Unimolecular Reversible Reaction

If Equation 8.35 is rewritten as x. - x = x. exp[-(k+ + kjt], it follows that a unimo-lecular reaction approaches equilibrium as a first-order reaction with the rate constant k = k+ -I- k. If we determine x for the reaction (8.30) at a number of times and furthermore measure x at equilibrium, we may determine k+ -i- k. The separate rate constants k+ and k may be obtained subsequently by using the stoichiometric equilibrium constant and Equation 8.31  

According to Equation 8.36, the stoichiometric equilibrium constant for a reversible, unimolecular reaction is given by the quotient between the rate constants for the forward reaction and the back reaction. The results are general. 

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To derive the corresponding kinetic expressions for a bimolecular-unimolecular reversible reaction proceeding via an Eley-Rideal mechanism (adsorbed A reacts with gaseous or physically adsorbed B), the term K Pt should be omitted from the adsorption term. When the surface reaction controls the rate the adsorption term is not squared and the term KgKg is omitted. 

Equation 6-136 is the basis for the r - T - XA chart as developed by Levenspiel [11]. Assuming that there is no product recycle (0R = 0) and that the reaction is unimolecular reversible reaction (dr = 1), Equation 6-136 becomes... 

The trans -> cis isomerisation of octafluorobut-2-ene is claimed by Schlag and Kaiser " to be a clean unimolecular reversible reaction. Studies by the static method using a seasoned quartz reaction vessel at 430-477 °C yielded the Arrhenius parameters, A = 3.4x 10 sec E = 56.4 kcal.mole L The E value is 6.4 kcal.mole lower than for the corresponding hydrocarbon - . Craig and Entemann have compared the standard enthalpy change for the cis trans isomerisation of 1,2-difluoroethylene with those for related halogenated ethylenes. The reported values are 4-928 cal.mole for difluoroethylene, 4-500 cal.mole for dichloroethylene, nearly zero for dibromoethylene, and —2000 cal.mole for diiodoethylene. 

The goal of discrete lumping is to group species based on their reactivity so that each lump follows the principle of invariant response the rate of reaction of the lump should depend only on the sum of the species and not on the individual species it contains. For a system of unimolecular, reversible reactions, equation (1) becomes... 

Any forward reaction that can take place is also accompanied, in principle at least, by the corresponding reverse reaction. Therefore, the unimolecular decay of 03 in step 1 of the two-step mechanism is accompanied by the formation reaction... 

The concoitradon of CHjNO decreased monotonically with temperature, but even at 800 °C a small concentration could be detected. The decrease could be due to unimolecular reactions, to biomolecular reactions with either CH,- or NO, or to a reverse reaction, CH3NO - CHj + NO. It is reasonable to assume that similar gas phase reactions would occur at much higher pressures however, we have not detected CH3NO during our catalytic experiments over the Sr/LajOj catalyst. Perhaps at much larger concentrations of NO the reaction CHjNO + NO - N O + CHjO- rapidly removes the nitrosomethane. 

The cis-trans isomerization of cyclopropanes is not restricted to the deuterium-substituted molecules, cis- and traws-l,2-Dimethylcyclo-propane have been shown to imdergo reversible geometrical isomerization as well as slower structural isomerization. All the processes are homogeneous and kinetically first order, and almost certainly unimolecular. The reaction scheme is shown below. 

The maximum rate for the reverse reaction (unimolecular dissociation, s ) is via separation by diffusion of the two molecules... 

The treatment of these simple associations directly follows that of the simple fission reactions discussed previously. For example, these reactions proceed via the formation of a loose transition state and without an activation energy barrier. The rates and rate parameters of simple associations can be determined either directly, by the application of bimolecular TST, or from their reverse, simple unimolecular fission reactions, through the use of the principle of microscopic reversibility. 

STEP TWO Number each enzyme form with a circled number, and indicate each arrow with the corresponding unimolecular or bimolecular rate constant. For bimolec-ular rate constants, the corresponding reactant species (i.e., substrate or product) should also be identified with the corresponding arrow. [To avoid errors by misplacing a minus sign, it is recommended that only positive numbers be used as subscripts for the rate constants (preferably odd numbers for forward reactions, even numbers for reverse reactions).] Thus, for our ordered Bi Bi scheme ... 

