Order of the reaction rate

The arylation of potassium phenoxide has been studied by Litvak and Shein (1976). In the absence of crown ether the rate of reaction with p-nitrobromobenzene in various solvents increases in the order dioxan < methanol < pyridine < DMSO. In the presence of either 18-crown-6 [3] or dibenzo-18-crown-6 [11], the order of the reaction rates in dioxan and methanol is reversed (Table 22). The effect of crown ether addition on the rate... 

A thorough analysis of the complex kinetics for this system is inappropriate here, and despite the lack of direct evidence for the intermediates in Scheme 19, the predicted acid dependence was observed. (Interestingly, aquation of the analogous [Co(en)2(ox)]+ ion is not add catalyzed.663) A relative ordering of the reaction rates gives (a) kCA > kBA > kAB > kAC > kDE x /cgE and (b)... 

Davis studied the hydrogenation of ethylene to ethane in a catalytic recycle reactor operated at atmospheric pressure (R. J. Davis, Ph.D. Thesis, Stanford University, 1989.) The recycle ratio was large enough so that the reactor approached CSTR behavior. Helium was used as a diluent to adjust the partial pressures of the gases. From the data presented, estimate the orders of the reaction rate with respect to ethylene and dihydrogen and the activation energy of the reaction. 

An important step in using this method to describe the gelation process of biopolymers is that order of the reaction rate can be evaluated, a parameter that can be difficult... 

R to P. Also, in the infinite time limit C(t -> oo) -> 0 because at long time x(0) and /i[ (f)] are not coiTelated. However, this relaxation to zero is very slow, of the order of the reaction rate k, because losing this correlation implies that the trajectory has to go several times between the wells. 

Because all of the HOOH is consumed in the experiments of Table 4-2, the reaction efficiency for the Fe(n)-HOOH system represents a crude measure of the relative rate of reaction for the adduct with substrate and HOOH. The relative order of the reaction rates for the substrates of Table 4-2 has been determined via a series of competition experiments with equimolar amounts of RH and Ph2SO. Hence, the extent of oxidative conversion of RH relative to Ph2SO from the slow addition of dilute HOOH (0.5 mmol) to an MeCN solution that contains 0.5 mmol of RH, 0.5 mmol of Ph2SO, and 0.5 mmol of Fe(II) has been measured the results are summarized in Table 4-3 as relative amounts reacted. The bond energies for the weakest R-H bond of the substrate also are tabulated. ... 

Solvent effects. In the PNO-catalyzed IPTC reaction of PhCOCl and benzoate ion, the order of the reaction rate in different two-phase media was H2O/CH2CI2 > -C6H]4 /H2O > CbHb/H20 and the yield of benzoic anhydride in H2O/CH2CI2 was considerably higher than those in the other two media. Similar results were generally observed for other benzoyl chlorides and carboxylate ions [191,192,194-196]. For example, for [PhCOCl]iorg = 0.01 M, [PhCOONa] = 0.5 M, and [PNO] = 6 x lO M, the values... 

These considerations clearly explain the experimental finding that the order of the reaction rate constant changes from second order in the high-pressure regime to third order in the low-pressure hmits. The expression for A (2). can be deter-... 

The steric effect of the amino group adjacent to the site of substitution is rather small and, therefore, the order of the reaction rates of nucleophilic displacement is 0-NH2, > NHg, since the resonance interaction from the para position is more marked than from the ortho position. 

Ammonia decomposition on a clean tungsten surface was studied by direct and simultaneous measurements of the reaction at 773-1473 K under an ammonia pressure of 10 -10 Pa [174]. The order of the reaction rate with respect to ammonia pressure changed with temperature from first order at 1478 to 2/3 order at 773 K. No hydrogen was adsorbed on the surface in any form above 973 K and an increase in the hydrogen partial pressure (Ph2) during the reaction had no effect on either the reaction rate or on the amount of surface nitrogen ( n)-... 

If certain species are present in large excess, their concentration stays approximately constant during the course of a reaction. In this case the dependence of the reaction rate on the concentration of these species can be included in an effective rate constant The dependence on the concentrations of the remaining species then defines the apparent order of the reaction. Take for example equation (A3,4.10) with e. The... 

This is the situation exploited by the so-called isolation method to detennine the order of the reaction with respect to each species (see chapter B2.1). It should be stressed that the rate coefficient k in (A3,4,10) depends upon the definition of the in the stoichiometric equation. It is a conventionally defined quantity to within multiplication of the stoichiometric equation by an arbitrary factor (similar to reaction enthalpy). 

Nitration in aqueous solutions of nitric acid Added water retards nitration in concentrated nitric acid without disturbing the kinetic order of the reaction. The rate of nitration of nitrobenzene was depressed sixfold by the addition of 5 % of water, (c. 3 2 mol 1 ), but because of the complexity of the equilibria involving water, which exist in these media, no simple relationship could be found between the concentration of water and its effect on the rate. 

