Reaction order, overall

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... 

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 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. 

Kinetic Models Used for Designs. Numerous free-radical reactions occur during cracking therefore, many simplified models have been used. For example, the reaction order for overall feed decomposition based on simple reactions for alkanes has been generalized (37). 

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. 

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. 

The power a is called the order of reaction with respect to reactant A, b is the order with respect to B, and the sum (a + b. ..) is the overall order of the reaction. Many rate equations are of forms different from Eq. (1-11)—for example, concentration teims may appear in the denominator—and then the concept of reaction order is not applicable. 

The units of the rate constant depend upon the overall reaction order. 

The isolation technique showed that the reaction is first-order with respect to cin-namoylimidazole, but treatment of the pseudo-first-order rate constants revealed that the reaction is not first-order in amine, because the ratio k Jc is not constant, as shown in Table 2-2. The last column in Table 2-2 indicates that a reasonable constant is obtained by dividing by the square of the amine concentration hence the reaction is second-order in amine. For the system described in Table 2-2, we therefore find that the reaction is overall third-order, with the rate equation... 

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. 

In the case of stoichiometric reactions the overall order can be readily estimated from the plot of the fraction a of the reactants, remaining at time t, against logm t304,330). For a d 11 order reaction the experimental plot of a vs. logi0t can be superimposed on the dft curve of the following theoretical set of functions ad ... 

Fiery1 252-254) studied only the last stage of the reactions, i.e. when the concentration of reactive end groups has been greatly decreased and when the dielectric properties of the medium (ester or polyester) no longer change with conversion. Under these conditions, he showed that the overall reaction order relative to various model esterifications and polyesterifications is 3. As a general rule, it is accepted that the order with respect to acid is two which means that the add behaves both as reactant and as catalyst. However, the only way to determine experimentally reaction orders with respect to add and alcohol would be to carry out kinetic studies on non-stoichiometric systems. 

Manakov and Hasan307 studied the system pentanoic acid/l-heptanol/n-decane and found an overall reaction order of three. 

Several results were reported by Russian authors. They are completely different from those reported above. Sorokin14 found an overall reaction order of 2 for the system heptanoic acid/l,2-ethanediol/diphenyl oxide. Bolotina16 studied the reaction of 2-ethylhexyl hydrogenphthalate with 2-ethylhexanol in the corresponding diester and found an order of 1 with respect to acid and of 2 with respect to alcohol. 

In all calculations [RCOOH] is a variable parameter and the final rate equation is a function of [RCOOH] and of K n is the overall reaction order when the reaction is carried out with stoichiometric amounts of add and alcohol. However, it is important to mention that it is the global acidity x of the medium and not [RCOOH] which is measured ... 

Robins6 investigated the reaction of 1,2-propanediol with maleic add and found an overall reaction order of 3 which is in agreement with Flory s assumptions. The same order was found by Ivanov325 for the l,10-decanediol/2-propylheptanedioic system. 

Ueberreiter and Hager19 rather surprisingly found an overall reaction order of 6 at the beginning of ethanediol esterification. They explained this with the existence of hydrogen-bonded dimers. 

In spite of a rather surprising overall reaction order of 6 (see Sect. 6.1.2.2) and of E values noticeably above those generally found, Ueberreiter and Hager19 reported some interesting variations of E in the early stages of the reaction of 1,2-ethanediol with the following dicarboxylic acids ... 

Reactions between oligomers to-hydroxypolyoxyethylene and experimental data with the established kinetic law230. This is presumably due to the hydrophilicity of polyoxyethylene which retains the reaction water and therefore favours the hydrolysis of the catalyst. Consequently, it is not surprising that only low values of rate constants were obtained. The best fit was found for an overall reaction order close to 2.5. 

Orders with quotation marks mean that the rate constants given by the authors are complex parameters depending on the add concentration. (In this case see corresponding reference.) The overall reaction order does not indude the order with respect to catalyst. 

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. 

What is the order with respect to each species What is the overall reaction order What are the dimensions of k ... 

The extent to which anode polarization affects the catalytic properties of the Ni surface for the methane-steam reforming reaction via NEMCA is of considerable practical interest. In a recent investigation62 a 70 wt% Ni-YSZ cermet was used at temperatures 800° to 900°C with low steam to methane ratios, i.e., 0.2 to 0.35. At 900°C the anode characteristics were i<>=0.2 mA/cm2, Oa=2 and ac=1.5. Under these conditions spontaneously generated currents were of the order of 60 mA/cm2 and catalyst overpotentials were as high as 250 mV. It was found that the rate of CH4 consumption due to the reforming reaction increases with increasing catalyst potential, i.e., the reaction exhibits overall electrophobic NEMCA behaviour with a 0.13. Measured A and p values were of the order of 12 and 2 respectively.62 These results show that NEMCA can play an important role in anode performance even when the anode-solid electrolyte interface is non-polarizable (high Io values) as is the case in fuel cell applications. 

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. 

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