Reaction rate second-order

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

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. 

When the overflow clarity is independent of overflow rate and depends only on detention time, as in the case for high soHds removal from a flocculating suspension, the required time is deterrnined by simple laboratory testing of residual soHd concentrations in the supernatant versus detention time under the conditions of mild shear. This deterrnination is sometimes called the second-order test procedure because the flocculation process foUows a second-order reaction rate. 

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 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. 

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" ). 

Consecutive reactions involving one first-order reaction and one second-order reaction, or two second-order reactions, are very difficult problems. Chien has obtained closed-form integral solutions for many of the possible kinetic schemes, but the results are too complex for straightforward application of the equations. Chien recommends that the kineticist follow the concentration of the initial reactant A, and from this information rate constant k, can be estimated. Then families of curves plotted for the various kinetic schemes, making use of an abscissa scale that is a function of c kit, are compared with concentration-time data for an intermediate or product, seeking a match that will identify the kinetic scheme and possibly lead to additional rate constant estimates. 

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 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... 

Zero-order reaction First-order reaction Second-order reaction Rate constant... 

Second law of thermodynamics A basic law of nature, one form of which states that all spontaneous processes occur with an increase in entropy, 457 Second order reaction A reaction whose rate depends on the second power of reactant concentration, 289,317q gas-phase, 300t... 

In 75 % aqueous acetic acid, the bromination of fluorene at 25 °C obeys second-order kinetics in the presence of bromide ion and higher orders in its absence287, with Ea (17.85-44.85 °C) = 17.4, log A = 10.5 and AS = —12.4 however, these values were not corrected for the bromine-tribromide ion equilibrium, the constant for which is not known in this medium, and so they are not directly comparable with the proceeding values. In the absence of bromide ion the order with respect to bromine was 2.7-2.0, being lowest when [Br2]initial was least. Second- and third-order rate coefficients were determined for reaction in 90 and 75 wt. % aqueous acetic acid as 0.0026 and 1.61 (k3/k2 = 619), 0.115 and 12.2 (k3/k2 = 106) respectively, confirming the earlier observation that the second-order reaction becomes more important as the water content is increased. A value of 7.25 x 106 was determined for f3 6 (i.e. the 2 position of fluorene). 

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 rate of a second-order reaction may be proportional to two concentrations, v = [A][B] with [B]0 s> [A]o it follows first-order kinetics. Some authors refer to these as the order with respect to concentration and the order with respect to time. 

To illustrate this, we start first with a simple second-order reaction. Here, of course, no numerical solution is needed, because there is a simple solution. Nonetheless, we shall use this system because it illustrates well the numerical procedure. The rate law is... 

Equations will be presented for three cases—the second-order reactions of two polar molecules, two ions, and one of each. The result in each case suggests a linear relation between the logarithm of the rate constant and the inverse of the dielectric constant of the solvent. 

If one of the partners in a second-order reaction is not an ion, then in ideal solutions there will be little effect of added salts on the rate. The activity coefficient of a nonelectrolyte does not depend strongly on ionic strength the way that the activity coefficients of ions do. In a reaction with only one participating ion, it and the transition... 

Stopped-flow kinetics. If one uses an apparatus with a dead time of 2.3 ms, what fraction of a second-order reaction is missed if the initial concentrations are 2.0 X 10 3 M and 6.8 x 10 3 M, given a rate constant of 3.7 x 103Lmol 1 s-1 ... 

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