Second-order rate equations for

If cis the concentration of single-stranded DNA at time t, then the second-order rate equation for two complementary strands coming together is given by the rate of decrease in c ... 

Theoretical studies are primarily concentrated on the treatment of flame blow-off phenomenon and the prediction of flame spreading rates. Dunskii [12] is apparently the first to put forward the phenomenological theory of flame stabilization. The theory is based on the characteristic residence and combustion times in adjoining elementary volumes of fresh mixture and combustion products in the recirculation zone. It was shown in [13] that the criteria of [1, 2, 5] reduce to Dunskii s criterion. Longwell et al. [14] suggested the theory of bluff-body stabilized flames assuming that the recirculation zone in the wake of the baffle is so intensely mixed that it becomes homogeneous. The combustion is described by a second-order rate equation for the reaction of fuel and air. 

Rate laws of the type which describe bimolecular second order chemical reactions might be expected to be a model for ion exchange reactions, and indeed this was the case for exchangers of both natural and synthetic origin. For example, the rate of ion exchange could be described by a bimolecular second order rate equation for irreversible reaction of the form ... 

The integrated form of the second-order rate equation for the coupling reaction is... 

F or catalysis by the hydrogen ions of a sulphonic acid resin, we suppose that the reaction proceeds only in the resin phase where the concentration of hydrogen ion is equal to m and the rate coefficient U applies. The second-order rate equation for formation of product (P) (expressed in moles, n) by the resin-catalysed route is... 

Figure 6-8c Test of second-order rate equation for bromine decomposition.

The second-order rate law for bimolecular reactions is empirically well confinned. Figure A3.4.3 shows the example of methyl radical recombination (equation (A3.4.36)) in a graphical representation following equation (A3.4.38) [22, 23 and 24]. For this example the bimolecular rate constant is... 

Herein Pa and Pb are the micelle - water partition coefficients of A and B, respectively, defined as ratios of the concentrations in the micellar and aqueous phase [S] is the concentration of surfactant V. ai,s is fhe molar volume of the micellised surfactant and k and k , are the second-order rate constants for the reaction in the micellar pseudophase and in the aqueous phase, respectively. The appearance of the molar volume of the surfactant in this equation is somewhat alarming. It is difficult to identify the volume of the micellar pseudophase that can be regarded as the potential reaction volume. Moreover, the reactants are often not homogeneously distributed throughout the micelle and... 

Second-order rate coefficients for nitration in sulphuric acid at 25 °C fall by a factor of about 10 for every 10 % decrease in the concentration of the sulphuric acid ( 2.4.2). Since in sulphuric acid of about 90% concentration nitric acid is completely ionised to nitronium ions, in 68 % sulphuric acid [NO2+] io [HNO3]. The rate equation can be written in two ways, as follows ... 

Rate law flooding. The second-order rate constant for the reaction between the hydrated ions of vanadium(3+) and chromium(2+) depends on [H+ ]. From the data given, which refer to T = 25.0 °C and a constant ionic strength of 0.500 M, formulate a two-parameter equation that describes the functional dependence. Evaluate the two constants. Compare your result to the one derived in to Problem 1 -2. 

This reaction cannot be elementary. We can hardly expect three nitric acid molecules to react at all three toluene sites (these are the ortho and para sites meta substitution is not favored) in a glorious, four-body collision. Thus, the fourth-order rate expression 01 = kab is implausible. Instead, the mechanism of the TNT reaction involves at least seven steps (two reactions leading to ortho- or /mra-nitrotoluene, three reactions leading to 2,4- or 2,6-dinitrotoluene, and two reactions leading to 2,4,6-trinitrotoluene). Each step would require only a two-body collision, could be elementary, and could be governed by a second-order rate equation. Chapter 2 shows how the component balance equations can be solved for multiple reactions so that an assumed mechanism can be tested experimentally. For the toluene nitration, even the set of seven series and parallel reactions may not constitute an adequate mechanism since an experimental study found the reaction to be 1.3 order in toluene and 1.2 order in nitric acid for an overall order of 2.5 rather than the expected value of 2. 

Using the pseudo-first-order equation A obsd = 0 + co2 [COiKwhere kcoi is the second-order rate constant for the reaction of carbene with CO2 and ko is the rate of carbene decay in the absence of CO2), solution-phase values of kcoi for phenylchlorocarbenes 9 and 12, and diphenylcarbenes 14 and 15 in dichloromethane were estimated (Table 4.1). (The concentration of CO2 in saturated dichloromethane solution at 25°C and 1 atm is 196mmol/L. ) The trend of these estimated second-order order rate constants agrees with that observed in low-temperature matrices by Sander and co-workers. ... 

