Order of a reaction

Order of a Reaction.—In employing mea urements of reaction velocity for the purpose of determining the mechanism of a chemical reaction, the first point which has to be -settled is the order of the reaction. This is not always given by the number of reacting molecules as expressed in the ordinary chemical equation indeed, it is very seldom so given except in the case of the simplest reactions. 

For the purpose of deciding this important point, various methods may be employed. One of the most important consists in making several measurements of the velodty of the reaction, starting with difierent concentrations of the reacting substances, and determining, in each case, the time required for a certain fraction (say, one-half) of the total change to occur. For a monomolecular reaction, the times are independent of the initial concentration for a bimolecular reaction they are inversely proportional to the initial concentrations and, generally, for a reaction of the th order, they are inversely proportional to the ( —r) power of the initial concentrations. 

Experiment.—Determine the Order of Reaction in the Case of the Hydrolysis of an Ester in Presence of Acid. 

For this purpose, two experiments should be carried out with methyl acetate and hydrochloric acid (see p, 262), using the same amount of acid in each case, but twice as much methyl acetate in one case as in the other. The results should then be plotted in rectangular co-ordinates, the times of titration (in minutes) being plotted as ordinates, and the corresponding values of a — X (or — T ) as abscissae. From the curves obtained, the time should be read off corresponding to the abscissa a — 2 = fa (or T, — T = f(T — T,)). The time so found should be the same in the two cases. 

Experiment.—Determine the Order of the Reaction 6HI - -HBrO, = HBr -f aHjO + 

The rate, u, of a reaction is sometimes—but by no means always—related to the concentrations of reactants A, B, etc., by an equation of the type 

Note that the order of a reaction is a purely experimental quantity. 

A very simple case is when the rate is proportional to the first power of the concentration of a single reactant  

Such a reaction is said to be of the /irst order. An example is the conversion, of oxalosuccinate into a-ketoglutarate  

The rate of this reaction is proportional to the first power of the oxalosuccinate concentration. This reaction occurs readily if oxalosuccinate is heated. During metabolism oxalosuccinate is formed from isocitrate but it is not released into the cell instead it decomposes into a ketoglutarate. 

As stated impMcitly above, the rate of a reaction can be obtained from the slope of the concentration-time curve for disappearance of reac-tant(s) or appearance of product(s). Typical reactant concentration-time curves for zero-, first-, second-, and third-order reactions are shown in Fig. 1.1(a). The dependence of the rates of these reactions on reactant concentration is shown in Fig. 

If the rate of a reaction is independent of a particular reactant concentration, the reaction is considered to be zero order with respect to the concentration of that reactant (n = 0). If the rate of a reaction is directly proportional to a particular reactant concentration, the reaction is considered to be first-order with respect to the concentration of that reactant (n = 1). If the rate of a reaction is proportional to the square of a particular reactant concentration, the reaction is considered to be second-order with respect to the concentration of that reactant (n = 2). In general, for any reaction A -h B -h C H------ P, the rate equation can be generalized as 

The order of a reaction can be determined only by experiment. A common way to determine reaction order is the method of initial rates. In this method, the initial rate— the rate for a short period of time at the beginning of the reaction—is measured by running the reaction several times with different initial reactant concentrations to determine the effect of the concentration on the rate. For example, let s return to our simple reaction in which a single reactant. A, decomposes into products  

In an experiment, the initial rate is measured at several different initial concentrations with the following results  

In this data set, when the concentration of A doubles, the rate doubles—the initial rate is directly proportional to the initial concentration. The reaction is therefore first order in A, and the rate law takes the first-order form  

We can determine the value of the rate constant, k, by solving the rate law for k and substituting the concentration and the initial rate from any one of the three measurements (here we use the first measurement). 

Notice that the rate constant for a first-order reaction has units of s  

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When the overall order of a reaction is greater than three, the mechanism probably has one or more equilibria and intermediates prior to the rate-determining step. 

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. 

Reaktions-losigkeit,/. absence of reaction, nonreaction. -masse, /. reaction mass, mass resulting from a reaction, -mischung, /. reaction mixture, -mittel, n. reagent, -ord-nung, /. order of a reaction, -ort, m. field or sphere of reaction, -papier, n. test paper, -rohr, n., -rohre,/. reaction tube, -stufe,/. step or stage of a reaction, -teilnehmer, m. participant in a reaction, reactant. 

The order of a reaction must be determined experimentally it cannot be deduced from die coefficients in the balanced equation. This must be true because there is only one reaction order, but there are many different ways in which the equation for the reaction can be balanced. For example, although we wrote... 

One way to find the order of a reaction is to measure the initial rate (Le., the rate at t = 0) as a function of the concentration of reactant Suppose, for example, that we make up two different reaction mixtures differing only in the concentration of reactant A. We now measure the rates at the beginning of reaction, before the concentration of A has decreased appreciably. This gives two different initial rates (rate , rate2) corresponding to two different starting concentrations of A, [A]x and [A]2. From the rate expression,... 

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) ... 

According to the definition given, this is a second-order reaction. Clearly, however, it is not bimolecular, illustrating that there is distinction between the order of a reaction and its molecularity. The former refers to exponents in the rate equation the latter, to the number of solute species in an elementary reaction. The order of a reaction is determined by kinetic experiments, which will be detailed in the chapters that follow. The term molecularity refers to a chemical reaction step, and it does not follow simply and unambiguously from the reaction order. In fact, the methods by which the mechanism (one feature of which is the molecularity of the participating reaction steps) is determined will be presented in Chapter 6 these steps are not always either simple or unambiguous. It is not very useful to try to define a molecularity for reaction (1-13), although the molecularity of the several individual steps of which it is comprised can be defined. 

The order of a reaction cannot in general be predicted from the chemical equation a rate law is an empirical law ... 

