Second-order rate constants determination

Table 2. Second order rate constants determined for the reactions between chromate and some thiols, dithiols and ascorbate.

In the 1950 s the possibility of a chain reaction was investigated in detail by Benson and Srinivasan [10] and by Sullivan [11] who found the chain mechanism to contribute to reaction above 600 K and to be dominant above 750-800 K. New and accurate measurements of the rates of reaction at lower temperatures carried out by Sullivan [11,12] with more modem techniques confirmed the accuracy of the second-order rate constants determined by Bodenstein 60 years earlier. 

Kinetic measurements were performed employii UV-vis spectroscopy (Perkin Elmer "K2, X5 or 12 spectrophotometer) using quartz cuvettes of 1 cm pathlength at 25 0.1 C. Second-order rate constants of the reaction of methyl vinyl ketone (4.8) with cyclopentadiene (4.6) were determined from the pseudo-first-order rate constants obtained by followirg the absorption of 4.6 at 253-260 nm in the presence of an excess of 4.8. Typical concentrations were [4.8] = 18 mM and [4.6] = 0.1 mM. In order to ensure rapid dissolution of 4.6, this compound was added from a stock solution of 5.0 )j1 in 2.00 g of 1-propanol. In order to prevent evaporation of the extremely volatile 4.6, the cuvettes were filled almost completely and sealed carefully. The water used for the experiments with MeReOj was degassed by purging with argon for 0.5 hours prior to the measurements. All rate constants were reproducible to within 3%. 

Unfortunately, more detailed kinetic studies aimed at the determination of the second-order rate constants in the micellar pseudophase have not been published. 

Using Equation A3.4, the partition coefficient of 5.2 can be obtained from the slope of the plot of the apparent second-order rate constant versus the concentration of surfactant and the independently determined value of 1 . ... 

For most color photographic systems, development is the rate determining step, and within that step the formation of semiquinone is the slow process (37). The fate of the highly reactive QDI is deterrnined by the relative rates of a number of competing processes (38). The desired outcome is reaction with ionized coupler to produce dye (eq. 3). Typically, the second-order rate constant for this process with ionized coupler is about 10 to 10 ... 

The base-catalyzed tautomerization of 4-methyl-4//-cyclopenta[c]thio-phenes 193 to the corresponding 6-methyl derivative 194 has been investigated quantitatively. Second-order rate constants and activation parameters have been determined (75CS42). 

Hydroxyl radicals. The acid ionization constant of the short-lived HO transient is difficult to determine by conventional methods but an estimate can be made because HO, but not its conjugate base, O -, oxidizes ferrocyanide ions HO + Fe(CN) — OH- + Fe(CN)g . Use the following kinetic data26 for the apparent second-order rate constant as a function of pH to estimate Ka for the acid dissociation equilibrium HO + H20 =... 

Thus we can consider (kcJKM) as an apparent second-order rate constant. This constant is the most critical parameter in determining the specificity of... 

Kennedy and co-workers10 studied model cationic polymerization initiation and termination. They determined the effect of halogens in f-BuX and MeX on the rate of reaction between f-BuX and Me3Al. The pseudo second order rate constant decreased (Table 1) as ... 

Calculation of the second-order rate constant of carbonylation, kg, and the equilibrium constant, K = [t-C4H9CO+]/[t-C4H ][CO] = A c/fcD> requires knowledge of the concentration of CO. The constant a in Henry s law Pco = [CO] was determined to be 5-3 litre mole atm in HF—SbFs (equimolar) and 53 litre mole atm in FHSOs—SbFs (equimolar) at 20°C. From the ratio [t-C4HBCO+]/[t-C4HJ"] at a known CO pressure, values for k and K were obtained. The data are listed in Table 1, which includes the values for the rate and equilibrium constants of two other tertiary alkyl cations, namely the t-pentyl and the t-adamantyl ions (Hogeveen et al., 1970). 

