Estimation of rate and equilibrium constants

Chiang, Y. Kresge, J. Zhu, Y. Flash photolytic generation and study of /j-quinone methide in aqueous solution. An estimate of rate and equilibrium constants for heterolysis of the carbon-bromine bond in p-hydroxybenzyl bromide. J. Am. Chem. Soc. 2002,124, 6349-6356. 

Case B Estimation of Rate and Equilibrium Constants in a Reversible Esterification Reaction Using MADONNA... 

When the uncertainty associated with AHf is 5 kcal/mol, rate and equilibrium constants can be estimated within a factor of 10 at process temperatures, i.e., 500-1,500 K. This level of accuracy may be acceptable for preliminary mechanism development work and for the identification of important reactions in a DCKM. However, it would clearly be desirable to know AHf within 1 kcal/mol, which would lead to the determination of rate and equilibrium constants that are accurate within a factor of two. Since this level of accuracy is very close to the limits of accuracy of most experimental measurements, improvements in AHf are often difficult. Consequently, computational quantum chemistry holds a great promise for the accurate determination of AHf. 

Even without taking into account side reactions changing the concentrations of the active species, a great number of rate and equilibrium constants are required in order to describe the whole course of polymerization. So far, no data are available on equilibrium (25) from which the concentrations of lactam and polymer amide anions could be estimated. Therefore, the individual rate coefficients can be obtained only from measurements of the initial rates of the isolated reactions. In this case, the participation of the reaction products in subsequent reactions can be neglected. 

Endicott s group has measured and made an extremely detailed analysis of rate and equilibrium constants for transmethylation between various cobalt N4-macrocyclic systems (see Table 7.6 and accompanying structures). The reactions are first order in each reagent. Rates can vary by 10 (even for the back reactions where AG < 0). AG is analyzed into components, intrinsic free energy barriers to transmethylation being small for cobalt corrin and large for sterically hindered neutral macrocyclic complexes. Estimates for C0-CH3 bond energies are between 33 and 48 kcal mol the bond is stabilized by unsaturation in the N4 macrocycle, but is also very sensitive to stereochemistry. 

A value of kjkp = 17 000 has been determined for partitioning of the acetophenone oxocarbenium ion [12+] in water.15,16 It is not possible to estimate an equilibrium constant for the addition of water to [12+], because of the instability of the hemiketal product of this reaction. However, kinetic and thermodynamic parameters have been determined for the reaction of [12+] with methanol to form protonated acetophenone dimethyl ketal [12]-OMeH+ and for loss of a proton to form a-methoxystyrene [13] in water (Scheme 10).15,16 Substitution of these rate and equilibrium constants into equation (3) gives values of AMeoH = 6.5 kcal mol-1 and Ap = 13.8 kcal mol-1 for the intrinsic... 

Accumulated data to date indicates that is relatively insensitive to the details of the structure of species. Consequently, additivity rules and model compounds, in conjunction with statistical mechanics, can readily be used to estimate entropies and specific heats of molecules and radicals. These estimates generally are accurate within l.Ocal/mol-K, leading to uncertainties in rate and equilibrium constants well within 20%. 

In estimating these barriers Richard addresses a problem that so far has been avoided. When discussing the correlation of log h2o with pATR in Fig. 3, it was implied that the rate and equilibrium constants refer to the same reaction step. That is not strictly true, because attack of water on a carbocation yields initially a protonated alcohol which subsequently loses a proton in a rapid equilibrium step. As we are reminded in Equation (26) the equilibrium constant AR refers to the combination of these two steps. To calculate an intrinsic barrier for reaction of the carbocation with water therefore the equilibrium constant KR should be corrected for the lack of stoichiometric protonation of the alcohol. Fortunately, there have been enough measurements of pA,s of protonated alcohols240 (e.g. pAa = -2.05 for CthOHi1") for the required corrections to be made readily. 

Electrochemical simulations of the concentration and scan-rate dependence of the voltammetry potentially provide the composition of the intermediates formed during the reaction cycle together with estimates of the rate and equilibrium constants. As shown in the preceding section spectroscopic information can greatly assist the elucidation of the molecular details of these reactions, however, reliable deduction of the structure is greatly enhanced by the incorporation of structural and computational information (Section 1.6). The rapid advance in computer power and implementation of density-functional theory allows a more quantitative approach for evaluation of proposed structures based on spectroscopic information and estimation of the relative energies of the proposed spe-cies. The recent computational study of the electrocatalytic reaction cycle proposed for illustrates the opportunities presented by the approach. 

Thus, possibly identity rates and equilibrium constants can be estimated well enough to permit the estimation of rates for any SN2 reaction in sulfolane at 35 °C. Enough temperature dependencies are available so that correction to some other nearby temperature should not be too difficult. 

Fig. 10. Relation between rates and equilibrium constants for the reaction of ketones, esters, and keto-esters with bases. Open circles refer to systems in which K is known by direct measurement, filled circles to estimated values of K. (Values from Refs. 90-107 of Chapter 9, and Ref. 10 of Chapter 10.) Reactions involving solvent species have been omitted, and also those in which steric effects or other specific interactions are suspected.

Trifluoroacetylketene (91) has been generated in aqueous solution by flash photolysis. Rates of hydration to form the enol of 4,4,4-trifluoroacetoacetic acid (92e) have been measured, and also rates of the subsequent ketonization to the /3-keto acid (92k). Extensive rate and equilibrium constant data are reported for these reactions and for the ionizations of the tautomers. For example, the enol (92e) has acidity constants (in -logio form) of 1.85 and 9.95, for the acid and enol OH groups, respectively. Rates of enolization of (92k) have also been measured (by bromination) and, combined with an estimate of the hydration constant (K = 2900) of (92k), suggest that the keto-enol tautomeric constant is ca 0.5, about 100 times greater than that of its unfluorinated analogue. 

The kinetic equilibrium constant is estimated from the thermodynamic equilibrium constant using Equation (7.36). The reaction rate is calculated and compositions are marched ahead by one time step. The energy balance is then used to march enthalpy ahead by one step. The energy balance in Chapter 5 used a mass basis for heat capacities and enthalpies. A molar basis is more suitable for the current problem. The molar counterpart of Equation (5.18) is... 

The rate of the ammonia production can now be predicted if we can estimate all of the participating equilibrium constants and k. Where possible, one should take experimental values for the different constants. For instance, it is possible to measure the uptake of atomic nitrogen on the Fe or Ru surface and thereby determine... 

For species 11 we will use the intrinsic barrier for hydroxide addition to trimethyl phosphate, G = 19 (calculated using rate and equilibrium data from reference 100) and assume the same value for the attack of hydroxide at sulfur on dimethyl sulfate. This (nonobservable) rate will be estimated using a Brpnsted type plot from the rate constants for diaryl sulfates (diphenyl sulfate,and bis p-nitrophenyl sulfate), estimated from the rate for phenyl dinitrophenyl sulfate,assuming equal contributions for the two nitro groups. This gives ftg = 0.95, and thus for dimethyl sulfate log k = 11.3... 

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