Reversible reaction second-first order

Much of the language used for empirical rate laws can also be appHed to the differential equations associated with each step of a mechanism. Equation 23b is first order in each of I and C and second order overall. Equation 23a implies that one must consider both the forward reaction and the reverse reaction. The forward reaction is second order overall the reverse reaction is first order in [I. Additional language is used for mechanisms that should never be apphed to empirical rate laws. The second equation is said to describe a bimolecular mechanism. A bimolecular mechanism implies a second-order differential equation however, a second-order empirical rate law does not guarantee a bimolecular mechanism. A mechanism may be bimolecular in one component, for example 2A I. 

The most important forms for reversible reactions are first order, forward and reverse, and second order, forward and reverse. If change in the number of mols occurs and order follows stiochiometry, the reversible reactions can also have forward and reverse steps of different order. Since in the following presentation we treat the reactions as elementary steps, the ratio of rate constants does define the equilibrium constant for the reaction, K = kf/k. ... 

The reaction rate is second order and zero order for the catalyst concentration. The reverse reaction is first order. Data are presented below at 25°C ... 

C + D. Is each of the following statements true or false (a) The rate law for the reaction must be Rate = fc[A][B], (b) If the reaction is an elementary reaction, the rate law is second order, (c) If the reaction is an elementary reaction, the rate law of the reverse reaction is first order, (d) The activation energy for the reverse reaction must be greater than that for the forward reaction. 

For a simple order, the rate expression can be integrated and special plots utilized to determine the rate coefficient. A plot of MCa versus t or xjj -x versus t is used similarly for a second-order irreversible reaction. For reversible reactions with first order in both directions a plot of ln(Ci - Qeq)/(Qo - Qeq) or ln(l - XaIxa versus f yields ( i + ki) from the slope of the straight line. Using the thermodynamic equilibrium constant K = kxlkz, both k and kz are obtained. Certain more complicated reaction rate forms can be rearranged into such linear forms. These plots are useful for an estimate of the "quality" of the fit to the experimental data and can also provide initial estimates to formal regression techniques that will be systematically discussed in Chapter 2. 

The forward reaction is second order, and the reverse reaction is first order with respect to B and first order with respect to C. Write a computer program using Euler s method to integrate the rate differential equations for the case that the initial concentration of A is nonzero and those of B and C are zero. ... 

If the forward reaction is pseudo first order and the reverse reaction second order, then, as discussed in Sections 1.4.4 and 1.4.5 in Volume 3, the rate equation may be written as ... 

The method for solving Equation 2-14 for the general initial condition is instructive because it is the method to solve all second-order reversible reactions. The first step is to note that the terms inside the braces in the right-hand side of Equation 2-14 is a quadratic form +([H+]o+[OH ]o) +([H+]o[OH ]o fCw), which can be rewritten as i)( 2), with and 2 being the two zeros of the... 

The base-catalysed Aldol reaction is shown in Equation 3.11 [3, 4], and a mechanism to account for the global process in Scheme 3.1. At low concentrations of acetaldehyde, reverse of the proton-abstraction steps is fast compared with the forward bimolecular enolate capture (k [CH3CHO] <rate limiting. Under these conditions, the kinetics are second order in [CH3CHO] and show specific base catalysis, i.e. the reaction is first order in [HCY ] and, even though B is involved in the mechanism, it does not appear in the rate law [5]. According to this mechanism, therefore, the overall rate law is given by Equation 3.12 ... 

The mechanisms of the reductive eliminations in Scheme 5 were studied [49,83], and potential pathways for these reactions are shown in Scheme 6. The reductive eliminations from the monomeric diarylamido aryl complex 20 illustrate two important points in the elimination reactions. First, these reactions were first order, demonstrating that the actual C-N bond formation occurred from a monomeric complex. Second, the observed rate constant for the elimination reaction contained two terms (Eq. (49)). One of these terms was inverse first order in PPh3 concentration, and the other was zero order in PPh3. These results were consistent with two competing mechanisms, Path B and Path C in Scheme 6, occurring simultaneously. One of these mechanisms involves initial, reversible phosphine dissociation followed by C-N bond formation in the resulting 14-electron, three-coordinate intermediate. The second mechanism involves reductive elimination from a 16-electron four-coordinate intermediate, presumably after trans-to-cis isomerization. 

