Isomerization equilibrium constants

A good way to determine the rate coefficients klP and k2Q from experimental results is first to find k from the slope of a first-order plot for the respective reactant or an equivalent numerical method, then to calculate ki and k2Q from it, the isomerization equilibrium constant KI2, and the product concentrations at complete conversion ... 

To estimate the isomerization rate coefficients, eqn 5.8 is applied to the time required for close approach to the straight-line behavior of the first-order curves. Judging this time to be about 25 minutes for a 90% approach to the steady-state isomer distribution, eqn 5.8 yields k 0.1 min-1. With this value and an isomerization equilibrium constant Kn = 20 at 150°C calculated from thermochemical data [5,6] (with 2-cis and 2-trans pentene lumped into a single pseudo-component), eqns 5.40 give as rough estimates... 

The ratio fAR/fAB is an isotopic isomerization equilibrium constant, while fAR A ffaba is an isotopic exchange constant. The latter is usually larger than the isomerization constant6 and for weak complexing a larger correction must be applied to the intermolecu-lar than to the intramolecular reaction. 

Because of the severe demands placed on us for aceuraey if we tre to calculate an equilibrium constant, let us choose a simple reaction, the isomerization of but-2-eiic,... 

From a general point of view, the tautomeric studies can be divided into 12 areas (Figure 20) depending on the migrating entity (proton or other groups, alkyl, acyl, metals. ..), the physical state of the study (solid, solution or gas phase) and the thermodynamic (equilibrium constants) or the kinetic (isomerization rates) approach. 

Cycloheptatrienes are in many cases in rapid equilibrium with an isomeric bicy-clo[4.1.0]heptadiene. The thermodynamics of the valence isomerism has been studied in a number of instances, and some of the data are given below. Calculate the equilibrium constant for each case at 25°C. Calculate the temperature at which K= for each system. Are the signs of the enthalpy and entropy as you would expect them to be Can you discern any pattern of substituent effects from the data ... 

Between 1951 and 1953 investigations by three English groups clearly demonstrated the preponderance of the oxo forms of pyrimidin-2- and -4-ones by comparing the ultraviolet spectra of these compounds with those of the N and 0-alkylated derivatives, The o-quinonoid form 91 (R = H) is favored by the evidence that A -methylation of the 6-methyl derivative of 89a does not cause a bathochromic shift in the ultraviolet spectrum (A -methylation of pyrid-4-one causes a bathochromic shift, but this is not observed for pyrid-2-one) The isomeric A -methyl derivatives of pyrimidin-4-ones [e.g., 91 (R = Me) and 90 (R = Me)] form similar cations (e.g., 92 and 93), and hence the equilibrium constant between... 

Catalytic reformers are normally designed to have a series of catalyst beds (typically three beds). The first bed usually contains less catalyst than the other beds. This arrangement is important because the dehydrogenation of naphthenes to aromatics can reach equilibrium faster than the other reforming reactions. Dehydrocyclization is a slower reaction and may only reach equilibrium at the exit of the third reactor. Isomerization and hydrocracking reactions are slow. They have low equilibrium constants and may not reach equilibrium before exiting the reactor. 

The isomerization of A to B yielded kinetic data that conformed to a first-order rate law. but the apparent first-order rate constant depended on the initial concentration of A. The authors propose competing unimolecular and bimolecular processes, and they show that the system reduces to a first-order expression when the equilibrium constant K is unity that is,... 

In discussing the elFect of structure on the stabilization of alkyl cations on the basis of the carbonylation-decarbonylation equilibrium constants, it is assumed that—to a first approximation—the stabilization of the alkyloxocarbonium ions does not depend on the structure of the alkyl group. The stabilization of the positive charge in the alkyloxocarbonium ion is mainly due to the resonance RC = 0 <-> RC = 0+, and the elFect of R on this stabilization is only of minor importance. It has been shown by Brouwer (1968a) that even in the case of (tertiary) alkylcarbonium ions, which would be much more sensitive to variation of R attached to the electron-deficient centre, the stabilization is practically independent of the structure of the alkyl groups. Another argument is found in the fact that the equilibrium concentrations of isomeric alkyloxocarbonium ions differ by at most a factor of 2-3 from each other (Section III). Therefore, the value of K provides a quantitative measure of the stabilization of an alkyl cation. In the case of R = t-adamantyl this equilibrium constant is 30 times larger than when R = t-butyl or t-pentyl, which means that the non-planar t-adamantyl ion is RT In 30= 2-1 kcal... 

