Rate constant second-order reactions

Observed and Calculated Rate Constants for Second-Order Gas-Phase Reactions... 

The half-life is thus seen to depend on the initial concentration for the second order reaction considered. This is in contrast to first-order reaction where the half-life is independent of concentration. For this reason half-life is not a convenient way of expressing the rate constant of second-order reactions. 

Catalyst] = [substrate] = 1.00 X 10 3 M. b Second-order rate constants (reactions first-order in substrate and first-order in catalyst). c First-order, sec.-1 (substrate only) d SA2 = salicylate anion. Tiron"4 = 3,5-disulfopyrocatechol anion. f HQS 2 = 5-sulfo-8-quinolinol anion. 0 SSA 3 = 5-sulfo-8-hydroxyquinoline anion. 

Bimolecular reactions of two molecules, A and B, to give two products, P and Q, are catalyzed by many enzymes. For some enzymes the substrates A and B bind into the active site in an ordered sequence while for others, bindingmay be iii a random order. The scheme shown here is described as random Bi Bi in a classification introduced by Cleland. Eighteen rate constants, some second order and some first order, describe the reversible system. Determination of these kinetic parameters is often accomplished using a series of double reciprocal plots (Lineweaver-Burk plots), such as those at the right. 

The rate constants are so defined that a constant has fys+ixa-n as the rate constant for the reverse reaction. This means that the rate constants for the fore and back reactions must lie at an equal distance taken symmetrically from either side of the all-zero off-diagonal of the matrix. From inspection of the matrix, it can be seen that there are v(v— 1) different rate constants for second-order interchanges leading to chemically different molecules. 

Because the rate constants are second order, the solvent dependence of the calculated activation parameters for these reactions, 5m AX, can be represented in terms of three functions [eqn (39) cf. p. 213]. Based on our previous discussion it is possible to understand... 

The rate constants of second-order reactions in which the two reactants, although different, have the same initial concentration, are also determined with the help of Eq. 2.26. 

Lampe, Franklin and Field (59) discussed this problem of rates of ion molecule reactions at some length and surveyed the known data at that time. A few typical rate constants for second order ion-molecule reactions are given in Table XI. It will be observed that many of them are in the order of 10 9 cc./molecule/sec. However, values as small as 10"13 cc./molecule/sec. have been reported for some reactions. The values in the neighborhood of 10 9 cc./molecule/sec. represent reactions that must occur at essentially every collision in that they have cross sections considerably larger than ordinary collision cross sections. The values... 

Figure 5.1. The Sherwood number against the rate constant of second-order surface chemical reaction 1, by formula (5.1.5) 2, for a solid sphere 3, for a circular cylinder and 4, for a spherical drop or bubble...

Dimensionless effluent concentration versus dimensionless rate constant for second-order reaction. 463... 

Recognizing that Cao b is in every term, we can divide through by the product of this concentration parameter and the rate constant for the reverse reaction. This product has units of inverse time as the rate constant is second order. Therefore on the left-hand side we have which is just the same as where dr = CAokadt. This puts the equations in complete dimensionless form ... 

Action of Alkali. The kinetics of the alkaline saponification of the methyl ester of polygalacturonic acid cannot be described by a rate constant for second order reactions (Table I). The saponification of the methyl ester of galacturonic acid, however, obeys this law. The unusual behavior of pectin seems to be caused by the increasing negative charge of the chain molecules during saponification (4). There-... 

Aj Michaelis constant see equation (3-74) k reaction rate constant, a for first order kj deactivation rate constant see equation (4-152) ki initiation rate constant, normally second order k() pre-exponential factor, a for first order kp propagation rate constant... 

The differential rate law described by this equatioa is mathematically equivalent to the differential rate law described by equatioa 16. Thus the reaction will appear to follow first-order kinetics but is in reali a second-order reaction. Such a reaction is referred to as a pseudo ferst-order reaction and the rate constant BCobs determmed fiom this reaction is a pseudo first-order rate constant The second-order rate constant may be evaluated by plotting BCobs versus Cb for different concentrations of B obtained fiom a batch reactor system. The slope of the linear trace obtained fiom such a plot will have a value numerically equal to K. 

Table 1. Rate Constants for Second Order Reactions (continued)...

---