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Third-order reactions, equations

There was a solvent kinetic isotope effect on the tribromide reaction in CHCla/CDCla, with ku/kx) = 1.175, but there was no solvent isotope effect for the addition of Bra. Reaction with Bra (the third-order reaction, equation 9.7) gave a AH value of -8.4 kcal/mol, while the reaction with tribromide (equation 9.8) gave a AH value of -t- 6.0 kcal/mol. For reactions exhibiting third-order kinetics, the rate-limiting step appears to involve formation of a bromonium ion-tribromide ion pair from a complex of one alkene and two bromine molecules. With tetra-n-butylammonium tribromide as the source of bromine, the rate-limiting step is thought to be a backside nucleophilic attack at an olefin-Bra charge transfer complex (in equilibrium with Brs" and the olefin) by the ammonium bromide ion pair that has become detached from Bra at the moment of formation of the CT complex or that is present as added salt. ... [Pg.559]

Find the integrated rate equation for a third-order reaction having the rate equation —dc/ ldt = kCf,. ... [Pg.54]

Schmid (1936 a) was the first to observe a third-order reaction in the diazotization of aromatic amines in the presence of sulfuric acid, and he proposed the kinetic equation of Scheme 3-3. In subsequent work (1936b, 1937 Schmid and Muhr, 1937), he investigated the course of the reaction in dilute hydrochloric or hydrobromic acid, which could be described by incorporating an extra term for the halide ion with only a first-order dependence on (HNO2), as in Scheme 3-4. [Pg.40]

Fig. 3. Reduced time plots, tr = (t/t0.9), for the contracting area and contracting volume equations [eqn. (7), n = 2 and 3], diffusion-controlled reactions proceedings in one [eqn. (10)], two [eqn. (13)] and three [eqn. (14)] dimensions, the Ginstling— Brounshtein equation [eqn. (11)] and first-, second- and third-order reactions [eqns. (15)—(17)]. Diffusion control is shown as a full line, interface advance as a broken line and reaction orders are dotted. Rate processes become more strongly deceleratory as the number of dimensions in which interface advance occurs is increased. The numbers on the curves indicate the equation numbers. Fig. 3. Reduced time plots, tr = (t/t0.9), for the contracting area and contracting volume equations [eqn. (7), n = 2 and 3], diffusion-controlled reactions proceedings in one [eqn. (10)], two [eqn. (13)] and three [eqn. (14)] dimensions, the Ginstling— Brounshtein equation [eqn. (11)] and first-, second- and third-order reactions [eqns. (15)—(17)]. Diffusion control is shown as a full line, interface advance as a broken line and reaction orders are dotted. Rate processes become more strongly deceleratory as the number of dimensions in which interface advance occurs is increased. The numbers on the curves indicate the equation numbers.
The kinetics of alkylation by triphenylmethyl compounds have been studied. Hart and Cassis353 found that the alkylation of phenol and o-cresol by triphenylmethyl chloride in o-dichlorobenzene gave non-linear kinetic plots which were, however, rendered linear by presaturation of the reaction mixture with hydrogen chloride, precise third-order kinetics, equation (182)... [Pg.148]

This third-order rate equation is interpreted as meaning that the process is first-order in each reactant, viz. N-chloroacetanilide, chloride ion and hydrogen ion. This has been confirmed10 for the reaction of N-chloroacetanilide with hydrogen bromide in a variety of aqueous media, under conditions where the dechlorination is rate-determining. The rate equation is... [Pg.435]

This equation is known as the rate law for the reaction. The concentration of a reactant is described by A cL4/df is the rate of change of A. The units of the rate constant, represented by k, depend on the units of the concentrations and on the values of m, n, and p. The parameters m, n, and p represent the order of the reaction with respect to A, B, and C, respectively. The exponents do not have to be integers in an empirical rate law. The order of the overall reaction is the sum of the exponents (m, n, and p) in the rate law. For non-reversible first-order reactions the scale time, tau, which was introduced in Chapter 4, is simply 1 /k. The scale time for second-and third-order reactions is a bit more difficult to assess in general terms because, among other reasons, it depends on what reactant is considered. [Pg.96]

The reaction, 2 FeCl3 + SnCl2 Products, was studied with stoichiometric proportions of reactants. The data are time in minutes and tin chloride (B) mol/liter. Check the third order rate equation corresponding to the stoichiometry. [Pg.150]

