K Uncatalyzed Reactions

References Koros and Orban (1978), Orban and Koros (1978), Koros and Orban (1980). 

Koros and Orban have studied (1978-1, 2, 1980) the uncatalyzed bromination of aromatic compounds and observed oscillations. 

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A. K. Galwey, Reactions in the Sohd State, in Bamford and Tipper, eds.. Comprehensive Chemical Kinetics, vol. 22, Elsevier, 1980. Galwey, A. K., Chemistry of Solids, Chapman and Hall, 1967. Sohn, H. Y, and W. E. Wadsworth, eds.. Rate Frocesses of Extractive Metallurgy, Plenum Press, 1979. Szekely, J., J. W. Evans, and H. Y. Sohn, Gas-Solid Reactions, Academic Press, 1976. Uhmann, ed., Enzyklopaedie der technischen Chemie, Uncatalyzed Reactions with Solids, vol.. 3, 4th ed., Verlag Chemie, 1973, pp. 395-464. 

Some authors use O] instead of cr as the substituent constant in such correlations.) An example is provided by the aminolysis of phenyl esters in dioxane the substrates RCOOPh were reacted with -butylamine, and the observed first-order rate constants were related to amine concentration by = k2 [amine] kj [amine]. The rate constants kz and k could be correlated by means of Eq. (7-54), the reaction constants being p = +2.14, b = + 1.03 (for A 2) and p = -1-3.03,8 = -1-1.08 (for ks). Thus, the two reactions are about equally sensitive to steric effects, whereas the amine-catalyzed reaction is more susceptible to electronic effects than is the uncatalyzed reaction. 

Based on the reaction scheme shown below, derive an expression for k /k, the ratio of the rate constants for the catalyzed and uncatalyzed reactions, respectively, in terms of the free energies of activation for the catalyzed (AGe ) and the uncatalyzed (AG ) reactions. 

Nitrones are a rather polarized 1,3-dipoles so that the transition structure of their cydoaddition reactions to alkenes activated by an electron-withdrawing substituent would involve some asynchronous nature with respect to the newly forming bonds, especially so in the Lewis acid-catalyzed reactions. Therefore, the transition structures for the catalyzed nitrone cydoaddition reactions were estimated on the basis of ab-initio calculations using the 3-21G basis set. A model reaction indudes the interaction between CH2=NH(0) and acrolein in the presence or absence of BH3 as an acid catalyst (Scheme 7.30). Both the catalyzed and uncatalyzed reactions have only one transition state in each case, indicating that the reactions are both concerted. However, the synchronous nature between the newly forming 01-C5 and C3-C4 bonds in the transition structure TS-J of the catalyzed reaction is rather different from that in the uncatalyzed reaction TS-K. For example, the bond lengths and bond orders in the uncatalyzed reaction are 1.93 A and 0.37 for the 01-C5 bond and 2.47 A and 0.19 for the C3-C4 bond, while those in... 

Page 303 has a two-point equation relating k (the rate constant) and T (temperature). Derive a two-point equation relating k and activation energy for a catalyzed and an uncatalyzed reaction at the same temperature. Assume that A is the same for both reactions. 

Carbanions (counterions M = K +, Na +, Li+ or R4N+) bearing acceptor-substituents A, c.g., — M- or — I-substitucnts, vinyl, or phenyl groups, add to carbonyl compounds in uncatalyzed reactions preferentially at the x-position. 

Pure parathion is a pale yellow, practically odorless oil, which crystallizes in long white needles melting at 6.0° C. (17). It is soluble in organic solvents, except kerosenes of low aromatic content, and is only slightly soluble in water (15 to 20 p.p.m. at 20° to 25° C.). Peck (35) measured its rate of hydrolysis to diethyl thiophosphate and nitro-phenate ions in alkaline solutions. He found that the reaction kinetics are first order with respect to the ester and to hydroxyl ion. In normal sulfuric acid the rate of hydrolysis was the same as in distilled water. Peck concluded that hydrolysis takes place by two mechanisms—a reaction catalyzed by hydroxyl ions and an independent uncatalyzed reaction with water. He calculated that at a pH below 10 the time for 50% hydrolysis at 25° C. is 120 days in the presence of saturated lime water the time is 8 hours. The over-all velocity constant at 25° C. is k = 0.047 [OH-] + 4 X 10-6 min.-1... 

This uncatalyzed reaction occurs at an acceptable rate at room temperature (298 K), a = (15/14)aq/(15/14)gas = 1.055. The value calculated from spectroscopic data is 1.096 (Chapter 4), so parasitic bleed to species other than NO(g) and HN03(aq) is indicated (the chemistry shown in Equation8.13 is oversimplified). In the exchange aqueous acid trickles down through a packed column countercurrent to a rising NO stream. A two column cascade was employed in which 4% of the acid flow is... 

The only indirect selection that led to a catalytic DNA is a deoxyribozyme that catalyzes the same class of porphyrin metallation as the aforementioned ribozyme. The ssDNA oligonucleotide showed a k at of 13 h" for the insertion of into mesoporphyrin IX [93, 96-99]. This corresponds to a rate enhancement of 1400 compared to the uncatalyzed reaction which is as good as a catalytic antibody for the same reaction. 

