Reaction rate second-order reaction

ENCOUNTER-CONTROLLED RATE SECOND-ORDER REACTiON CHEMICAL KINETICS ORDER OF REACTION NOYES EQUATION MOLECULARITY AUTOCATALYSIS FIRST-ORDER REACTION... 

Reaction-limited second-order reaction For a second-order reaction of the form 2A —> products, or in the more general case of a reaction of the form a A + bB -> products of second order with respect to A, the intrinsic reaction rate is... 

As ice crystals grow in the freezing system, the solutes are concentrated. In addition to increased ionic strength effects, the rates of some chemical reactions—particularly second order reactions—may be accelerated by freezing through this freeze-concentration effect. Examples include reduction of potassium ferricyanide by potassium cyanide (2), oxidation of ascorbic acid (3), and polypeptide synthesis (4). Kinetics of reactions in frozen systems has been reviewed by Pincock and Kiovsky (5). 

The reactivity of the model phenols and benzyl alcohols with phenyl isocyanate was determined in the presence of a tertiary amine (DMCHA) and a tin catalyst (DBTDL) by measurement of the reaction kinetics. The experimental results based on initial equal concentrations of phenyl isocyanate and protic reactants showed that the catalyzed reactions followed second order reaction with respect to the disappearance of isocyanate groups (see Figure 1). It was also found that a linear relationship exists between the experimental rate constant kexp, and the initial concentration of the amine catalyst (see Figure 2). In the case of the tin catalyst, the reaction with respect to catalyst concentration was found to be one-half order (see Figures 3-4). A similar relationship for the tin catalyzed urethane reaction was found by Borkent... 

The rates of reaction of phenacyl bromide with thiosemicarbazide and its phenylated derivative were determined by conductivity measurements in ethanol (517). The reaction is second order up to 85% completion. The activation energies are 10.5 to 11.3 kcal/mole with the phenyl thiosemicarbazide and 8.5 to 9.3 kcal/mole for the unsubstituted derivatives. 

Overall the reaction exhibits second order kinetics Both the ester and the base are involved m the rate determining step or m a rapid step that precedes it... 

Thus, for a second-order reaction, a plot of [A] versus f is linear, with a slope of k and an intercept of [A]o h Alternatively, a reaction can be shown to be second-order in A by observing the effect on the rate of changing the concentration of A. In this case, doubling the concentration of A produces a fourfold increase in the reaction s rate. 

The transfer reactions follow second-order kinetics, the general rate law being... 

Although the reaction is second order in acryUc acid concentration, the rate of dimer formation for neat acryUc acid available commercially is quite adequately expressed by... 

Rate studies show that base-cataly2ed reactions are second order and depend on the phenolate and methylene glycol concentrations. The most likely path involves a nucleophilic displacement by the phenoxide on the methylene glycol (1), with the hydroxyl as the leaving group. In alkaline media, the methylolated quinone intermediate is readily converted to the phenoxide by hydrogen-ion abstraction (21). 

When even second-order reactions are included in a group to be analyzed, individual integration methods maybe needed. Three cases of coupled first- and second-order reactions will be touched on. All of them are amenable only with difficulty to the evaluation of specific rates from kinetic data. Numerical integrations are often necessary. 

This is the equation for a plug flow reactor. It can be derived directly from the rate equations with the aid of Laplace transforms. The sequences of second-order reactions of Figs. 7-5n and 7-5c required numerical integrations. 

Tubular flow reaclors operate at nearly constant pressure. How the differential material balance is integrated for a number of second-order reactions will be explained. When n is the molal flow rate of reactant A the flow reactor equation is... 

A second order reaction is conducted in two equal CSTR stages. The residence time per stage is T = 1 and the specific rate is /cCq = 0.5. Feed concentration is Cq. Two cases are to be examined (1) with pure solvent initially in the tanks and (2) with concentrations Cq initially in both tanks, that is, with Cio = Coq = Cq. 

The reaction kinetics approximation is mechanistically correct for systems where the reaction step at pore surfaces or other fluid-solid interfaces is controlling. This may occur in the case of chemisorption on porous catalysts and in affinity adsorbents that involve veiy slow binding steps. In these cases, the mass-transfer parameter k is replaced by a second-order reaction rate constant k. The driving force is written for a constant separation fac tor isotherm (column 4 in Table 16-12). When diffusion steps control the process, it is still possible to describe the system hy its apparent second-order kinetic behavior, since it usually provides a good approximation to a more complex exact form for single transition systems (see Fixed Bed Transitions ). 