A third order reaction can be the result of the reaction of a single reactant, two reactants or three reactants. If the two or three reactants are involved in the reaction they may have same or different initial concentrations. Depending upon the conditions the differential rate equation may be formulated and integrated to give the rate equation. In some cases, the rate expressions have been given as follows. [Pg.28]

In this method, the initial concentrations of all reactants are determined. The concentration of the reacting substances is then determined by analysing the reaction mixture at different intervals of time. The different values of a and x are then substituted in rate expressions of the first, second and third order reactions. The order of reaction is given by that equation which gives a nearly constant value of k. This method, therefore, involves the trial of one equation after another till the correct one is found. This method is extensively used for simpler reactions. [Pg.228]

Consider a reaction involving a reactant such that A —> products. The rate equations corresponding to a zero, first, second, and third order reaction together with their corresponding units are ... [Pg.115]

Example Staring from the full rate equation, determine the units of the rate constant k for (a) a zero-order reaction (b) a first-order reaction (c) a second-order reaction (d) a third-order reaction and (e) a half-order reaction. Assume that concentrations are expressed in molar units and time in seconds. [Pg.52]

The mathematics involved for higher-order reactions become more difficult and such a treatment is beyond the scope of this book. For example, the integrated rate equations for the three types of third-order reactions are given in Table 3.2. [Pg.57]

Table 3.2. Integrated rate equations for the three types of third-order reactions... Table 3.2. Integrated rate equations for the three types of third-order reactions...
There are two other implications (1) the relative magnitude of the rates validates Hui and Hameilec s simplifying assumption that lead to a third-order rate equation for thermal initiation (2) the uncertainty in the prediction of k precludes any argument for or against the possibility that acid catalyzes the Diels-Alder reaction as well as the aromatization of DH. [Pg.143]

Trautz and Wachenheim have studied the formation of NOCl from NO and CI2 by following the change in total pressure as a function of time. They suggest that reactions (I) and (2) are not adequate to account for their observations since CI2 enhances the rate coefficient of the reaction. Welinsky and Taylor criticize this interpretation because of the manner in which Trautz and Wachenheim handled their data. Upon recalculating the rates in a more reliable manner it is shown that within experimental error no effect of chlorine on the rate coefficient is observed. This appears to be consistent with the data of Welinsky and Taylor, Waddington and Tolman, Kiss ", and Krauss and Saracini . In every case the production of NOCl (1) follows the third-order rate equation. All of these workers followed the reaction via the change in total pressure with time. [Pg.239]

Third-order reactions are only rarely encountered in dmg stability studies involving, as they do, the simultaneous collision of three reactant molecules. The overall rate of ampi-cillin breakdown by simultaneous hydrolysis and polymerisation may be represented by an equation of the form... [Pg.106]

Reactions in melts, vitreous materials, polymers, etc. can justifiably be analyzed by equations based on a concentration dependence of rate. Some reactions proceeding in vitreous reactant phases have been shown to conform to second or even third-order rate equations. Progressive melting of a solid reactant during decomposition results in acceleratory behaviour [52,71-73] and comprehensive melting before dehydration was observed to result in an approximately constant rate of water evolution [74,75]. [Pg.100]

Some of the isothermal relative rate [= (dfli d/V(da/d/LJ - time plots corresponding to the rate equations in Table 3.3. (a) sigmoid models (b) geometrical and reaction order (RO) models. (NOTE (i) the relative rate - time plots for the third-order rate equation and the difhision models are too deceleratory for usehil comparison and (ii) calculation on an arbitrary basis, e.g. that a = 0.98 at / = 100 min., results in plots of relative rates against a, in place of time, having similar shapes). [Pg.109]

For indirect reactions between the hydroxyl radical and the solute, the rate of reaction mainly depends on the rate of ozone decomposition, which in turn, significantly depends on the nature of solutes in water. Because the solutes vary from water to water, it is difficult to express the indirect reactions in a general rate law. Numerous researchers have conducted investigations on rate equations of ozone decomposition, and have derived the equations with different complexity and different orders (half-, first-, second-, or third-order reactions with respect to the ozone). More details can be found in Ref.. It has also been found that pH is a very important parameter for ozone decomposition. Generally, when pH <7, it has a small effect on the rate of ozone decomposition. However, at higher pH, the rate of ozone decomposition increases significantly with... [Pg.1994]