The hexacyanoferrate(II)/(III) electron exchange reaction is strongly catalyzed by cations such as K" ". However if the K" " is complexed by, e.g., 18-crown-6 or the cryptand [2.2.2] then the rate constant for the uncatalyzed reaction can be determined. Carbon-13 NMR spectroscopy has established that is 240 s (at 298 K), with AVyyJ = —11.3 cm mol Pressure effects on... 

In the absence of an enzyme, the reaction rate v is proportional to the concentration of substance A (top). The constant k is the rate constant of the uncatalyzed reaction. Like all catalysts, the enzyme E (total concentration [E]t) creates a new reaction pathway, initially, A is bound to E (partial reaction 1, left), if this reaction is in chemical equilibrium, then with the help of the law of mass action—and taking into account the fact that [E]t = [E] + [EA]—one can express the concentration [EA] of the enzyme-substrate complex as a function of [A] (left). The Michaelis constant lknow that kcat > k—in other words, enzyme-bound substrate reacts to B much faster than A alone (partial reaction 2, right), kcat. the enzyme s turnover number, corresponds to the number of substrate molecules converted by one enzyme molecule per second. Like the conversion A B, the formation of B from EA is a first-order reaction—i. e., V = k [EA] applies. When this equation is combined with the expression already derived for EA, the result is the Michaelis-Menten equation. 

The cardinal feature of catalysis is that the equilibrium constant of a chemical reaction is unaffected by the presence of a catalyst. This is true as long as the concentration of the catalyst is insignificant relative to the concentra-tion(s) of the least abundant reactant(s) or product(s). Thus for an uncatalyzed reaction (A B) with rate constants k+ and k- (for the forward and reverse rates, respectively), the equilibrium constant K q = k+lk-. In the presence of catalyst, the rate constants are increased, say to xk+ and yk-, and the new equilibrium constant Keq = xk+lyk- = (xly) k+/k-) = x y)K q. Because the rate enhancement in the presence of enzyme will always be the same for forward and reverse reactions, x = y, such that Ksq must still equal K q. 

The derivation (Sec. 2-2b) of the kinetics of catalyzed polyesterification assumes that the catalyzed reaction is much faster than the uncatalyzed reaction, that is, k 3> k. This assumption is usually valid and therefore one can ignore the contribution by the uncatalyzed polyesterification to the total polymerization rate. For example, k is close to two orders of magnitude larger than k for a typical polyesterification. For the atypical situation where k is not negligible relative to k , the kinetic expression for [M] or Xn as a function of reaction time must be derived [Hamann et al., 1968] starting with a statement of the polymerization rate as the sum of the rates of the catalyzed and uncatalyzed polymerizations ... 

The natural log term on the right side of Eq. 2-35 is the contribution of the uncatalyzed reaction. Its relative importance increases as k/k increases. (When k/k is very small, Eq. 2-35 converts to Eq. 2-32.)... 

The literature on this model reaction is already vast and a complete bibliography would be of great use to the mathematical modeler. Of particular interest are A. d Anna, P. G. Lignola, and S. K. Scott. The application of singularity theory to isothermal autocatalytic open systems The elementary scheme A + mB = (m + 1) B. Proc. Roy. Soc. Lond. A 403, 341-363 (1986) and S. R. Kay, S. K. Scott, and P. G. Lignola. The application of singularity theory to isothermal autocatalytic open systems The influence of uncatalyzed reactions. Proc. Roy. Soc. Lond A 409, 433-448 (1987). 

In the areas b (pH > 7) and u (pH 5) the contributions of the base-catalyzed and uncatalyzed reactions dominate, respectively. The slopes in region b are +1 (the rates are proportional to base concentration c0He with an apparent rate coefficient = k K /Kyj for base catalysis), but base... 

In most cases, the rate constants kucK were converted to k [Equation (18)] assuming that mechanism (b) of Scheme 6 accounts for the uncatalyzed reaction. Clearly, the rate constant kfc for phorone should not be converted to k e, because the uncatalyzed reaction is due to an intramolecular 1,5-H shift rather than to pre-equilibrium ionization of the enol. Conversion of kjf = 2.6 s-1 would give k = 1.8 x 10um-1s-1, which is higher than any of the values observed for simple enols and more than two orders of magnitude higher than that predicted by the Marcus equation for k . 

To prove that an antibody-catalyzed reaction indeed preferentially stabilizes the transition state, the ratio of dissociation constants for substrate Ks and transition-state K is frequently compared to the ratio of the antibody-catalyzed rate constant kAb and the rate constant of the uncatalyzed reaction kun [Eq. (18.1), which is equivalent to Eq. (2.8)]. 

The addition of a catalyst to a certain reaction provides an alternative pathway in which the energy of activation is less than that of the uncatalyzed reaction by 14.7 kJ/mol. By what factor is the rate constant increased by the catalyst at a temperature of 420 K By what factor is the rate constant of the reverse reaction increased (Assume that the... 

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