Order of a rate law

The order of a reaction (this is the common parlance more precisely,2 the order of a rate law) is the sum of the exponents of the concentration factors in the rate law. One can also refer to the order with respect to a particular species. Consider the reaction in Eq. (1-11), with the rate law given by Eq. (1-12) ... 

As with homogeneous reactions, rate laws for heterogeneous reactions are kinetic statements and must be determined experimentally. The exponents (called orders) of a rate law depend on the reaction mechanism. 

Demonstrate that the overall order of a rate law is determined by the units on k. 

Establishing the form of a rate law experimentally for a particular reaction involves determining values of the reaction rate parameters, such as a, and y in equation 3.1-2, and A and EA in equation 3.1-8. The general approach for a simple system would normally require the following choices, not necessarily in the order listed ... 

The units of the specific rate depend on the order of a power law rate equation and on the units of the rate of reaction which are basically, (mass)/(time) (volume). 

As can be seen from this plot, the data points arc not exactly linear. However, to use the method of differentiat analysis of rate data, we must find a best-iit line for (be data. That best-fit tne is drawn in the plot, and the slope is 1.4S41. This slope coiresponds to the order of the rate law (n). Therefore, the rate law is now ... 

The mechanisms of most common reactions consist of two or more elementary steps, reactions that occur in one step and depict a single chemical change. The molecu-larity of an elementary step equals the number of reactant particles and is the same as the reaction order of its rate law. Unimolecular and bimolecular steps are common. The rate-determining, or rate-limiting (slowest), step determines how fast the overall reaction occurs, and its rate law represents the overall rate law. Reaction intermediates are species that form in one step and react in a later one. The steps in a... 

Distinguish between the differential rate law and the integrated rate law. Which of these is often called just the "rate law" What is A in a rate law, and what are orders in a rate law Explain. 

The reaction rate is properly defined in terms of the time derivative of the extent of reaction [eqnation (3.0.1)]. One must define /c in a similar fashion to ensnre nniqneness. Definitions of k in terms of the various r, would lead to rate constants that would differ by the ratios of their stoichiometric coefficients. The units of the rate constant will vary depending on the overall order of the reaction. These units are those of a rate divided by an mth power of concentration (where m is the overall order of the rate law). Thns, from examination of equations (3.0.17) and (3.0.18),... 

The units of the rate constant depend on the overall reaction order of the rate law. In a reaction that is second order overall, for example, the units of the rate constant must satisfy the equation ... 

Understand the form and meaning of a rate law including the ideas of reaction order and rate constant. (Section 14.3)... 

The individual steps in a reaction mechanism are called elementary steps. Unlike the overall stoichiometric equation, the coefficients for reactants in an elementary step do provide the exponents in the rate law for that step. According to our reasoning above, only three types of elementary steps are likely to occur, those involving one, two, or three molecules. Steps with one reactant are called unimolecular, and those with two and three reactants are called bimolecular and termolecular, respectively. The molecularity tells us the overall order of the rate law for the elementary step, as summarized in Table 11.1. 

Solve (a) As we move from experiment 1 to experiment 2, [A] is held constant and [B] is doubled. Thus, this pair of experiments shows how [B] affects the rate, allowing us to deduce the order of the rate law with respect to B. Because the rate remains the same when [B] is doubled, the concentration of B has no effect on the reaction rate. The rate law is therefore zero order in B (that is, = 0). 

This is a method for determining the concentration dependence of a rate law that avoids the need for an integrated rate law or pseudo-first-order conditions. It is based on the assumption that the reactant concentrations are essentially constant during the initial 10% of reaction. The use of this method requires that observation can begin very soon after mixing the reactants and that the detection method is sensitive enough to provide precise data over the small extent of reaction. The latter condition usually means that the reaction half-time is about ten seconds or longer, so that this method is convenient and efficient for slow reactions. Observation over a short initial period may avoid, but also may hide, kinetic and chemical complications that only are clearly apparent later in the reaction. 

The qualitative features of reaction mechanisms in solutions are substantially different from those in gases. Unimolecular processes still occur via collisional activation. However, solvent molecules which can affect activation are always in high concentration. In terms of a rate law such as (5.22) the experiments are being carried out under conditions where kJ[M] kd or A [A] and A /[M] A +[A] here [M] represents the concentration of solvent, always in large excess. There is significant short-range order in liquids as solvent molecules are loosely bound to one another and form transient structures which reduce the mobility of the products of a decomposition. Thus the rate at which products separate by diffusion must limit the rate of unimolecular reaction in solution.Unimolecular decomposition may still be considered a two-step process ... 

The temperature dependence of a rate law corresponding to a steady-state approximation is more comphcated than that of the previous example. Write the temperature dependence of the apparent first-order rate constant for the decomposition of N2O5 given in Eq. (12.4-34). 

Neither (A3.4.15) nor (A3.4.17) is of the fonn (A3,4,10) and thus neither reaction order nor a unique rate codficient can be defined. Indeed, the number of possible rate laws that are not of the fonu of (A3.4.10) greatly exceeds those cases following (A3.4.10). However, certain particularly simple reactions necessarily follow a law of type of (A3.4.10). They are particularly important from a mechanistic point of view and are discussed in the next section. 

First-order nitrations. The kinetics of nitrations in solutions of acetyl nitrate in acetic anhydride were first investigated by Wibaut. He obtained evidence for a second-order rate law, but this was subsequently disproved. A more detailed study was made using benzene, toluene, chloro- and bromo-benzene. The rate of nitration of benzene was found to be of the first order in the concentration of aromatic and third order in the concentration of acetyl nitrate the latter conclusion disagrees with later work (see below). Nitration in solutions containing similar concentrations of acetyl nitrate in acetic acid was too slow to measure, but was accelerated slightly by the addition of more acetic anhydride. Similar solutions in carbon tetrachloride nitrated benzene too quickly, and the concentration of acetyl nitrate had to be reduced from 0-7 to o-i mol 1 to permit the observation of a rate similar to that which the more concentrated solution yields in acetic anhydride. 

The effects of added species. The rate of nitration of benzene, according to a rate law kinetically of the first order in the concentration of aromatic, was reduced by sodium nitrate, a concentration of io mol 1 of the latter retarding nitration by a factor of about Lithium nitrate... 

Furthermore kinetic studies reveal that electrophilic addition of hydrogen halides to alkynes follows a rate law that is third order overall and second order in hydrogen halide... 

The integrated form of the rate law for equation 13.4, however, is still too complicated to be analytically useful. We can simplify the kinetics, however, by carefully adjusting the reaction conditions. For example, pseudo-first-order kinetics can be achieved by using a large excess of R (i.e. [R]o >> [A]o), such that its concentration remains essentially constant. Under these conditions... 

Direct-Computation Rate Methods Rate methods for analyzing kinetic data are based on the differential form of the rate law. The rate of a reaction at time f, (rate)f, is determined from the slope of a curve showing the change in concentration for a reactant or product as a function of time (Figure 13.5). For a reaction that is first-order, or pseudo-first-order in analyte, the rate at time f is given as... 

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