Pseudo rate constant

This section deals with the experimental determination of the rate of oil solubilization in aqueous solutions of AOS and IOS [70]. The experimental method [71] consists of injecting 25 pi of n-hexadecane (containing 5 wt % Dobanol 45-3 as an emulsifier) into 50 ml water this produces a turbid macroemulsion upon vigorous stirring. At the start of the experiment, a concentrated solution of the surfactant under test is injected and the decrease in turbidity is followed with a photometer. The time elapsed to reach 90% of the initial turbidity is recorded (t ) and the pseudo rate constant of oil solubilization is calculated from... 

The effect of chain length on the pseudo rate constant is shown in Fig. 18. Clearly, the optimum chain length for AOS is 16 carbon atoms. However, at this optimum the rate of oil solubilization for AOS is still below that observed for the reference compound DOBS 103, a sodium alkylbenzenesulfonate with 10-13 carbon atoms in the alkyl chain. Increasing the chain length of IOS subjected to an aging step before hydrolysis with NaOH (IOSa in Fig. 18) leads to a continuously increasing rate of oil solubilization. The highest rate was... 

FIG. 18 The effect of chain length on the pseudo rate constants (Km (100 90)) of n-hexadecane solubilization by olefinsulfonates/dobanol 45-3 solutions at 40°C. AOS, a-olefinsulfonate IOS a, aged I-olefinsulfonate IOS d, directly hydrolyzed I-olefin-sulfonate. 

TABLE 25 Pseudo rate constants (Km (100/90) of n-Hexadecane Solubilization by Olefinsulfonate/DOBANOL 25-9 Solutions at 40 °C... 

If one takes the ratio of the pseudo rate constant for adsorption to that for desorption as an equilibrium constant for adsorption (K), equation 6.2.4 can be written as... 

The Langmuir Equation for the Case Where Two or More Species May Adsorb. Adsorption isotherms for cases where more than one species may adsorb are of considerable significance when one is dealing with heterogeneous catalytic reactions. Reactants, products, and inert species may all adsorb on the catalyst surface. Consequently, it is useful to develop generalized Langmuir adsorption isotherms for multicomponent adsorption. If 0t represents the fraction of the sites occupied by species i, the fraction of the sites that is vacant is just 1 — 0 where the summation is taken over all species that can be adsorbed. The pseudo rate constants for adsorption and desorption may be expected to differ for each species, so they will be denoted by kt and k h respectively. 

The published quantification of the rate of hydrogenation of the dienes COD and NBD of a large number of cationic rhodium(I) chelate complexes allows a good estimation of expected effects on the rate of enantioselective hydrogenation of prochiral alkenes. From the first-order pseudo-rate constants the time needed for complete hydrogenation of the diene introduced as part of the rhodium precursor can be easily calculated as six- to seven-fold the half life. It is recommended that the transfer into the solvent complex be followed by NMR spectroscopy. 

Writing a pseudo rate constant k without an order implies that it is pseudo first order. 

Strategy. (1) We ascertain the order of reaction, (2) we determine the pseudo rate constant k , (3) from k , we determine the value of the second-order rate constant k2. 

Table 23.1 HMF formation kinetics in isothermal heating as a function of treatment temperature, first order reaction pseudo rate constant and regression coefficients...

Notice that k here relates to a first-order reaction. In this case. A is a pseudo-rate constant, implying that the allyl alcohol was in excess. The true rate constant is... 

It should be emphasized that in the case that A is in deficiency over other reactants, B etc., then k, relating to loss of A, is a pseudo rate constant and the effect of the other reactants on the rate must still be assessed separately (Sec. 1.4.4). 

Having obtained the exponent a in (1.15) by monitoring the concentration of A in deficiency we may now separately vary the concentration of the other reactants, say B and C, still keeping them however in excess of the concentration of A. The variation of the pseudo rate-constant k with [B] and [C] will give the order of reaction b and c with respect to these species, leading to the expression... 

The values of the reaction rate, for polyhalogenated alkanes in Fe(II)/goe-thite suspensions are noted in Table 16.3 together with their pseudo-rate constants and half-lives. The reaction rates are affected by contact time, sorption density, and solution pH. Pecher et al. (2002) note that a contact time of 20 hours is necessary... 

