Hypothetical reaction

Kinetic data provide information only about the rate-determining step and steps preceding it. In the hypothetical reaction under consideration, the final step follows the rate-determining step, and because its rate will not affect the rate of the overall reaction, will not appear in the overall rate expression. The rate of the overall reaction is governed by the second step, which is the bottleneck in the process. The rate of this step is equal to A2 multiplied by the molar concentration of intermediate C, which may not be directly measurable. It is therefore necessary to express the rate in terms of the concentrations of reactants. In the case under consideration, this can be done by recognizing that [C] is related to [A] and [B] by an equilibrium constant ... 

A useful approach that is often used in analysis and simplification of kinetic expressions is the steady-state approximation. It can be illustrated with a hypothetical reaction scheme ... 

Let us apply this method to the hypothetical reaction coordinate diagram of Fig. 5-11, which consists of two sections. The requisite energy differences are for the vertical distances (T2 — R) and (T3 — I2). Because (T3 — I2) > (T2 — R), the second section contains the rds, which must be the I2 —> T3 step. Note that T3 actually has a lower free energy than do Ti and T2 it is the change in free energy from the valley at the beginning of the section that determines the rate. 

An alternative, total energy, will be used throughout this workbook. The total energy is the heat of a hypothetical reaction that creates a molecule from a collection of separated nuclei and electrons. Like the heat of formation, total energy cannot be measured directly, and is used solely to provide a standard method for expressing and comparing energies. 

Further investigation of pyrrole polymer would be of considerable interest. Rather similar to the foregoing hypothetical reaction is the attempted quaternization of (21), which leads directly to (22), no quaternary salt surviving at all. ... 

In the previous section we saw that the stability of a nucleus is affected by its neutron/proton ratio. Even among those nuclei that we consider stable, however, there is a variation in the forces which hold the nucleus together. In order to study this variation in nuclear binding energy, let us consider the process of building a nucleus from protons and neutrons. For an example, let us look at the hypothetical reaction... 

See Gray and Scott for a detailed analysis of this (hypothetical) reaction system. 

On the other hand, the yield of ferrocene in a [CpFe(CO)2]2 matrix (50) is not altered up to 80° C, so that here either Cp transfer is not possible or the position on the Fe atom is blocked by CO groups. It seems plausible to consider a rapid ligand condensation as a very early prethermal competitive reaction. One can thus set up a hypothetical reaction scheme such as [using PhHCr(CO)3 as the matrix compound] ... 

C15-0076. Problem asks about a mechanism for the hypothetical reaction of AB with C. Assume that the first step described in Problem is fast and reversible and your second step is rate-determining. Derive the rate law under these assumptions. 

C15-0126. Consider the following hypothetical reaction, which is order overall and half order in 1... 

The product branching ratio / is defined as the quantity of each chemically distinguishable set of reaction products n compared to the quantity of all products. As an example, consider the hypothetical reaction... 

If the equation of the decomposition reaction is not known, this calculation is carried out using the equation of the hypothetical reaction that releases the strongest energy theoretically possible. 

The main problem is knowing how to write the equation of the most energetic hypothetical reaction. Here are some rules that can be applied in the simplest case in which the molecule contains C, H, O, N, X p< = halogen) atoms ... 

The formation of hydrogen sulphide produces -20.6/2 kj ie -10.3 kj per hydrogen atom whereas the formation of methane produces -74.82/4 kJ ie -18.705 kJ per hydrogen atom. Maximum methane has then to be formed in this hypothetical reaction. To be thorough, the potential formation of carbon disulphide has to be analysed, but this substance is endothermic. ... 

A large number of type 1 dioxygen adducts are reported in the literature (25, 76, 80). The vast majority of metal complexes which take up dioxygen to form type I adducts contain cobalt(ll) as the metal ion. Ochiai (81) considered the hypothetical reactions ... 

The rate expression is a mathematical description of the rate of the reaction at any time t in terms of the concentration(s) of the molecular species present at that time. By using the hypothetical reaction aA + bB —> products, the rate expression can be written as... 

