Reaction rate comparison 56, pseudo first-order

It is an oversimplification to fit the hydrolysis reactions with a pseudo-first-order rate analysis, but this does allow comparison among different systems. Even with these complications, some general observations can be made. Shown in Table 2 are the results from different systems at ambient temperature under... 

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

A reagent in solution can enhance a mass transfer coefficient in comparison with that of purely physical absorption. The data of Tables 8.1 and 8.2 have been cited. One of the simpler cases that can be analyzed mathematically is that of a pseudo-first order reaction that goes to completion in a liquid film, problem P8.02.01. It appears that the enhancement depends on the specific rate of reaction, the diffusivity, the concentration of the reagent and physical mass transfer coefficient (MTC). These quantities occur in a group called the Hatta number,... 

Metathesis activity. A quantitative comparison of metathesis activities was made in the gas phase homometathesis of propylene. The reaction kinetics are readily monitored since all olefins (propylene, ethylene, cis- and fra/3s-2-butylenes) are present in a single phase. Metathesis of 30 Torr propylene was monitored in a batch reactor thermostatted at 0 °C, in the presence of 10 mg catalyst. The disappearance of propylene over perrhenate/silica-alumina (0.83 wt% Re) activated with SnMe4 is shown in Figure 2a. The propylene-time profile is pseudo-first-order, with kob (1.11 + 0.04) X 10" slightly lower rate constant, (0.67 constants are linearly dependent on Re loading. Figure 3. The slope yields the second-order rate constant k = (13.2 + 0.2) s (g Re) at 0°C. 

The role of the isothermal and pseudo-first-order reaction assumptions on the observed value of activation energy was assessed to allow comparison of our data to previous work by modifying Malkin s autocatalytic equation so that the autocatalytic term b is equal to zero. The values of the activation energy and front factor were calculated using short-time, low-conversion data. By making the autocatalytic term equal to zero, the modified Malkin autocatalytic model becomes a first-order rate reaction. Table 1.2 shows that by assuming a... 

A variety of concave pyridines 3 (Table 1) and open-chain analogues have been tested in the addition of ethanol to diphenylketene (59a). Pseudo-first-order rate constants in dichloromethane have been determined photometrically at 25 °C by recording the disappearance of the ketene absorption [47]. In comparison to the uncatalyzed addition of ethanol to the ketene 59a, accelerations of 3 to 25(X) were found under the reaction conditions chosen. Two factors determine the effectiveness of a catalyst basicity and sterical shielding. Using a Bronsted plot, these two influences could be separated from one another. Figure 4 shows a Bronsted plot for some selected concave pyridines 3 and pyridine itself (50). 

Where dianions are the effective bases the reproportionation reaction, (reaction 5 in Eq. (4)), is in competition with the protonation step (reaction 3). In this instance the pseudo-first order rates of protonation of dianions cannot be precisely determined using the comparison of experimental current-time relationships with those derived by theory for an EEC reaction (i.e. reactions 1-3 in Eq, (4))... 

The kinetic parameters chosen for comparison are rate constants and t1/2. Radiation influences and the effect of reactor design are usually identical when these kinetic data are compared between the various AOPs tested. The values for pseudo first-order kinetics and half-lives for various processes are given in Table 14.3. In most cases, the values of f3/4 are equal to two times those of t1/2 therefore, the reactions obey a first-order kinetics. Figure 14.5. shows that Fenton s reagent has the largest rate constant, e.g., approximately 40 times higher than UV alone, followed by UV/F C and Os in terms of the pseudo first-order kinetic constants. Clearly, UV alone has the lowest kinetic rate constant of 0.528 hr1. 

If one considers that the ratio of lc2, the first order rate constant of eq. (4.1), to kn, the second order rate constant of eq. (4.2), is 5 M, the expression in eq. (4.8) permits the comparison of the observed pseudo first-order rate constant for modification according to eq. (4.1) (/c bs) and eq. (4.2) The reaction which proceeds according to eq. (4.2) can be considered the rate of modification of the free amino acid. 

