Second 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... 

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. 

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. ... 

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... 

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... 

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. 

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 ... 

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... 

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. 

The displacement was monitored by observing the changing distribution of radioactive 128I between the inorganic (sodium) iodide and 2-iodooctane, and it was found, under these conditions, to be second order overall (first order with respect to 128Ie and to 2-iodooctane) with k2 = 3-00 + 0-25 x 10-5 (at 30°). 

The reaction is believed to be first order in each reactant and second order overall. The following data were reported for their experiments at 20 °C using an iodine concentration of 0.422 x 10 3 kmoles/m3. 

If the surface is nearly covered (0A 1) the reaction will be first-order in the gas phase reactant and zero-order in the adsorbed reactant. On the other hand, if the surface is sparsely covered (0A KAPA) the reaction will be first-order in each species or second-order overall. Since adsorption is virtually always exothermic, the first condition will correspond to low temperature and the second condition to high temperatures. This mechanism thus offers a ready explanation of a transition from first-to second-order reaction with increasing temperature. 

The forward reaction is third-order (second-order with respect to monomer and first-order with respect to catalyst). The reverse reaction is second-order overall (first-order with respect to both catalyst concentration and dimer). The reaction is catalyzed by tributylphosphine at a concentration of 0.05 moles/liter. 

For the reaction, 2N02 - 2NO + 02, the rate constant units, Mr1-min-1, tell us that the reaction is second order overall. Since the reaction has only one reactant, N02, the reaction is second order with respect to N02. 

S2082. Experiments 2 and 3 produce a similar conclusion. In Experiments 4 and 5, [(NH4)2S2Og]is the same (0.20 M) while [KI] is halved, from 0.10 to 0.050 M. As a consequence, the time to produce a color change nearly doubles, that is, the rate is halved. This indicates that reaction (a) is also first-order in I". Reaction (a) is (1 + 1) second-order overall. 

The reaction between ethylene bromide and potassium iodide in 99% methanol (inert) has been found to be first-order with respect to each reactant (second-order overall) (Dillon, 1932). The reaction can be represented by C2liiBr2 + 3K1 —> C2H4 + 2KBr + KI3 or A + 3B - products. 

Two stirred tanks are available, one 100 m3 in volume, the other 30 m3 in volume. It is suggested that these tanks be used as a two-stage CSTR for carrying out a liquid phase reaction A + B product. The two reactants will be present in the feed stream in equimolar proportions, the concentration of each being 1.5 kmol/m3. The volumetric flowrate of the feed stream will be 0.3 x 10-3 m3/s. The reaction is irreversible and is of first order with respect to each of the reactants A and B, i.e. second order overall, with a rate constant 1.8 x 10-4 m3/kmols. 

A batch reactor and a single continuous stirred-tank reactor are compared in relation to their performance in carrying out the simple liquid phase reaction A + B —> products. The reaction is first order with respect to each of the reactants, that is second order overall. If the initial concentrations of the reactants are equal, show that the volume of the continuous reactor must be 1/(1 — a) times the volume of the batch reactor for the same rate of production from each, where a is the fractional conversion. Assume that there is no change in density associated with the reaction and neglect the shutdown period between batches for the batch reactor. 

Although the polymerisations were externally of an order greater than one with respect to m, the Stannett group treated them as if they were of first order, i.e., of second order overall and they assumed that the polymerisations obeyed the normal bimolecular kinetics... 

Thus, for a first order reaction a plot of ln[A] versus time should be linear, with a gradient corresponding to - k. This first order relationship can break down when one or more of the reactants is limited, or there is a build-up of product. In these cases, a term to describe the limiting concentration should be introduced. The simplest, and often most common example is where the rate of the reaction is second order overall, but first order with respect to each of the reactants and in this case the rate of the reaction can be described by ... 

TABLE 1. Reaction of l-fluoro-2,4-dinitrobenzene (DNFB) with piperidine in aprotic solvents at 15°C48a second-order overall rate coefficients ... 

The reaction is second order overall. The second order rate... 

A reaction described as Sn2, abbreviation for substitution, nucleophilic (bimolecular), is a one-step process, and no intermediate is formed. This reaction involves the so-called backside attack of a nucleophile Y on an electrophilic center RX, such that the reaction center the carbon or other atom attacked by the nucleophile) undergoes inversion of stereochemical configuration. In the transition-state nucleophile and exiphile (leaving group) reside at the reaction center. Aside from stereochemical issues, other evidence can be used to identify Sn2 reactions. First, because both nucleophile and substrate are involved in the rate-determining step, the reaction is second order overall rate = k[RX][Y]. Moreover, one can use kinetic isotope effects to distinguish SnI and Sn2 cases (See Kinetic Isotope Effects). 

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