Suppose that the two sites are identical (an oversimplification) and that the binding of the first molecule of agonist does not affect the affinity of the site that remains vacant. The dissociation equilibrium constant for each site is denoted by KA and the equilibrium constant for the isomerization between A2R and A2R by E, so that [A2R ] = [A2R],... 

D. For this simulation the equilibrium constant for isomerization between AR and the AR has been set so that few of the receptors are in the active state even in the presence of a large concentration of A on its own. However, with B also present at increasing concentrations, the equilibria shown in Figure 1.28 are shifted toward the active forms so that the maximum response to A rises to a point at which almost all of the receptors can be activated. In effect, B is acting as a co-agonist. Note that it causes little receptor activation when [A] is small. 

We see from this that the value of the fourth equilibrium constant (for isomerization between the active and inactive forms of the occupied receptor) is determined by the other three, E0, KL, and K] ... 

The following temperature-time-con version data was obtained for the batch experiments in the gas phase for the isomerization of reactant A to product B. The equilibrium constant for the reaction is large over the temperature range concerned in Table 6.17. 

Fig. 3. Variation of autocorrelation function with changes in the equilibrium constant in the fast reaction limit. A and B have different diffusion coefficients but the same optical (fluorescence) properties. This figure illustrates how, for the simple isomerization process, A B, a change in the diffusion coefficient is sufficient to indicate the progress of the reaction. This example is calculated for a two-dimensional (planar) system in the fast reaction limit (kf + k ) 4Dj /w2. Therefore, only a single diffusion process is...

Anderson and Avery s bond shift mechanism has the consequence of predicting that a quaternary carbon atom cannot be generated in the hydrocarbon product. In fact, Anderson and Avery (24) showed that in the isomerization of isopentane over platinum films, only a very small amount (<1%) of neopentane was produced (although the equilibrium constant for isopentane <= neopentane is 0.16 at 278°C). Furthermore,... 

K (277°C) and 650°K are 0.63 and 103 atm,3 respectively. Above about 350°C the equilibrium constants for this type of reaction are such that the aromatic is always highly favored thermodynamically over the corresponding cycloalkane. Moreover, olefin which is itself capable of further dehydrogenation to an aromatic (e.g., cyclohexene) is never observed in significant amounts under isomerization conditions. 

E. Taskinen and K. Nummelin, J. Org. Chem., 50, 4833 (1985). These authors performed the isomer equilibration at several temperatures and so could use the experimentally derived equilibrium constant to derive the enthalpy of rearrangement. There was no need for assuming the entropy of isomerization is 0 or just determined by symmetry number corrections. 

The reaction between cellulose and acrylamide was studied by quantitative, chromatographic separation of the substituted D-glucoses obtained on acid hydrolysis of the reaction product,320 followed by an analysis by Spurlin s method.249 Although, apparently, no check was made on the stability of the ethers to the conditions of hydrolysis, it might be expected that the ethers would isomerize only under basic conditions. The ratios of the relative equilibrium-constants for reaction at 0-2, 0-3, and 0-6 were 9 1 19, and these are attributable to the high, relative stability of the primary ether, together with the low reactivity of 0-3, also observed in rate-controlled reactions. 

Referring to the plot of G vs. T for the isotropic and nematic fluids, a uni-molecular isomerization process would show the same characteristics if one of the isomers had a higher entropy of formation than the other. In the molecular case, however, the equilibrium constant at a given temperature would derive from the free energies on a per molecule basis, while for the phases this free energy is per collective volume of molecules. The similarities to a molecular isomerization, however, are more important than the differences for the purposes of this discussion. The transition from isotropic fluid to nematic LC can be considered a temperature-driven, or thermotropic, isomerization. 

Worked Example 4.15 The isomerization of 1-butene (X) to form frans-2-butene (XI). The equilibrium constants of reaction are given below. Determine the enthalpy of reaction AH using a suitable graphical method. 

Figure 4.8 The equilibrium constant K for the isomerization of 1-butene depends on the temperature van t Hoff isochore plot of In K (as y) against 1 7 (as x) from which a value of A//°...

Worked Example 8.19 The data below relate to the first-order isomerization of 2-hexene at 340 K, a reaction for which the equilibrium constant is known from other studies to be 10.0. What are the rate constants k and k i ... 

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