The complexity of the integrated form of the second-order rate equation makes it difficult to apply in many practical applications. Nevertheless, one can combine this equation with modem computer-based curve-fitting programs to yield good estimates of reaction rate constants. Under some laboratory conditions, the form of Equation (A1.25) can be simplified in useful ways (Gutfreund, 1995). For example, this equation can be simplified considerably if the concentration of one of the reactants is held constant, as we will see below. 

Let us look again at the association reaction described by Equation (A 1.22). If we set up the system so that there is a large excess of [/] relative to [E], there will be little change in [/] over the time course of El complex formation. For example, suppose that we set up an experiment in which E = InM (0.001 pM) and [/] = 1 pM. The maximum concentration of El that can be formed is limited by the lowest reactant concentration, in this case by [E. Hence, at infinite time, the concentration of free I will be [/] - [El] = 1.000 - 0.001 = 0.999 pM (Figure A1.5). This is such a small change from the starting concentration of free I that we can ignore it and treat [/] as a constant value in the second order rate equation. Thus... 

The reaction has been shown to follow a second order rate equation, rate = fc2[ROH][SOCI2], but clearly cannot proceed by the simple Sn2 mode for this would lead to inversion of configuration (p. 87) in the product, which is not observed. 

Frost and Schwemer have developed a time-ratio technique based on equations 5.4.21 and 5.4.16 in order to facilitate the calculation of second-order rate constants for the class of reactions under consideration. Data for A/A0 versus t at various values of k are presented in Table 5.2, and time ratios are given in Table 5.3. The latter values may be used to determine k by using various time ratios from a single kinetic run if one recognizes that (tf/rf) = t1/t2). Once k has been determined, Table 5.2 may be used to determine the t values at a given A/A0 and k. Equation 5.4.18 may then be used to determine... 

Sauer, Sustmann and coworkers59 have reported second-order rate constants for the reaction of trans-1 -substituted 1,3-butadienes with tetracyanoethylene (TCNE) in dichloro-methane at 20 °C their values are X, log 6 OMe, 7.935, vinyl, 5.456 Ph, 5.814 Me, 5.243 H, 3.228. The data were correlated with the CR equation the best regression equation is ... 

To determine the activities for the various Lal+( OR) we analyze the k2bs data as a linear combination of individual rate constants (Equation 8), where ki4, kf2... " are the second-order rate constants for each La2+( OR) promoting ethanolysis and methanolysis of 1 and 2 respectively. 

A two liter flask was filled with pure HI at 1.24 atm and 683°K, and the decomposition was followed by measuring the absorption of light by the iodine produced. Immediately after the last reading the flask was chilled and an analysis for iodine showed 1.17 g. Evaluate the constants of the second order rate equation. 

This system of second order rate equations is solved numerically for M and several values of Pn with these values ... 

The second-order rate constant for the reaction of iodide and iodine is 6.2XlO M s in water at 298 K while the first-order rate constant for the dissociation of triiodide is 8.5 X 10 s at 298 The dissociation constant, Kq, for this reaction is on the order of 10 M for the dissociation of triiodide, which is comparable in magnitude to Kq for the R2Se-l2 complexes (5 X 10 M). Consequently, added iodide should compete for iodine as effectively as the diorganochalcogenides and limit the available concentration of I4 in situ. Thus, equation (9) must be followed to a greater extent in the presence of added iodide. 

Aromatic sulfonamides are specific inhibitors of carbonic anhydrase (E). The apparent second-order rate constants for association of p-nitrobenzenesulfonamide with (a) carbonic anhydrase-B and (b) the carboxymethylated derivative of the enzyme are shown against pH in Figure 1.14. Estimate using equations (1.225) and (1.226) the values for pAig, and k and he two possible schemes shown for both carbonic... 

In a series of reports published over the last 10-15 years, Mayr and co-workers obtained second-order rate constants for reactions of carbocations and other electrophiles such as metal-7i complexes with a series of nucleophiles, especially 7t-nucleophiles where a C C bond is formed. An impressive body of reactivity data has been accumulated, and, including data from other groups, correlated by the following equation. 

Selectivity is an intrinsic properly of enzymatic catalysis. [3] Following the nomenclature proposed by Cleland [24, 25], the pseudo second-order rate constant for the reaction of a substrate with an enzyme, kml/KM, is known as the specificity constant, ksp. [26] To express the relative rates of competing enzymatic reactions, involving any type of substrates, the ratio of the specificity constants appears to be the parameter of choice [3]. Since the authoritative proposition by Sih and coworkers [27], the ratio of specificity constants for the catalytic conversion of enantiomeric substrates, R and S, is commonly known as the enantiomeric ratio or E -value (Equation 1) ... 

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