Third-order reactions are uncommon. Fractional orders exist when the reaction represents a sequence of several elementary steps. Procedures for establishing the order and rate constants for these cases are similar to those given above. Experimental data that suggest fractional-order rate equations should be examined carefully for effects of physical resistances. Sometimes these effects, rather than a sequence of elementary processes, can be responsible for the fractional order. An example is the study of the hydrochlorination of lauryl alcohol with zinc chloride as a homogeneous catalyst ... [Pg.62]

This situation is typical of metal radicals, the relatively low M-H bond strengths prohibit direct attack on H2 for thermodynamic reasons. Kinetic studies75 showed that oxidative addition of H2 obeyed an overall third-order rate law d[PJ/dr /c "Cr (CO)3Cp ]2[H2] with All1 0 kcal/mol and AS = -47 cal/(molK). The proposed mechanism for the third-order reaction is shown in Equation 10.57. [Pg.450]

Kinetics. In aqueous solution, second-order kinetics (Equation 39) are found for condensation of simple carboxylic acids and amines (10). Studies of polyamidation when a 90% conversion level is reached indicate second-order kinetics for this reaction (11). At conversions above 90%, evidence suggests that a carboxyl-catalyzed third-order reaction assumes increasing importance and becomes predominant. [Pg.169]

Chemical engineers deal with many reactions that are not elementary. Most industrially important reactions go through a complex kinetic mechanism before the final products are reached. The mechanism may give a rate expression far different than Equation 1.15 even though it involves only short-lived intermediates that never appear in conventional chemical analyses. Elementary reactions are generally limited to the following types first order, second order unimolecular, and second order with two reactants. Third-order reactions exist but are rare. [Pg.8]

Flory (loc. dt.) analysed only the last 20% of reaction and showed that over this range the results can be fitted to a third-order kinetic equation. [Pg.458]

The above relationships appear deceptively simple since they would seem to be predictable from a glance at tbe chemical equation. This is not, however, the case. The decomposition of arsine could have just as well been found to quadruple in rate were arsine s concentration doubled. In this hypothetical case, the reaction rate would be proportional to [AsH3]. Van t Hoff noted that first-order and second-order reactions are relatively common, and third-order reactions are uncommon. He provided the example of the oxidation of hydriodic acid by hydrogen peroxide ... [Pg.56]

We may develop similar expressions for second- and third-order reactions in which two or three molecules of A collide in the rate-limiting step. See, for example, Gordon, A. J. Ford, R. A. The Chemist s Companion lohn Wiley Sons New York, 1972 p. 135 for a listing of the differential and integrated forms of zero-, first-, and second-order rate equations. [Pg.343]

The methanolysis of p-nitrobenzoyl chloride in acetonitrile is a mixed second-and third-order reaction in methanol (equation A). When a chloride salt is present, the kinetics are strictly third-order (equation B) ... [Pg.357]

Some important hydride complexes are available by a reaction that appears to be the hydrogenolysis of a metal-metal single bond (Equation 3.103). However, this reaction occurs only when the metal-metal bond is weak, and probably proceeds via the third-order reaction with of the two metalloradicals [i.e., CofCO) ] formed when the metal-metal bond dissociates. - More recent observations of the reaction of monomeric metalloradicals with Hj are shown in Equations 3.104 and 3.105. - ... [Pg.125]

Markovic and co-workers [13] investigated the effects of the phenol to formaldehyde ratio used for the preparation of novolac and the nature of methylene linkages on the curing behaviour of the novolac/HMTA system using rheological studies. Cure kinetics were described by a third-order phenomenological equation, which took into account the self-acceleration effect that arises from the chemical reaction and phase separation. The reaction rate was found to increase with an increase in phenol to formaldehyde ratio. For the same phenol to formaldehyde ratio, the reaction rate increased with an increase in o, o methylene linkages (Table 2.2). [Pg.68]

Okkerse (29) determined the apparent order of the polymerization by measuring the rate of disappearance of monomer, at different silica concentrations and pH. The equations for second and third order reactions are... [Pg.256]

Plot of integrated form of rate equation for third-order reaction. [Pg.27]

The differential method of analysis (Problem 2.2) indicates that the reaction is third order. For a third-order reaction, the integral form of the rate equation is... [Pg.35]


See other pages where Third-order reactions, equations is mentioned: [Pg.464]    [Pg.11]    [Pg.61]    [Pg.967]    [Pg.50]    [Pg.13]    [Pg.290]    [Pg.186]    [Pg.323]    [Pg.76]    [Pg.268]    [Pg.24]    [Pg.60]    [Pg.3]    [Pg.239]   
See also in sourсe #XX -- [ Pg.21 , Pg.22 ]




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