By noting that the temperature rise in this system takes the feedback role that was played by the autocatalytic species B in the previous chapter, we may recognize the resemblance between the rate constant k2 of the previous chapter (rate constant for decay of B) with l/rN here (a pseudo-rate constant for decay of the temperature rise). For a system in which heat transfer is slow, fN will be large if heat transfer across the surface is rapid, tN will be small. The dimensionless time, therefore, becomes... 

If [B] is in excess and effectively constant throughout reaction, then [B]/J is also effectively constant throughout reaction, and can be taken with k to give rate = k [A] where k is called the pseudo-rate constant - meaning as if. ... 

Find the order with respect to A, and the pseudo-rate constant k. In a further series of experiments, with B still in large excess, the pseudo-rate constant k varied with the concentration of B as... 

Equation 1.5 is the familiar form of first-order rate equation and indicates that the rate of absorption is proportional to drag concentration. K, is a pseudo-rate constant and is dependent on the factors D, A, k and h. 

Then k, which is the pseudo-rate constant of the homogeneous reaction, is calculated from the relationship... 

The rate model represented by equation 6.9 is particularly interesting since it will be shown shortly that a similar function arises from a consideration of formal diffusion theory. Therefore, providing it is established by experiment that the pseudo rate constant is truly constant over the range of experimental boundary conditions employed a, b, Xg) it remains perfectly valid to equate its value to appropriate mass transfer parameters required by diffusion theory. 

Thus, in a general situation, an electron transfer between a donor D and an acceptor A must be considered in terms of, at least, the three successive elementary steps outlined in Scheme 3. This representation may be even more segmented when, for example, different ion pairs are involved, such as [A , solvent, D" or [A , (solvent)n, D". Yet it is sufficient her to consider the simplest situation represented in Scheme 3 [45]. The formation or dissociation of cages in Scheme 3, each a physical process, is normally handled on physicochemical grounds. Yet following a notation by Debye their effects may be represented under the form of pseudo-rate constants k if (reactant pair) and k j. (product pair). Using this notation, it follows [46] that the overall kf and backward rate constant kb are given by Eqs. (48) and (49) as a function of the activation rate constants kp and kb relative to the pairs. 

Both pseudo-rate constants may then be evaluated from a suitable description of the work terms Wr(x) and Wp(x) necessary to bring the reactant centers or those of the products, respectively, from infinity to a distance x. When the work terms are negligible, straightforward integration of Eqs. (50) and (51) yields... 

One obtains the pseudo-rate constant k = ko[A]"[B]. .. Thus dimensionless analysis affords the differential equation in Eq. (211), which describes the concentration profile of the P species when A, is given as in Eq. (212). 

In Eq. (2), a< is the amount of the species A<, 0<, is the pseudo-rate-constant for the reaction from the jth to the fth species and is independent of the amounts of the various species, and is some unspecified function of the amounts of the various species and time. This concept may be further generalized to give pseudo-mass-action systems. These are defined as systems in which all rates of change of the various species are given by mass action terms of various integral order each multiplied by the same function of composition and time. 

It is desirable to make one of the pseudomonomolecular rate constants unity by dividing each element of the n X n matrix of Eq. (332) by one of the determinants fcai G , I m and multiplying the general function by fco/ G ). Let the zjth pseudo-rate-constant for this normalized system be designated d a and the rate constant matrix by . Then... 

Equations (333) and (335) or Eqs. (337) and (338) may be used to determine the explicit relations between the pseudo-rate-constants and the true rate constants since the matrices G and U are in terms of the true rate constants for the system. Let us apply Eqs. (333) and (335) to determine this relation for the reaction in scheme (314). From Eqs. (331), (321), and (322), we have for species Ai... 

Now let us turn to the scheme (351). It also leads to a pseudomono-molecular system. We shall not, however, treat the general case but give the equation for a special case from which the reader may infer the general form of the relation between the pseudo-rate-constants and the rate constants for the detailed kinetic scheme. The scheme to be considered is... 

---