In acid-base catalysis, both an acid (or base) and its conjugate base (or acid) take part in different reaction steps and are eventually restored. Such reactions are first order in acid (or base) if the link-up with that species controls the rate, or first order in H+ (or OH") if a subsequent step involving the conjugate base (or acid) does so. Traditionally, the first alternative is called "general" acid or base catalysis the second, "specific" acid or base catalysis. However, this distinction is not always applicable as there may be no clear-cut rate-controlling step, and reversibility of later steps may produce a more complex behavior. 

In the range pH 9-11 the rate of formation of the diester is slow enough at 0 °C to be followed by conventional spectrophotometry. The kinetics are those of a reversible reaction, second-order in the forward direction and first-order in the reverse direction, in agreement with the reaction scheme... 

The rate of a-chymotrypsin-catalyzed hydrolysis as a function of overall GPANA concentration in CTAB reversed micelles and in aqueous solution are shown in Figure 5. It is apparent that the reaction rate in the reversed micellar solution is on the order of 50 times more rapid than in the aqueous system. Furthermore, in the reversed micellar system there is no indication of enzyme saturation as the reaction is first order in substrate concentration. As enzyme saturation kinetics are not observed, it is impossible to differentiate between the parameters kcat and Kg. Instead a second order bimolecular rate constant for both the micelle interior ( micelle) and for what is experimentally observed ( observed) is defined. 

Analysis of this rate equation shows that it takes into consideration the reversible reaction step in the steam reforming. The rate equation implies that the forward reaction is first order with respect to methane, zero order with respect to steam (possibly due to the high steam /C ratio in the experiments) and is inhibited by hydrogen. The reverse reaction is independent of the methane concentration, second order in hydrogen, first order in CO and is inhibited by H2O. 

The reaction is first order in NAD and first order in lactic acid, and its overall order is therefore two. The reverse reaction is also second order under certain conditions, the rate of formation of lactic acid from pyruvic acid being, at constant... 

Reactions of the (3S ) and (3R )-3-chloro-2,4,7-trioxa-3-phospha-bicyclo-[4.4.0]decane 2-sulphides (88) with nucleophiles proceed with predominant inversion of configuration at phosphorus. Differences in rates of displacement of axial and equatorial leaving groups were observed in, for example, propanolysis. Two studies have dealt with thiol-thione isomerization. The conversion of a S5mimetrical monothiopyrophosphate into its unsymmetrical isomer has, thus far, been considered in terms of a cyclic process, but a dissociative mechanism is now proposed. In the free base form, the esters (89) can be rather unstable, although stabilization is achieved as the oxalate salts. The isomerization of the free base into the, S55-triester may be intramolecular, reversible, and of first order (e.g., for R = Et or Bu, R = Et, n = 2), or it may be irreversible, intermolecular, and of second order (e.g., for R = Pr, R = Et, n = 3). ... 

Some data are available about catalysis in 1,2-cycloadditions. Tributyl phosphine catalyses dimerisation of phenyl isocyanate to uretidinedione in toluene . The reaction is kinetically of first order with respect to catalyst and overall third order the reverse process is first order with respect to catalyst and overall second order. The mechanism is complex, as revealed by the value of the apparent activation energy of the forward reaction (E= l.l 0.7 kcal.mole" ), which presumably results from the combined temperature dependence of two or more steps, including formation of an isocyanate-phosphine complex (see eqn. (13), p. 113). 

CrC(OCH3)C6Hs indicates that the reaction is kinetically complex (HeckI et al., 1968 Werner et al., 1971). In hexane, the rate of reaction is first order in carbene complex and third order in amine. In dioxane, the reaction is first order in carbene complex and second order in amine. The high kinetic order in amine is undoubtedly due to the hydrogen bonding requirements of cyclohexylamine in nonpolar solvents. The reaction is thought to proceed by reversible nucleophilic attack of the amine at the carbene carbon atom which... 

Kinetic studies showing that the reaction is first order in acid, and second order overall, a solvent isotope effect ( h2S04 AD2SO4) of 0.91, a Hammett p value of -6.5, a AS of -37.2 Jmol K and theoretical calculations at the B3LYP/TZVP level of theory, have shown that the acid-mediated solvolysis of a-methylene-j0-hydroxy- 0-phenyl esters to allylic acetamides in acetonitrile occur by a rate-determining formation of a benzylic carbenium ion intermediate, that is, by an 5n 1 mechanism, after a rapid, reversible protonation by the acid catalyst. " ... 

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