The inactivation is normally a first-order process, provided that the inhibitor is in large excess over the enzyme and is not depleted by spontaneous or enzyme-catalyzed side-reactions. The observed rate-constant for loss of activity in the presence of inhibitor at concentration [I] follows Michaelis-Menten kinetics and is given by kj(obs) = ki(max) [I]/(Ki + [1]), where Kj is the dissociation constant of an initially formed, non-covalent, enzyme-inhibitor complex which is converted into the covalent reaction product with the rate constant kj(max). For rapidly reacting inhibitors, it may not be possible to work at inhibitor concentrations near Kj. In this case, only the second-order rate-constant kj(max)/Kj can be obtained from the experiment. Evidence for a reaction of the inhibitor at the active site can be obtained from protection experiments with substrate [S] or a reversible, competitive inhibitor [I(rev)]. In the presence of these compounds, the inactivation rate Kj(obs) should be diminished by an increase of Kj by the factor (1 + [S]/K, ) or (1 + [I(rev)]/I (rev)). From the dependence of kj(obs) on the inhibitor concentration [I] in the presence of a protecting agent, it may sometimes be possible to determine Kj for inhibitors that react too rapidly in the accessible range of concentration. ... 

To determine the rate constant one uses the same methods as mentioned under the first-order reaction, i.e. a plot of log[A] versus time. The product k[B]o assumes the role of a pseudo-first order rate constant, from which the true second-order rate constant is easily obtained. 

In order to determine the efficiency of the polymers as reagents in nucleophilic catalysis, it was decided to study the rate of quaternization with benzyl chloride. Table I shows the second-order-rate constants for the benzylation reaction in ethanol. Comparison with DMAP indicates that poly(butadiene-co-pyrrolidinopyridine) is the most reactive of all the polymers examined and is even more reactive than the monomeric model. This enhanced reactivity is probably due to the enhanced hydrophobicity of the polymer chain in the vicinity of the reactive sites. 

The kinetics formation of [Ni([9]aneN3)2]3+ have been studied in great detail. Inter alia, the volume of activation for peroxodisulfate oxidation of [Ni([9]aneN3)2]2+ has been determined (—25.8 2.3 cm3 mol 1),105 and the kinetics of this reaction have been determined as a function of peroxodisulfate concentration and temperature.106 The reaction is first-order in both reagents (second-order rate constant 1.13 mol dm 3 s 1 at 298 K), and the activation energy is 38 1.8 kJ mol-1. In mixed solvents, the rate is slower. 

For comparison, included in Table 14.3 are the kq values obtained in detergent micelles along with kq values obtained in homogeneous solvent benzene. As can be seen, the second-order rate constant for 02 quenching in a liposomal environment is a factor of 4 lower for (3-CAR compared to the second-order rate constant obtained in the aromatic solvent. While, there is a marked 80-130 fold difference between the kq values determined in liposomal environments compared to the kq values determined in the aromatic solvent for the XANs. 

The first step [Eq. (5)] was postulated to be rate determining because of the Tafel slope of 107 mV/ decade and the first-order dependence of the reduction current on the C02 concentration. The second-order rate constant of Eq. (6) was estimated to be 7.5 x 103 M-1 s-1. 

Frost and Schwemer have developed a time-ratio technique based on equations 5.4.21 and 5.4.16 in order to facilitate the calculation of second-order rate constants for the class of reactions under consideration. Data for A/A0 versus t at various values of k are presented in Table 5.2, and time ratios are given in Table 5.3. The latter values may be used to determine k by using various time ratios from a single kinetic run if one recognizes that (tf/rf) = t1/t2). Once k has been determined, Table 5.2 may be used to determine the t values at a given A/A0 and k. Equation 5.4.18 may then be used to determine... 

These investigators report that the second-order rate constant for reaction B is equal to 1.15 x 10 3 m3/mole-ksec at 20 °C. Determine the volume of plug flow reactor that would be necessary to achieve 40% conversion of the input butadiene assuming isothermal operating conditions and a liquid feed rate of 0.500 m3/ksec. The feed composition is as follows. 

At 500 °C the second-order rate constant is 1.7 m3/kmole ksec. Determine ... 

The rate constant for the exponential relaxation of the latter system to the starting system was calculated to be 1.4 x 10 s . From this value, an approximate second order rate constant of 1.0 x 10 L mol" -s"l was calculated for the reaction between IV and CO. Given the above determination of the limiting rate constant for CO dissociation... 

Values of pA"R for the addition of water to carbocations to give the corresponding alcohols. The equilibrium constants KR (m) were determined as the ratio Hoh/ h> where fcHOH (s 1) is the first-order rate constant for reaction of the carbocation with water and H (m 1 s ) is the second-order rate constant for specific acid-catalyzed cleavage of the alcohol to give the carbocation.9,12 13... 

To determine the activities for the various Lal+( OR) we analyze the k2bs data as a linear combination of individual rate constants (Equation 8), where ki4, kf2... " are the second-order rate constants for each La2+( OR) promoting ethanolysis and methanolysis of 1 and 2 respectively. 

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