Second order reaction irreversible, 59-64 rate equation

An irreversible, elementary reaction must have Equation (1.20) as its rate expression. A complex reaction may have an empirical rate equation with the form of Equation (1.20) and with integral values for n and w, without being elementary. The classic example of this statement is a second-order reaction where one of the reactants is present in great excess. Consider the slow hydrolysis of an organic compound in water. A rate expression of the form... 

There are two other limiting forms of these equations that are also of interest. If k 1 k2, the first step is very rapid compared to the second, so that it is essentially complete before the latter starts. The reaction may then be treated as a simple irreversible second-order reaction with the second step being rate limiting. On the other hand, if k2 ku the first step controls the reaction so the kinetics observed are those for a single second-order process. However, the analysis must take into account the fact that in this case 2 moles of species A will react for each mole of B that is consumed. 

One way to ensure that back reactions are not important is to measure initial rates. The initial rate is the limit of the reaction rate as time reaches zero. With an initial rate method, one plots the concentration of a reactant or product over a short reaction time period during which the concentrations of the reactants change so little that the instantaneous rate is hardly affected. Thus,by measuring initial rates, one can assume that only the forward reaction in Eq. (35) predominates. This would simplify the rate law to that given in Eq. (36) which as written would be a second-order reaction, first-order in reactant A and first-order in reactant B. Equation (35), under these conditions, would represent a second-order irreversible elementary reaction. 

Derive an integrated rate equation similar to Equation 3.22 for the irreversible second-order reaction, when reactants A and B are introduced in the stoichiometric ratio ... 

For an irreversible bimolecular second-order reaction as the example reaction, the rate equation is... 

For an irreversible second-order reaction, the optimization of the reaction temperature and feed rate can be performed by using the following equation [14] ... 

The kinetics of the C step are not always first order or pseudo-first order. A second-order reaction will produce qualitatively similar effects to those described above. However, the relative magnitude of the reverse peak current associated with the E step and hence the extent of reversibility and the shift in peak potential will depend on the concentration of the electroactive species for an EC2 mechanism. A process of this type will have a reversible E step at low concentrations or fast scan rates and an irreversible E step at high concentrations or slow scan rates. An example of an EQ-type reaction (Bond et al., 1983, 1989) is the electrochemical oxidation of cobalt (III) tris(dithiocarbamates) (Co(S2CNR2)3) at platinum electrodes in dichloromethane/0.1 M (C4H9)4NPp6 [equations (44) and (45)]. 

The simplest case of parallel second-order steps is that of formation of two different dimers of a reactant A, corresponding to the network 5.23 and rate equations 5.24 (see next page). At all times, both products are formed in the same ratio rP rQ = kAP kAQ, so that the decay of A is an ordinary second-order reaction with rate coefficient k = kAP + kAQ. Likewise, the product formations are ordinary second-order reactions. (One could think of the initial amount of A as divided into two portions in the ratio kAV kAQ that react independently of one another and at the same rate, one to P and the other to Q.) All equations and plots for irreversible second-order reactions thus are valid (see Section 3.3.1). 

If we assume that every collision is effective in reaction, then cT (A, B) from equation (2-12) gives us the rate of the reaction A -I- B products directly. Previously, we had written for the irreversible, second-order reaction between A and B, for constant-volume conditions,... 

An irreversible second-order reaction A + B - C + D with rate equation (-r ) = kC Cg is carried out in a constant-volume batch reactor at constant temperature. The reactor contains 1 kmol/m of A and 2 kmol/m of B at the time of start-up. Variation of concentration of A with time is measured and reported in the table below. 

The rate equation for an irreversible second order reaction of the type A + B- X is... 

Boeker, E. A. (1985). Integrated rate equations for irreversible enzyme-catalyzed first-order and second-order reactions. Biochem. J. 226,29-35. 

A soluble gas is absorbed into a liquid with which it undergoes a second-order irreversible reaction. The process reaches a steady-state with the surface concentration of reacting material remaining constant at (.2ij and the depth of penetration of the reactant being small compared with the depth of liquid which can be regarded as infinite in extent. Derive the basic differential equation for the process and from this derive an expression for the concentration and mass transfer rate (moles per unit area and unit time) as a function of depth below the surface. Assume that mass transfer is by molecular diffusion. 

Rate laws of the type which describe bimolecular second order chemical reactions might be expected to be a model for ion exchange reactions, and indeed this was the case for exchangers of both natural and synthetic origin. For example, the rate of ion exchange could be described by a bimolecular second order rate equation for irreversible reaction of the form ... 

The VERSE method was extended to describe the consequences of protein de-naturation on breakthrough curves in frontal analysis and on elution band profiles in nonlinear isocratic and gradient elution chromatography [45]. Its authors assumed that a unimolecular and irreversible reaction taking place in the adsorbed phase accormts properly for the denaturation and that the rate of adsorption/desorption is relatively small compared with the rates of the mass transfer kinetics and of the reaction. Thus, the assumption of local equilibrium is no longer valid. Consequently, the solid phase concentration must then be related to the adsorption and the desorption rates, via a kinetic equation. A second-order kinetics very similar to the one in Eq. 15.42 is used. 

From this information determine the first-order and second-order specific rates, and kj, assuming that the reaction is irreversible over the conversion range covered by the data. Use both the integration and the differential method, and compare the results. Which rate equation best fits the experimental data ... 

A reaction 2A - B is being studied in a fluidized-bed reactor at atmospheric pressure and 200°F. It appears that the global rate of reaction may be approximated by a second-order irreversible equation... 

One does not need a road map to conclude that it is possible in most instances of simple-order reactions to evaluate both order(s) and rate parameter(s) by plotting a suitable linearized form of the particular rate law it is desired to test. For example, to test for first-order, irreversible kinetics, one would plot, according to equation (1-35), -ln(CA/CAo) versus time. If these kinetics are obeyed, the concentration data plot will be linear with a slope of k. Similarly, a second-order test according to equation (1-42) would require a plot of —ln[(CA/CAo)(CBo/CB)] versus time, yielding a straight line of slope (Cbo — Cao) - Analogous forms employing the conversion can also be used in all cases. 

If we neglect distinctions among ortho-, meta- and para-products (no information given), then x is the total conversion variable. These reactions were carried out in the liquid phase, so volume changes associated with reaction are negligible. The rate equation to try first is second-order irreversible... 

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