Figure 19-2 Intermediates observed in the single turnover cycle of diferrous MMOH in the presence of MMOB after rapid mixing with O2 and substrate containing solution. The rates shown are for the reaction in pH 7.7 buffer at 4 °C. The intermediate R is proposed from chemical rather than kinetic studies. The rate of the reaction of Q with substrates depends on the specific substrate used and appears to be second order overall, but for comparison, a typical pseudo first-order rate constant is given for the reaction of Q with nitrobenzene at a concentration of 2.S mM.

The mechanism suggested on the basis of H NMR and ESR studies of the reaction mixtures and kinetic measurements involves the formation of intermediate radical species 6 (Scheme 7). The reaction is very fast in comparison with dequaternization of A -alkylpyridinium cations. Indeed, the observed pseudo-first-order rate constants iobs. for dequaternization of a number of l-alkyl-l,2,4-triazinium salts proved to be approximately 10 s at 25 °C, while A -alkylpyridinium salts are dequaternized much more slowly (iobs. = 10 s at 100 °C) <1995MC104>. 

Instead the analysis brings up a second order rate constant characterising the attack of B on A c H (if A was the reaction partner u in excess to define pseudo first order conditions and to saturate the host H, sre Scheme 2), which may be identical to but alternatively may also represent kcai/ B- The comparison of and kun reveals the change in reactivity experienced by guest A towards B on binding to the host molecule. 

For intermediate reaction rates the use of the enhancement factor is not consistent with the standard approach of diffusional limitations in reactor design and may be somewhat confusing. Furthermore, there are cases where there simply is no purely physical mass transfer process to refer to. For example, the chlorination of decane, which is dealt with in the coming Sec. 6.3.f on complex reactions or the oxidation of o-xylene in the liquid phase. Since those processes do not involve a diluent there is no corresponding mass transfer process to be referred to. This contrasts with gas-absorption processes like COj-absorption in aqueous alkaline solutions for which a comparison with C02-absorption in water is possible. The utilization factor approach for pseudo-first-order reactions leads to = tfikC i and, for these cases, refers to known concentrations C., and C . For very fast reactions, however, the utilization factor approach is less convenient, since the reaction rate coefficient frequently is not accurately known. The enhancement factor is based on the readily determined and in this case there is no problem with the driving force, since Cm = 0- Note also that both factors and Fji are closely related. Indeed, from Eqs. 6.3.C-5 and 6.3.C-10 for instantaneous reactions ... 

The authors noticed no C-H/C-D isotope effect for the reaction of 13 with methanol and ferf-butanol, but saw a KIE k Jk = 1.4) for the O-H/O-D bond, suggesting that the stronger O-H bond is activated preferentially over the weaker C-H bonds (Pig. 12). In addition, the authors observed the formation of acetone upon the oxidation of tert-butanol. Upon comparison of rate constants (which have been normalized to account for the amount of hydrogens available for abstraction), tert-butanol reacts 50 times faster than cyclohexane. The authors propose a proton-coupled electron transfer event is responsible for the observed selectivity this complex represents a rare case in which O-H bonds may be homolyzed preferentially to C—H bonds. In further study, 13 was shown to oxidize water to the hydroxyl radical by PCET [95]. Under pseudo-first-order conditions, conversion of 13 to its one-electron reduced state was found to have a second-order dependence on the concentration of water, in stark contrast to the first-order dependence observed for aUphatic hydrocarbons and alcohols. Based on the theimoneutral oxidation of water (2.13 V v. NHE in MeCN under neutral conditions [96]) by 13 (2.14 V V. NHE in MeCN under neutral conditions) and the rate dependence, the authors propose a proton-coupled electron transfer event in which water serves as a base. While the mechanism for O-H bond cleavage of alcohols and water is not well understood in these instances, the capacity to cleave a stronger O-H bond in the presence of much weaker C-H bonds is a tremendous advance in metal-oxo chemistry and represents an exciting avenue for chemoselective substrate activation. 

Several methods have been utilized to determine the rate of the following chemical reaction from a series of CVs at different scan rates. The simplest involves a comparison of ip,e and i . The cathodic peak current is measured from the zero current baseline, while the anodic current baseline is established by the current at which the potential is switched. The experimental peak current ratios can then be compared to a previously calculated theoretical working curve to find the rate constant (for a first-order or pseudo-first-order reaction. Parker has emphasized the use of working curves based on derivative cyclic voltammetry, which discriminates to some degree against capacitive background current. ... 

---