Overall order

More recent determinations of by the more direct method of observing changes in the absorbance of the solution at 290 nm gave values which were not in very good agreement with these earlier ones (10 kjl mol i s i at 4-0, lo-o and 25-0 °C was i6-o, 30-0, and 95-120, respectively). The reaction was first order in the concentration of nitric acid ([HNO3] = 0-04-0-2 mol 1 at 25 ° C) and thus first-order overall. 

The rate of this reaction is observed to be directly proportional to the concentration of both methyl bromide and sodium hydroxide It is first order m each reactant or second order overall... 

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 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 conditions chosen make the reaction appear to be first-order overall, although the reaction is really not first-order overall, unlessjy and happen to be 2ero. If a simple exponential is actually observed over a reasonable extent (at least 90—95%) of decay the assumptions are considered vaUdated and is obtained with good precision. The pseudo-first-order rate constant is related to the k in the originally postulated rate law by... 

Much of the language used for empirical rate laws can also be appHed to the differential equations associated with each step of a mechanism. Equation 23b is first order in each of I and C and second order overall. Equation 23a implies that one must consider both the forward reaction and the reverse reaction. The forward reaction is second order overall the reverse reaction is first order in [I. Additional language is used for mechanisms that should never be apphed to empirical rate laws. The second equation is said to describe a bimolecular mechanism. A bimolecular mechanism implies a second-order differential equation however, a second-order empirical rate law does not guarantee a bimolecular mechanism. A mechanism may be bimolecular in one component, for example 2A I. 

The reaction is second-order overall, with the rate given by A [R2C=0][NaBH4]. The interpretation of the rate data is complicated slightly by the fact that the alkoxyborohy-drides produced by the first addition can also fimction as reducing agents, but this has little apparent effect on the relative reactivity of the carbonyl compoimds. Table 8.3 presents some of the rate data obtained from these studies. 

The study of PF polymerization is far more difficult than that of methylolation due to the increased complexity of the reactions, the intractability of the material, and a resulting lack of adequate analytical methods. When dealing with methylolation, we saw that every reactive ring position had its own reaction rate with formaldehyde that varied with the extent of prior reaction of the ring. Despite this rate sensitivity and complexity, all reactions kinetics were second-order overall, first-order in phenol reactive sites and first-order in formaldehyde. This is not the case with the condensation reactions. 

Figure 3-7 gives plots of Equations 3-54 and 3-58, respeetively. Consider the seeond order reaetion 2A-I-B—produets, whieh is first order with respeet to both A and B, and therefore seeond order overall. The rate equation is ... 

Nc = 0.0 gmol, Nq = 0.0 gmol, respectively. A mixture of A and B is charged into a 1-liter reactor. Determine the holding time required to achieve 90% fractional conversion of A (X = 0.9). The rate constant is k = 1.0 X 10 [(liter) /(gmoP min)] and the reaction is first order in A, second order in B and third order overall. 

Assume that the reaetion is irreversible and first order with respeet to eaeh speeies A and B and seeond order overall. The reaetion rate for eomponent A is represented by (-r ) = kC Cg. 

The rate is proportional to the concentrations of both A and B. Because it is proportional to the product of two concentration terms, the reaction is second-order overall, first-order with respect to A and first-order with respect to B. (Were the elementary reaction 2A P + Q, the rate law would be = A[A] second-order overall and second-order with respect to A.) Second-order rate constants have the units of (concentration) time) as in M sec. ... 

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 rapid formation of the (Z)-diazoate is followed by the slower (Z/J )-isomeri-zation of the diazoate (see Scheme 5-14, reaction 5). Some representative examples are given in Table 5-2. Both reactions are first-order with regard to the diazonium ion, and the first reaction is also first-order in [OH-], i.e., second-order overall. So as to make the rate constants k and k5 directly comparable, we calculated half-lives for reactions with [ArNj ]0 = 0.01 m carried out at pH = 9.00 and 25 °C. The isomerization rate of the unsubstituted benzenediazonium ion cannot be measured at room temperature due to the predominance of decomposition (homolytic dediazoniations) even at low temperature. Nevertheless, it can be concluded that the half-lives for (Z/ )-isomerizations are at least five powers of ten greater than those for the formation of the (Z)-diazohydroxide (reaction 1) for unsubstituted and most substituted benzenediazonium ions (see bottom row of Table 5-2). Only for diazonium ions with strong -M type substituents (e.g., N02, CN) in the 2- or 4-position is the ratio r1/2 (5)/t1/2 (1) in the range 6 x 104 to 250 x 104 (Table 5-2). 

More recently, the kinetics of bromination of benzene in water have been examined296. The reaction is second-order overall and the slope of the plot kobs... 