The order of a reaction is the power to which the concentration of the species is raised in the rate law the overall order is the sum of the individual orders. 

Determine the order of a reaction, its rate law, and its rate constant from experimental data (Examples 13.1 and L3.2 and Self-Tests 13.2 and 13.3). 

The occurrence of a compensation effect can be readily deduced from Eqs. (1.6) and (1.7). The physical basis of the compensation effect is similar to that of the Sabatier volcano curve. When reaction conditions or catalytic reactivity of a surface changes, the surface coverage of the catalyst is modified. This change in surface coverage changes the rate through change in the reaction order of a reaction. 

For example, experimental studies show that the rate law for the reaction of O3 with NO2 to give N2 O5 and O2 is first order in each reactant 2 NO2 + O3 N2 O5 + O2 Experimental rate = [N02 ][03 ] Notice that for this reaction, the order of reaction with respect to NO2 is 1, whereas the stoichiometric coefficient is 2. This shows that the order of a reaction for a particular species cannot be predicted by looking at the overall balanced equation. We describe additional examples in Section 15-1. 

Another term often used in reaction kinetics is molecularity . In order to distinguish this term from order of a reaction, present reference is drawn to the formation of N H3 from H2 and N2, as shown in the equation below ... 

The order of the above reaction is, therefore, 1.5 + 0.5 = 2. This is typical of situations where the order of reaction and the molecularity of the reaction are the same. It may, however, be noted that the form of rate law, which determines the order of a reaction, can only be derived by actual experiment, and that may or may not be equal to the molecularity of the reaction as provided by the equation representing that reaction. Thus, a general reaction... 

The order of the reaction is 2 + 1 = 3, whereas the molecularity of the reaction, as given by the equation is 4. This reaction can be treated as a representative example which shows that the order of a reaction is strictly an experimental quantity, being concerned solely with the manner in which the rate depends on concentration. In other words, the order of a reaction should be regarded as a mathematical convenience and not as a fundamental property of the reaction. It must be mentioned here that the order of a reaction corresponds to the... 

Therefore, if In C is plotted against t, as shown in Fig. 2, the plot will be a straight line with an intercept (at t = 0) of In Co, and the slope of the line (m) will be — k. Such plots are commonly used to determine the order of a reaction that is, if a plot of In C versus time is a straight line, the reaction is assumed to be a first-order or pseudo-first-order process. 

The order of the reaction, n, can be defined as n = a + b. Extended to the general case, the order of a reaction is the numerical sum of the exponents of the concentration terms in the rate expression. Thus if a = b = 1, the reaction just described is said to be second-order overall, first-order relative to A, and first-order relative to B. In principle, the numerical value of a or b can be integral or fractional. 

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 ... 

The order of a reaction is the same as the number of concentration terms in the rate expression. Consider the general rate equation ... 

Care the molecularity and the order of a reaction need not be the same. 

The rate of loss of reactant is negative because the concentration decreases with time The gradient at the start of the reaction is called the initial rate. Analysing the initial rates method is an extremely powerful way of determining the order of a reaction. 

The preferred general method is the vacuum reaction calorimeter because of its wide range and flexibility, and because the enthalpy of the reactions is a good indicator of whether a polymerisation has gone to completion in any case, tests for residual monomer by glc must not be omitted. The complete reaction curve, however acquired, can reveal not only the internal order of a reaction, and whether it changes with conversion, and it is a far firmer base for calculating rate-constants than the initial rate or a maximum rate. 

There is not necessarily a simple relationship between molecularity and order of reaction. For differentiating between molecularity and order of a reaction, let us consider some examples. 

However, the average rates calculated by concentration versus time plots are not accurate. Even the values obtained as instantaneous rates by drawing tangents are subject to much error. Therefore, this method is not suitable for the determination of order of a reaction as well as the value of the rate constant. It is best to find a method where concentration and time can be substituted directly to determine the reaction orders. This could be achieved by integrating the differential rate equation. 

In order to confirm the order of a reaction, the left hand side of the expression, when plotted against time, should give a straight line. Thus, if a plot of (1 /a-x) versus time is a straight line, reaction would be of second order. This is a simple and accurate method and is applied generally for determination... 

How the graphical method is most useful in determining the order of a reaction ... 

The limiting cases are liniso 0 e = 1 and limV0 x e = 0. The normalized elasticity can be interpreted as a measure of the kinetic order of a reaction. 

The interpretation of the elements of the matrix 0 is slightly more subtle, as they represent the derivatives of unknown functions fi(x) with respect to the variables x at the point x° = 1. Nevertheless, an interpretation of these parameters is possible and does not rely on the explicit knowledge of the detailed functional form of the rate equations. Note that the definition corresponds to the scaled elasticity coefficients of Metabolic Control Analysis, and the interpretation is reminiscent to the interpretation of the power-law coefficients of Section VII.C Each element 6% of the matrix measures the normalized degree of saturation, or likewise, the effective kinetic order, of a reaction v, with respect to a substrate Si at the metabolic state S°. Importantly, the interpretation of the elements of does again not hinge upon any specific mathematical representation of specific... 

The reaction is first-order with respect to X, second-order with respect to Y and third-order overall k is the rate constant. Note that the order of a reaction does not necessarily have to have integral values. 

Response-surface methodology has also been used to gain theoretical insight into a reacting system (B19) and to determine the order of a reaction (P3). 

The units of k, the rate constant, depend on the overall order of a reaction. For what overall reaction order does the rate constant have the same units as the reaction rate ... 

Reinmuth notation A useful shorthand notation for abbreviating the order of a sequence of electrochemical ( E ) and chemical ( C ) reactions (see Section 6.4.3). The order of a reaction is read from the left of the Reinmuth code to the right. 

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