ii) that determines the rate of a bimolecular reaction. This conclusion is supported by the fact that the rates of these reactions do not depend upon the viscosity of the solvent. The rate should be effected by the solvent if diffusion of reactant is the rate determining step. 

Terjesen S.G., Erga O., Thorsen G. and Ve A. (1961) II. Phase boundary processes as rate determining steps in reactions between solids and liquids. Chem. Engn. Sci. 74, 277-288. 

When a reaction proceeds through several successive elementary steps, and one of these reactions is very much slower than any of the others, then the rate will depend on the rate of this single slowest step. The slow step is the rate-determining step. In the above example, reaction (9a) constitutes such a rate-determining step. In reactions (9a) and (9b), a steady state for [HBr02] is rapidly reached (so-called pseudosteady state). HBrOz formed in reaction (9a) is almost immediately consumed in reaction (9b). Hence, the formation of HOBr in (9b) occurs at the same rate as in (9a). From the condition of equality of the rates of the two reactions in a pseudosteady state, ra = rb, we obtain... 

In summary, the proposal that the rate-determining step in reactions between chro-mate and thiols at physiological pH is the rate of formation of thioester, explains why... 

The measurement of a from the experimental slope of the Tafel equation may help to decide between rate-determining steps in an electrode process. Thus in the reduction water to evolve H2 gas, if the slow step is the reaction of with the metal M to form surface hydrogen atoms, M—H, a is expected to be about If, on the other hand, the slow step is the surface combination of two hydrogen atoms to form H2, a second-order process, then a should be 2 (see Ref. 150). 

With the potential energies shown on a common scale we see that the transition state for formation of (CH3)3C is the highest energy point on the diagram A reaction can proceed no faster than its slowest step which is referred to as the rate determining step In the reaction of tert butyl alcohol with hydrogen chloride formation of the... 

Assuming that the rate determining step in the reaction of cyclohexanol with hydrogen bro mide to give cyclohexyl bromide is unimolecular write an equation for this step Use curved arrows to show the flow of electrons... 

Notice that specific acid catalysis describes a situation in which the reactant is in equilibrium with regard to proton transfer, and proton transfer is not rate-determining. On the other hand, each case that leads to general acid catalysis involves proton transfer in the rate-determining step. Because of these differences, the study of rates as a function of pH and buffer concentrations can permit conclusions about the nature of proton-transfer processes and their relationship to the rate-determining step in a reaction. 

The details of proton-transfer processes can also be probed by examination of solvent isotope effects, for example, by comparing the rates of a reaction in H2O versus D2O. The solvent isotope effect can be either normal or inverse, depending on the nature of the proton-transfer process in the reaction mechanism. D3O+ is a stronger acid than H3O+. As a result, reactants in D2O solution are somewhat more extensively protonated than in H2O at identical acid concentration. A reaction that involves a rapid equilibrium protonation will proceed faster in D2O than in H2O because of the higher concentration of the protonated reactant. On the other hand, if proton transfer is part of the rate-determining step, the reaction will be faster in H2O than in D2O because of the normal primary kinetic isotope effect of the type considered in Section 4.5. 

In Fig. 3 there appears to be only one reaction step for the novolac from beginning to end. This indicates that novolac methylolation and condensation reactions occur simultaneously at all temperatures. This, in turn, shows that the activation energy for the condensation reaction is similar to or less than that for the methylolation. In other words, the methylolation is the rate-determining step in the process. 

The ratio of products 15 and 16 is dependent on the structures, base, and the solvent. The kinetics of the reaction is likewise dependant on the structures and conditions of the reaction. Thus addition or cyclization can be the rate-determining step. In a particularly noteworthy study by Zimmerman and Ahramjian, it was reported that when both diastereomers of 20 were treated individually with potassium r-butoxide only as-epoxy propionate 21 was isolated. It is postulated that the cyclization is the rate-limiting step. Thus, for these substrates, the retro-aldolization/aldolization step reversible. ... 

Once formed, 7 and 8 undergo a Michael reaction that gives rise to ketoenamine 9. Ring closure, to form 10, and loss of water then afforded 1,4-dihydropyridine 11. The presence of 9 and 10 could not be detected thus ring closure and dehydration were deduced to proceed faster than the Michael addition. This has the result of making the Michael addition the rate-determining step in this sequence. Conversely, if the reaction is run in the presence of a small amount of diethylamine, compounds related to 10 could be isolated. Diol 20 has been isolated in an unique case (R = CFb). Attempts to dehydrate this compound under a variety of conditions were unsuccessful. Stereoelectronic effects related to the dehydration may be the cause. In related heterocyclic ring formations, it has been determined that dehydration (20 —> 10) is about 10 times slower than diol formation (19 —> 20). Therefore, one would expect 20 to... 

Fig. 4. Dependence of relative concentrationa nj/nt of reaction components A, B, and C on time variable r (arbitrary units) in the case of consecutive (— — ) reactions according to scheme (Ha) or parallel (C ) reactions according to scheme (lib). Ads X, Ads A, Des Y denotes that the rate determining step in the overall transformation is adsorption or desorption of the respective substance Des (B + C) denotes that the overall rate is determined by simultaneous desorption of the substance B and C. Ki/Ki = 0.5 for consecutive, and Ki /Ki — 0.5 for parallel reactions, b nxVn. 0 = 2.5 for consecutive reactions Kt = 0.5, and for parallel reactions Ki/Ki — 0.5. c nxVnA0 = 2.5 fcdesBKi Ky/fcdesoXj Kx = 10 [cf. (53)]. d Ki = 1.75 for consecutive, and Ki/Ki = 1.75 for parallel reactions.

However, while it is generally accepted that the rate of radical-radical reaction is dependent on how fast the radical centers of the propagating chains (Pp and Pj ) come together, there remains some controversy as to the diffusion mechanism(s) and/or what constitutes the rate-determining step in the diffusion process. The steps in the process as postulated by North and coworkers30 3" arc shown conceptually in Scheme 5.5. 

The rate-determining step in the homo-coupling reaction of aryl halides could be the oxidative step or the reduction of Ni(II) to Ni(I) step. 

FIGURE 6.2. A schematic description of the rate-determining steps in the catalytic reaction of lysozyme. 

---