Order of a reaction with respect

If the order of a reaction with respect to one or more species increases as the concentration of those species increases, it is an indication that the reaction may be proceeding by two or more parallel paths. 

If there is a decrease in the order of a reaction with respect to a particular substance as the concentration of that species increases, the dominant form of that species in solution may be undergoing a change caused by the change in concentration. 

It is important to recognize the difference between the order of a reaction with respect to a specific reactant and the overall order of a reaction. The /order of a reaction with respect to a particular reactant is the power to which the concentration of that reactant must be raised to have direct proportionality between concentration and reaction rate. According to Equation 8-2 the rate of the chloromethane-hydroxide ion reaction is first order with respect to chloromethane and first order with respect to hydroxide ion. In Equation 8-1 the rate is first order with respect to chloromethane and zero order with respect to hydroxide ion because [OH0]0 = 1. The overall order of reaction is the sum of the orders of the respective reactants. Thus Equations 8-1 and 8-2 express the rates of overall first-order and second-order reactions, respectively. 

Modem treatments of chemical kinetics (e.g., see, Kopelman, 1986 Newhouse and Kopelman, 1986) have shown that the kinetic order of a reaction with respect... 

Here is the rate constant for the reaction, and a, b, and c do not necessarily equal nA, b, and nc, respectively. In this expression, the overall order of the reaction is a + b + c, and the order with respect to A is a, the order with respect to B is b, and the order with respect to C is c. The order of a reaction with respect to a certain reagent is frequently a whole number, but fractional order is possible, and the order can be 0. 

The order of a reaction with respect to a component is the exponent to which the concentration of the components influencing the rate of the reaction are to be raised in order to get the rate expression. The order of the reaction is the sum of the orders with respect to all the components. The basic assumption of mass action kinetics is that the orders of an elementary reaction with respect to the components are given by the stoichiometric coefficients or molecularities as in (1.2). 

Earlier we stressed that the orders of a reaction with respect to particular reactants, and therefore the overall order and rate expression, can only be determined experimentally. 

The order of a reaction with respect to a reactant can also be determined from a concentrationtime graph. If the reaction is zero order with respect to a reagent, then the graph produced is a straight line (Figure 16.1). 

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). 

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. 

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. 

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. 

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. 

Four experiments were conducted to discover how the initial rate of consumption of Br03 ions in the reaction Br03 (aq) + 5 Br (aq) + 6 HijO laq) — 3 Br2(aq) + 9 H20(1) varies as the concentrations of the reactants are changed, (a) Use the experimental data in the following table to determine the order of the reaction with respect to each reactant and the overall order, (b) Write the rate law for the reaction and determine the value of k. 

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. 

In general, each concentration has some exponent (here, y and z). Each exponent is called the order of the reaction with respect to that particular species. In Equation, y is the order of reaction with respect to species A, and z is the order with respect to species B. When the value of y is 1, the reaction is called first order in A when the value of z is 2, the reaction is called second order in B, and so on. Orders of reaction are small integers or simple fractions. The most common orders are 1 and 2. The sum of the exponents is known as the overall order of the reaction. 

A quantity of earlier work exists on chromic acid oxidation of hydrocarbons. It was noted that diphenylmethane and other hydrocarbons in glacial acetic acid solution are oxidised rapidly during the initial stages but that reaction is auto-retarded The autoretardation is eliminated on adding 2.5 % of sulphuric acid. The orders of the reaction with respect to diphenylmethane and Cr(VI) are one and two respectively , the latter differing from that found by Wiberg and... 

In its application to specific kinetics studies this general procedure may take on a variety of forms that are minor modifications of that outlined above. One modification does not require an explicit assumption of the form of 0(Q) including numerical values of the orders of the reaction with respect to the various species, but merely an assumption that the rate expression is of the following form. 

The constants k and m may be determined from a log-log plot of the rate versus CA. This procedure leads to a value for the overall order of the reaction. Experiments with nonstoichiometric ratios of reactants can then be used to determine the orders of the reaction with respect to each of the individual species. 

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