Not all sensitized photochemical reactions occur by electronic energy transfer. Schenck<77,78) has proposed that many sensitized photoreactions involve a sensitizer-substrate complex. The nature of this interaction could vary from case to case. At one extreme this interaction could involve a-bond formation and at the other extreme involve loose charge transfer or exciton interaction (exciplex formation). The Schenck mechanism for a photosensitized reaction is illustrated by the following hypothetical reaction ... 

Scheme 4. Hypothetical reaction scheme for the formation of 2 starting from an icosahedral AI12 compound.

SCHEME 5. Hypothetical reaction scheme for the insertion reaction of MX into MX bonds leading to a cluster compound. 

Figure 6.2 A free-energy diagram for a hypothetical reaction with a positive free-energy change.

Figure 7.8 Free-energy diagram for the hydrogenation of an alkene in the presenceof a catalyst and the hypothetical reaction in the absence of a catalyst. The free energy of activation [AG (i)] is very much larger than the largest free energy of activation for the catalyzed reaction [AG (2,].

FIGURE 8.1 The variation of a versus time for a hypothetical reaction in the solid state. Curve I shows the evolution of a gas (A) followed by an induction period (B) before the maximum rate is reached, curve II represents a reaction that shows an induction period (B) before reaching maximum rate, and curve III represents a reaction that begins at the maximum rate. 

The meaning of this observation is seen by considering Scheme 1. AH° (3) and AH0(4) are the enthalpies of hypothetical reactions of a family of compounds ML , where reactants and products are in the standard reference states and in the gas phase, respectively, and AHy are vaporization or sublimation enthalpies. 

Knowing the chemical potential function for each species in a reaction defines the reaction s equilibrium point. Consider a hypothetical reaction,... 

The question of the choice of the appropriate symmetry number for con-formationally labile molecules is a subtle one and is at best an approximation. It is the opinion of this author that, if a = 18 for the n-alkanes is accepted as correct, then for the sake of consistency the a-values for all of the cycloalkanes have to be set at 2n, as shown by the following example. Consider the hypothetical reaction (36) for which a statistical correction is clearly... 

Table 5 lists equilibrium data for a new hypothetical gas-phase cyclisation series, for which the required thermodynamic quantities are available from either direct calorimetric measurements or statistical mechanical calculations. Compounds whose tabulated data were obtained by means of methods involving group contributions were not considered. Calculations were carried out by using S%g8 values based on a 1 M standard state. These were obtained by subtracting 6.35 e.u. from tabulated S g-values, which are based on a 1 Atm standard state. Equilibrium constants and thermodynamic parameters for these hypothetical reactions are not meaningful as such. More significant are the EM-values, and the corresponding contributions from the enthalpy and entropy terms. 

B We determine the value for the hypothetical reaction s cell potential. 

The Case of High Plant Costs, Hypothetical Reaction.212... 

A hypothetical reaction with assumed properties was taken, since no real-case reaction was available for demonstration. Liquid-phase operation for a homogeneously catalyzed pseudo-first-order reaction was... 

Figure 8.4 Hypothetical reaction coordinate diagrams for CO hydrogenation on Pd and Ni the dissociation of CO is more difficult on Pd, making methanol synthesis more favorable than methane formation, which requires C-0 dissociation, and is the preferred pathway on Ni...

Additional mechanistic insight into the reductive nitrosylation of ferri-heme proteins was obtained from kinetic studies carried out on aqueous solutions of Cytm, metMb, and metHb at various pH values (67). For example, Cytm undergoes reduction by NO to Cyt11 in aqueous solutions at pH values > 6.5. A hypothetical reaction mechanism is shown in Scheme 2 which would predict the rate law presented in Eq. (31) (67). 

Such Al-O-Al linkages in zeolites, however, are not altogether impossible, if suitable counter ions are present, as indicated by the calculations on the following hypothetical reactions, analogous to reactions (2). .. (6). 

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