Like added nitrate, sulphuric acid is not involved in the condition which determines the order of the reaction, and therefore its only effect will be to increase the observed rate constants. The rate under zeroth-order conditions is given by the first of the two expressions below,... 

The rate of a process is expressed by the derivative of a concentration (square brackets) with respect to time, d[ ]/dt. If the concentration of a reaction product is used, this quantity is positive if a reactant is used, it is negative and a minus sign must be included. Also, each derivative d[ ]/dt should be divided by the coefficient of that component in the chemical equation which describes the reaction so that a single rate is described, whichever component in the reaction is used to monitor it. A rate law describes the rate of a reaction as the product of a constant k, called the rate constant, and various concentrations, each raised to specific powers. The power of an individual concentration term in a rate law is called the order with respect to that component, and the sum of the exponents of all concentration terms gives the overall order of the reaction. Thus in the rate law Rate = k[X] [Y], the reaction is first order in X, second order in Y, and third order overall. 

Retardation of the reaction rate by the addition of dimethyl sulfide is in accord with this mechanism. Borane—amine complexes and the dibromoborane—dimethyl sulfide complex react similarly (43). Dimeric diaLkylboranes initially dissociate (at rate to the monomers subsequentiy reacting with an olefin at rate (44). For highly reactive olefins > k - (recombination) and the reaction is first-order in the dimer. For slowly reacting olefins k - > and the reaction shows 0.5 order in the dimer. 

Related to the preceding is the classification with respect to oidei. In the power law rate equation / = /cC C, the exponent to which any particular reactant concentration is raised is called the order p or q with respect to that substance, and the sum of the exponents p + q is the order of the reaction. At times the order is identical with the molecularity, but there are many reactions with experimental orders of zero or fractions or negative numbers. Complex reactions may not conform to any power law. Thus, there are reactions of ... 

When a conversion and an RTD are known, the specific rate can be found by trial Values of k are estimated until one is found that makes the segregated integral equal to the known value. Moreover, if a series of conversions are known at several residence times, the order of the reaction can be found by trying different orders and noting which give a constant series of specific rates. A catch here, however, is that the RTD depends on the hydrodynamics of the process and may change with the residence time. 

The latter kind of formulation is described at length in Sec. 7. The assumed mechanism is comprised of adsorption and desorption rates of the several participants and of the reaction rates of adsorbed species. In order to minimize the complexity of the resulting rate equation, one of the several rates in series may be assumed controlling. With several controlling steps the rate equation usually is not exphcit but can be used with some extra effort. 

The goal of a kinetic study is to establish the quantitative relationship between the concentration of reactants and catalysts and the rate of the reaction. Typically, such a study involves rate measurements at enough different concentrations of each reactant so that the kinetic order with respect to each reactant can be assessed. A complete investigation allows the reaction to be described by a rate law, which is an algebraic expression containing one or more rate constants as well as the concentrations of all reactants that are involved in the rate-determining step and steps prior to the rate-determining step. Each concentration has an exponent, which is the order of the reaction with respect to that component. The overall kinetic order of the reaction is the sum of all the exponents in the... 

Figure 3-24 shows the relationship between 1/C as a function of time t. The graph is a straight line, therefore, the assumed order of the reaction is correct. The slope of the line from the regression analysis is the rate constant k. 

The power a is called the order of reaction with respect to reactant A, b is the order with respect to B, and the sum (a + b. ..) is the overall order of the reaction. Many rate equations are of forms different from Eq. (1-11)—for example, concentration teims may appear in the denominator—and then the concept of reaction order is not applicable. 

Chemical processing under "extreme conditions" of high temperatures and pressures requires more tliorough analysis and extra safeguards. As discussed in Chapter 7, e.xplosions at liigher initial temperatures and pressures are much more severe. Therefore, chemical processes under extreme conditions require specialized equipment design and fabrication. Otlier factors tlrat should be considered when evaluating a chemical process are rate and order of the reaction, stability of the reaction, and tlie healtli hazards of the raw materials used. 

The power to which the concentration of reactant A is raised in the rate expression is called the order of the reaction, m. If tn is 0, the reaction is said to be zero-order If m = 1, the reaction is first-order if mi = 2, it is second-order and so on. Ordinarily, the reaction order is integral (0,1,2,...), but fractional orders such as are possible. 

Strategy Choose the first two concentrations, 0.20 M and 0.30 M. Calculate the ratio of the rates, the ratio of the concentrations, and finally the order of the reaction, using the general relation derived above. 

Once the order of the reaction is known, the rate constant is readily calculated. Consider, for example, the decomposition of acetaldehyde, where we have shown that the rate expression is... 

When more than one reactant is involved, the order can be determined by holding the initial concentration of one reactant constant while varying that of the other reactant From rates measured under these conditions, it is possible to deduce the order of the reaction with respect to the reactant whose initial concentration is varied. 

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