In batch classification, the removal of fines (particles less than any arbitrary size) can be correlated by treating as a second-order reaction K = (F/Q)[l/x(x — F)], where K = rate constant, F = fines removed in time 0, and x = original concentration of fines. 

The rate of destruction of active sites and pore structure can be expressed as a mass-transfer relation for instance, as a second-order reaction... 

The classical example of a second-order reaction is the formation of HI(g) which was discussed above for which the reaction rate is given by... 

In mutual termination the rate of reaction is determined by the concentration of growing radicals and since two radicals are involved in each termination the reaction is second order. 

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. 

In summary, it is clear that methylolation is a bimolecular, second-order reaction. As methylol groups are added to the ring, the ring undergoes general activation. Addition of o-methylol groups increases the acidity of the phenolic hydroxyl, which could increase reaction rates. However, all methylol groups ap-... 

Determine the second order reaction rate constant. 

Assuming that the reaction is second order in a constant volume batch system, the rate equation is... 

Adesina has shown that it is superfluous to carry out the inversion required by Equation 5-255 at every iteration of the tri-diagonal matrix J. The vector y"is readily computed from simple operations between the tri-diagonal elements of the Jacobian matrix and the vector. The methodology can be employed for any reaction kinetics. The only requirement is that the rate expression be twice differentiable with respect to the conversion. The following reviews a second order reaction and determines the intermediate conversions for a series of CFSTRs. 

A second order reaction is performed adiabatically in a CESTR. Use die data in Example 6-11 to plot bodi conversions for die mass and heat balance equations. The second order rate constant k is... 

Therefore, for this type of second-order reaction, a plot of 1/ca vs. t is linear, with the slope equal to k. The usual units of a second-order rate constant are liters per mole-second (M s" ). 

Choice of initial conditions. To give a very obvious example, in Chapter 2 we saw that a second-order reaction A -I- B —> products could be run with the initial conditions Ca = cb, thus permitting a very simple plotting form to be used. For complex reactions, it may be possible to obtain a usable integrated rate equation if the initial concentrations are in their stoichiometric ratio. 

In 1950 French " and Wideqvist independently described a data treatment that makes use of the area under the concentration-time curve, and later authors have discussed the method.We introduce the technique by considering the second-order reaction of A and B, for which the differential rate equation is... 

Kinetic schemes that include both first-order and second-order reactions possess an ambiguity related to the different dimensions of the rate constants. We wilt use Scheme XXI to examine this. 

In these circumstances a decision must be made which of two (or more) kinet-ically equivalent rate terms should be included in the rate equation and the kinetic scheme (It will seldom be justified to include both terms, certainly not on kinetic grounds.) A useful procedure is to evaluate the rate constant using both of the kinetically equivalent forms. Now if one of these constants (for a second-order reaction) is greater than about 10 ° M s-, the corresponding rate term can be rejected. This criterion is based on the theoretical estimate of a diffusion-controlled reaction rate (this is described in Chapter 4). It is not physically reasonable that a chemical rate constant can be larger than the diffusion rate limit. 

Another means is available for studying the exchange kinetics of second-order reactions—we can adjust a reactant concentration. This may permit the study of reactions having very large second-order rate constants. Suppose the rate equation is V = A caCb = kobs A = t Ca, soAtcb = t For the experimental measurement let us say that we wish t to be about 10 s. We can achieve this by adjusting Cb so that the product kc 10 s for example, if A = 10 M s , we require Cb = 10 M. This method is possible, because there is no net reaction in the NMR study of chemical exchange. 

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 kinetic rate constant may be computed from the adiabatic temperature rise [38] or the isothermal heat release [37]. For a second order reaction ... 

Second-order reaction (Section 11.2) A reaction whose rate-limiting step is bimolecular and whose kinetics are therefore dependent on the concentration of two reactants. 

If you are taking a course in calculus, you may be surprised to learn how useful it can be in the real world (e.g chemistry). The general rate expressions for zero-, first-, and second-order reactions are... 

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