Analysis of the first-order rate coefficient in terms of the two consecutive reactions which were occurring, yielded values of 5.3 xlO-4 and 2.64 xlO-4 the latter value was confirmed as arising from reaction on the first reaction product, 3,4-dichlorodiphenylmethane, because separate 3,4-dichlorobenzylation of this gave a rate coefficient of 2.98 x 10-4. The first-order (overall) rate coefficients obtained at 15 °C (0.665 x 10-4) and 35 °C (6.1 x 10-4) yielded Ea = 19.6, and log A = 14.3, the rate ratio for the consecutive reactions being the same (0.5) at both temperatures later studies have tended to confirm this order of activation energy. 

Some results which are consistent with this mechanism have been obtained by Ishii and Yamashita385, who found that the kinetics of the reaction of m-xylene with formaldehyde and hydrogen chloride (to give the 4-substituted product) were third-order overall. However, this was followed by a slow di-chloromethylation which was of zeroth-order, but no interpretation or further mechanistic details are available. 

The reaction is second order in H30 and so fourth order overall. We can check our result by verifying that (1.5)2 = 2.3. 

Similar expressions can be written for third-order reactions. A reaction whose rate is proportional to [A] and to [B] is said to be first order in A and in B, second order overall. A reaction rate can be measured in terms of any reactant or product, but the rates so determined are not necessarily the same. For example, if the stoichiometry of a reaction is2A-)-B—>C- -D then, on a molar basis, A must disappear twice as fast as B, so that —d[A]/dt and -d[B]/dr are not equal but the former is twice as large as the latter. 

For the general case of a reaction first order in A and first order in B, second order overall, integration is complicated, but it can be simplified if equimolar amounts of... 

There is a large amount of evidence for the Sn2 mechanism. First, there is the kinetic evidence. Since both the nucleophile and the substrate are involved in the rate-determining step (the only step, in this case), the reaction should be first order in each component, second order overall, and satisfy the rate expression... 

Brown and Grayson reported that the rate of alkylation reactions with benzyl chloride was third order overall first order in aromatic component, first order in AICI3, and first order in benzyl chloride. This indicates that a rate determining nucleophilic attack by the aromatic component on a polar alkyl chloride-aluminum... 

When a reaction proceeds in a single elementary step, its rate law will mirror its stoichiometry. An example is the rate law for O3 reacting with NO. Experiments show that this reaction is first order in each of the starting materials and second order overall NO + 03- NO2 + O2 Experimental rate = i [N0][03 J This rate law is fully consistent with the molecular view of the mechanism shown in Figure 15-7. If the concentration of either O3 or NO is doubled, the number of collisions between starting material molecules doubles too, and so does the rate of reaction. If the concentrations of both starting materials are doubled, the collision rate and the reaction rate increase by a factor of four. 

Equation is used to test whether a reaction is first order overall. The concentration of reactant A is monitored as a... 

This is the first example where we have tested to see if the concentration of a product affects the rate of a reaction. It may seem intuitive that products should not be involved in rate laws, but as we show in Section 15-1. a product may influence the rate of a reaction. In careful rate studies, this possibility must be considered. It is common for some reagents in a chemical system to have no effect on the rate of chemical reaction. Although it is unusual for none of the reagents to affect the rate, there are some reactions that are zero order overall. Such reactions have a particularly simple rate law Rate = t. 

The predicted rate law is first order for a reaction whose first step is unimolecular and rate-determining. The predicted rate law is second order overall for a reaction whose first step is bimolecular and rate-determining. For example, the first step of the mechanism for the C5 Hi 1 Br reaction is unimolecular and slow, so the rate law... 

First, analyze the one-step mechanism CO -I- NO2 CO2 4-NO This process is analogous to the reaction of NO and O3 discussed in Section 15-1. In a simple one-step atom transfer, the reaction is first order in each of the starting materials and second order overall ... 

C15-0080. The reaction of NO with O2 to give NO2 is an important process in the formation of smog in Los Angeles 2 NO + O2 2 NO2 Experiments show that this reaction is third order overall. 

C15-0126. Consider the following hypothetical reaction, which is order overall and half order in 1... 

In the case of the hexacarbonyls, the rate-expression contains not only the same type of first-order term but in addition one second-order overall. For good entering groups (but not CO, for example) the rate expression contains a term strictly first-order in both the complex and the entering nucleophile. The first-order rates of CO exchange are practically identical with the rates of substitution in hydrocarbon solvents, but there is nevertheless some acceleration in ether (THF, dioxan) solutions. This solvent-dependence is not so well-marked ° as in the case of nickel tetracarbonyl. The second-order rate of substitution very strongly depends upon the basicity of the entering nucleophile... 

Thus, in contrast to what occurred in the jar, in an EPS the overall chemical reaction occurs in the form of two spatially separated partial electrochemical reactions. Electric current is generated because the random transfer of electrons is replaced by a spatially ordered overall process. 

S Reactions may be classified with an overall order, as well as orders with respect to the individual substances reacting. Which of these is classified as third order overall ... 

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