The above discussion shows that several possible pathways for the interconversion of sulfur rinp exist. However, none of these alone can explain all the experimental observations. It therefore seems likely that several of them are effective simultaneously. Unimolecular dissociation reactions as discussed under (a) and (d) will dominate at high temperatures due to the increase in entropy. At lower temperatures, however, bimolecular reactions like the dimerization (c) may be most important, at least in case of the small rings (Sg, S, Sg) whose unimolecular dissociation is strongly endothermic. Larger rings will probably decompose according to mechanism (d), which in a way is the reversal of the dimerization (c). 

First-Order Reversible Reactions. Though no reaction ever goes to completion, we can consider many reactions to be essentially irreversible because of the large value of the equilibrium constant. These are the situations we have examined up to this point. Let us now consider reactions for which complete conversion cannot be assumed. The simplest case is the opposed unimolecular-type reaction... 

Figure 3.13 Test for the unimolecular type reversible reactions of Eq. 53.

Marcus and Rice6 made a more detailed analysis of the recombination from the point of view of the reverse reaction, the unimolecular decomposition of ethane, C2Ha - 2CH3. By the principle of microscopic reversibility the transition states must be the same for forward and reverse paths. Although they reached no definite conclusion they pointed out that a very efficient recombination of CH3 radicals would imply a very high Arrhenius A factor for the unimolecular rate constant of the C2H6 decomposition which in turn would be compatible only with a very "loose transition state. Conversely, a very low recombination efficiency would imply a very tight structure for the transition state and a low A factor for the unimolecular decomposition. 

At the present time a number of gaseous unimolecular reactions are known. The view that none exist, although it appeared plausible for a time, has now been definitely abandoned. Nevertheless, unimolecular reactions are rather exceptional and appear to be confined to molecules of rather complex structure. It is possible that the decomposition of diatomic molecules into atoms at high temperatures is unimolecular but more probable that it is bimolecular, the reverse reaction of recombination being termolecular. Thus the rate of dissociation of chlorine would be k1 [Cl2]2 while the rate of recombination of the atoms would be 2 [Cl]2 [Clg], according to the Herzfeld theory (p. 111). 

A criterion of mechanism based on the Hammett acidity function, H0 (Section 3.2, p. 130),has long been used to decide the type of question raised by the choice between Mechanisms I and II in Scheme 8. Since in strongly acidic media the concentration of the protonated substrate should be proportional to h0, the reaction rate for a unimolecular decomposition of this protonated substrate (Mechanism I) should also be proportional to h0, whereas if a water molecule is required (Mechanism II), the rate should follow H30+ concentration instead. This test, known as the Zucker-Hammett hypothesis,76 when applied to acetal and ketal hydrolysis, appears to confirm the A-l mechanism, since a linear relationship is found between rate constant and h0 at high acidity.77 Inconsistencies have nevertheless been found in application of the Zucker-Hammett hypothesis, for example failure of the plots of log k vs. — H0 to have the theoretical slope of unity in a number of cases, and failure to predict consistent mechanisms for forward and reverse reactions the method is therefore now considered to be of doubtful validity.78 Bunnett has devised a more successful treatment (Equation 8.45), in which the parameter to measures the extent of... 

Subsequent to the rapid attainment of this near-equilibrium situation, the radicals decay more slowly by both unimolecular and bimolecular processes (discussed below). For this simple case, it can be shown that when the decay process is much slower than the rates of the forward and reverse reactions, the observed rate constant for the disappearance of R- is given by the expression k0bS = forward [02] + Reverse- When fc0bs of the decay of the hydroxycyclohexadienyl radicals is plotted as a function of the 02 concentration, the slope represents the rate constant of the forward reaction, and the intercept that of the reverse reaction (Fig. 8.3). 

Answer. When the unimolecular reaction is in the first order region the ratedetermining step is reaction, rather than activation. The reverse reaction must also have reaction as rate determining and this corresponds to the second order region of the recombination. Recombination and decomposition will be in the high pressure region. 

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