Order of the reaction

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. 

Added nitrate anticatalyses nitration under both conditions without affecting the order of the reaction, which is determined solely by the relative magnitudes of [ArH] and [HgO]. 

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,... 

Another difficulty is that the extent to which hydrogen bonded association and ion-pairing influence the observed kinetics has yet to be determined. However the high order of the reaction in the stoichiometric concentration of nitric acid would seem to preclude a transition state composed only of a nitronium ion and an aromatic molecule. 

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. 

The exponents describe the order of the reaction. It is said to be x-order in [ T],jy-order in [B], and. )-order overall. The exponents... 

The endpoint value for any changing concentration, such as [A ], sometimes referred to as the infinity point, is extremely important in the data analysis, particularly when the order of the reaction is not certain. The obvious way to determine it, ie, by allowing the reaction to proceed for a long time, is not always rehable. It is possible for secondary reactions to interfere. It may sometimes be better to calculate the endpoint from a knowledge of the... 

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 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... 

If the magnitude of the stoichiometric coefficient of a reactant exceeds the order of the reaction with respect to that species, there are one or more intermediates and reactions after the ratedetermining step. Before applying this rule, the stoichiometric equation must be formulated for the reaction such that all coefficients are integers. 

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. 

Thus, the technique consists of a transformation from the time differential dt to the area differential dQ, and the essential effect of this transformation is a reduction by one of the apparent order of the reaction. The variable 6 is the area under the curve of Cb vs. time from t = 0 to time t. With modem computer techniques for integrating experimental curves, this method should be attractive. 

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... 

In this equation m is referred to as the order of the reaction with respect to A. Similarly, n is The order of the reaction with respect to B. The overall order of the reaction is the sum of the exponents, m + n. If m = 1, n = 2, then the reaction is first-order in A, second-order in B, and third-order overall. 

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. 

Strategy To find the order of the reaction with respect to (CH3)3CBr, choose two experiments, perhaps 1 and 3, where [OH-] is constant. A similar approach can be used to find n compare experiments 2 and 5, where [(CH3)3CBr] is constant. To write the rate expression, use the calculated reaction orders. 

A reaction has two reactants A and B. What is the order with respect to each reactant and the overall order of the reaction described by each of the following rate expressions ... 

Starting from cydohexa- 1,4-diene the order of the reactions epoxidation and bromination can be reversed if appropriate substituents are located at one of the two C-C double bonds, giving products 9 and IQ.34,155... 

A special method, with only two examples, starts from 1,2,4-triazines.20 21 Diels-Alder reaction with the strained dienophile dimethyl tricyclo[4.2.2.02,5]deca-3,7,9-triene-7,8-dicarboxylate (14) is followed by an elimination of nitrogen via a retro-Diels-Alder process. The formed product, however, cannot be isolated, but reacts via another retro-Diels-Alder reaction and an electro-cyclic reaction to provide the azocine derivative 15. The sequence order of the reactions is not clear, but both pathways lead to the same product. 

The reason is soon discovered on making a serious attempt to investigate such a system on the one hand, numerous polymeric products (diazo tars) that are difficult to identify are formed at pH 6-11, and on the other hand these preparative and kinetic experiments are not readily reproducible. The material of the reaction vessel, light, and the atmosphere influence the product formation and the rate and order of the reaction to an extent rarely encountered in organic chemistry. 

This situation is called a substrate titration. That is, the change in rate with [H+] is the sole consequence of an equilibrium incidental to the main event. It is customary to display pH-dependent rates by plots of (v/[A]t) versus pH that is, by log versus pH. Two common patterns are shown in Fig. 6-1, for cases in which there is a single protonation equilibrium. The case in Fig. 6-la corresponds to Eq. (6-81) we return later to Fig. 6-1 b. The line bends down, as do all instances of substrate titration. The apparent order of the reaction with respect to [H+] is +1 in the limit of low [H+] and 0 at high. 

We say that the reaction is first order with respect to S2082- (or in S2Ox2 ) and first order in I. Doubling either the S2082- ion concentration or the I- ion concentration doubles the reaction rate. Doubling both concentrations quadruples the reaction rate. We say that the overall order of the reaction is 2. In general, if... 

The units of k depend on the overall order of the reaction and ensure that k X (concentration) 7 has the same units as the rate, namely concentration/time. Thus, when the concentration is expressed in moles per liter and the rate is expressed in mol-L 1 -s, the units of k are as follows ... 

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