Overall reaction order The sum

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. 

The order of the overall reaction is the sum of exponents of species on the rate expression. 

Several important points about the rate law are shown in equation A5.4. First, the rate of a reaction may depend on the concentrations of both reactants and products, as well as the concentrations of species that do not appear in the reaction s overall stoichiometry. Species E in equation A5.4, for example, may represent a catalyst. Second, the reaction order for a given species is not necessarily the same as its stoichiometry in the chemical reaction. Reaction orders may be positive, negative, or zero and may take integer or noninteger values. Finally, the overall reaction order is the sum of the individual reaction orders. Thus, the overall reaction order for equation A5.4 isa-l-[3-l-y-l-5-l-8. 

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... 

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. 

The overall reaction order a is the sum of the partial reaction orders ... 

A certain element of confusion is to be met with both in textbooks, and in the literature, over the use and meaning of the terms order (cf. p. 39) and molecularity as applied to reactions. The order is an experimentally determined quantity, the overall order of a reaction being the sum of the powers of the concentration terms that appear in the rate equation ... 

D) The overall order of the reaction is the sum of the orders of the individual reactants. Here, [A]2[B]1 = 2 + 1 = 3. For reactions with an overall order of 3, the rate is proportional to the cube of the concentration of the reactants. Reducing the volume by 1/3 effectively triples their concentration 3fconcj3fordcri = 27. 

Then the reaction would be said to be (Xth order with respect to A, [3th order with respect to B,. . . and the overall order of reaction would be a + 3 +. Thus, order of reaction with respect to a reactant is the power to which the concentration of the reactant is raised into the rate law, and the overall order of reaction is the sum of the powers of the concentrations involved in the rate law. 

Esterification reactions are acid catalyzed [18-21], and an overall reaction order of 3 (2 with respect to acid and 1 with respect to alcohol) is generally accepted [9], Thus, the acid behaves both as reactant and as catalyst. It can be assumed that the concentration of acid groups, cacid, is the sum of the concentrations of carboxylic end groups (tTPA) and carboxylic groups of the free acid (TPA). 

In considering chemical stability of a pharmaceutical, one musf evaluate the reaction order and reaction rate. The reaction order may be the overall order (the sum of the exponents of the concentration terms of fhe rate expression), or fhe order with respect to each reactant (the exponent of the individual concentration term in the rate expression). The reaction rate expression is a description of the drug concentration with respect to time. Most commonly, zero- and first-order reactions are encountered in pharmacy. 

In the above expression, the quantity to the right of the first equal sign indicates that the order of the reaction with respect to the specific reactants is one and zero, respectively and because the order with respect to hydroxide is zero, then [OH ]° = 1, and the overall reaction order is the sum of the orders of the respective reactants. Hence, a SnI reaction is first-order overall. 

Third-order. The observations are consistent with the rate law, Rate= [A] [B]. Tripling [A] increases the rate ninefold, and 3 =9. Doubling [B] doubles the rate, and 2 =2. The overall reaction order (3) is the sum of the individual reaction orders (the exponents on the individual reactant concentrations) 2 -H1 = 3. 

Many reactions can be classified according to their order in a particular species, the power to which the concentration of a species occurs in the rate law, and by their overall order, the sum of the individual orders. 

Ostwald process The production of nitric acid by the catalytic oxidation of ammonia, overall order The sum of the powers to which individual concentrations are raised in the rate law of a reaction. Example If the rate = [S02][S03]" l/2, then the overall order is f. 

The values of the exponents m and n determine the reaction order with respect to A and B, respectively. The sum of the exponents (m + n) defines the overall reaction order. Thus, if the rate law is... 

To find the reaction order with respect to each reactant, look at the exponents in the rate law, not the coefficients in the balanced chemical equation, and then sum the exponents to obtain the overall reaction order. 

The order is not a result of the nature of the chemical equation it is dependent on data collected from experiments. Those data are then used to determine a mathematical equation that fits, the rate equation. The overall order of a reaction is the sum of the orders with respect to various substances (the sum of the exponents). Further, the order of a reaction is stated with respect to a named substance in the reaction (see listing above). 

The sum of the individual reaction orders equals the overall reaction order. 

In the above general equation, k is called the rate constant, a and b are called reaction orders. Most reactions considered in introductory chemistry have a reaction order of zero, one, or two. The sum of all reaction orders for a reaction is called the overall reaction order. Rate laws cannot be predicted from the stoichiometry of a reaction. They must be determined by experiment or derived from knowledge of reaction mechanism. 

The k is the rate constant that is dependent on the temperature. The a and b exponents represent the order of the concentrations of A and B. These orders can be proportional to the stoichiometry of the reaction or other experimentally determined value. The concentrations of the reactants can be plotted over time to determine the exact order of each reactant. The overall reaction order is the sum of all the exponents. Several reactions and their rate laws are provided in Table 17.1. 

Overall reaction order is the sum of the orders for each reactant, For a discussion of how this term can be misleading, see John C. Reeve, "Some Provocative Opinions on the Terminology of Chemical Kinetics,"... 

The overall reaction order is the sum of n and m. For this reaction, n + m = 2. The reaction is second order overall. 

Molecularities, defined only for single elementary steps, state the number of reactant molecules involved. The reaction order with respect to a participant is the exponent of the concentration of that species in the (possibly empirical) power-law rate equation. The overall reaction order is the sum of all such exponents. The rank of a product is an empirical quantity derived from observed rate behavior and indicating whether that species is formed directly from reactants or indirectly from intermediates. 

The overall rate equation for a parallel reaction is the sum of the constants for each pathway. For example, for a decomposition of a drug X involving two pathways, each of which is first-order. 

Other reaction orders The overall reaction order of a chemical reaction is the sum of the orders for the individual reactants in the rate law. Many chemical reactions, particularly those having more than one reactant, are not first order. Consider the general form for a chemical reaction with two reactants. In this chemical equation, a and b are coefficients. 

The overall reaction order is third order (sum of exponents 2+1 = 3). 

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