Rate coefficient equivalence order

The variation in the second-order rate coefficients with time and with change in initial concentration of mercuric salt can also be explained on the basis of equilibria (213) and (214). At low acidities, conversion of mercuric acetate to acetoxymercury perchlorate is incomplete, and, therefore, decreasing the concentration of the acetate increases the concentration of free perchloric acid which thus increases the conversion of the acetate into the more reactive perchlorate, hence the second-order rate coefficients increase. Decreasing the concentration of mercuric perchlorate will, however, decrease the concentration of free perchloric acid and this effect will be particularly marked since solvation of the perchlorate produces two equivalents of perchloric acid the second-order rate coefficients will, therefore, decrease. In both cases, substitution changes the concentration... 

Paudler and Helmick515 have measured half-lives for deuteration of some heterocycles by deuterated sulphuric acid at 100 °C. The equivalent first-order rate coefficients (lO ) are as follows imidazo[l, 2-a]pyridine, 427(3-H) imidazo[l,2-a]pyridine-N-methiodide, 62(3-H) imidazo[l,2-a]pyrimidine, 123-(3-H) imidazo[l,2-a]pyrimidine-N-methiodide, < 6.4 (3-H, 5-H) 1,2,4-tri-azolo [1,5-a]pyridimidine, 128(5-H) 1,2,4-triazolo [1,5-a]pyrimidine-N-methiodide, 11.7 (5-H). The lower reactivity in each case of the corresponding methiodides shows that the bases react as such and not as the conjugate acids. 

The addition of the neutral salt (the second set of experiments) accelerates the reaction rate far more than does an equivalent concentration of excess amine. In the absence of the salt, a fifteen-fold increase in the initial amine concentration (from 0.1 M to 1.5 M) raises the measured rate coefficient by a factor of four, but at a salt concentration of 0.34 M the measured second-order rate coefficient is nine times larger than with the salt absent. 

A few results have been reported on the oxidation of cyclohexanol by acidic permanganate In the absence of added fluoride ions the reaction is first-order in both alcohol and oxidant , the apparent first-order rate coefficient (for excess alcohol) at 25 °C following an acidity dependence k = 3.5-1-16.0 [H30 ]sec fcg/A , depends on acidity (3.2 in dilute acid, 2.4 in 1 M acid) and D2o/ H20 is f-74. Addition of fluoride permitted observation of the reaction for longer periods (before precipitation) and under these conditions methanol is attacked at about the same rates as di-isopropyl ether, although dioxan is oxidised over twenty times more slowly. The lack of specificity and the isotope effect indicates that a hydride-ion abstraction mechanism operates under these conditions. (The reactivity of di-isopropyl ether towards two-equivalent oxidants is illustrated by its reaction with Hg(II).) Similar results were obtained with buffered permanganate. 

The remarkable inertness of dialkyl ethers to one-equivalent oxidants is good evidence that the readier oxidation of alcohols involves more than simple electron abstraction. Di-isopropyl ether is oxidised by Co(III) in CH3CN-H2O mixtures with complicated kinetics individual runs show first-order decay of Co(III) but the rate coefficients increase with increasing [Co(III)], and the order with respect to substrate is less than one but is neither fractional nor of a Michaelis-Menten type. The main product is acetone and the following reaction sequence is proposed... 

Assuming that all the radicals R- and R are trapped, it is easy to show that the second order rate coefficient for the trapping reaction is given by (18), where the subscript t - 0 reflects the zero-time extrapolation procedure. Before the onset of reactions which destroy the spin adducts, this is equivalent to (19). 

Spin-orbit relaxation of Rb(52P) appears to be abnormally slow in all the inert gases except helium (cross-section 10 17 cm2). In fact, according to Pitre et a/.123, the relaxation rate in Kr and Xe is slower than for the equivalent transitions of atomic Cs, which correspond to a three-fold larger change in internal energy. Pitre et al. discuss complications in the rubidium experiments, including the formation of van der Waals complexes with the inert gases, in order to account for the apparently abnormal relaxation rates. Efficient removal of Rb(5 2P) by radiationless processes could upset the derived rate coefficients. The results were discussed in relation to Zener s semi-classical equivalent of equation (14). 

A good way to determine the rate coefficients klP and k2Q from experimental results is first to find k from the slope of a first-order plot for the respective reactant or an equivalent numerical method, then to calculate ki and k2Q from it, the isomerization equilibrium constant KI2, and the product concentrations at complete conversion ... 

With this convention, and provided no step involves two or more molecules of intermediates as reactants, any reaction with or without co-reactants and coproducts and with actual rate coefficients kjk becomes mathematically formally equivalent to one composed exclusively of pseudo-first order steps with pseudo-first order rate coefficients Xjk. ... 

The pseudo-first order rate coefficients Xjk used here were first introduced by Christiansen [3] as "reaction probabilities" Uj. Equivalent quantities are also standard in generalized treatments of chain reactions [4,5]. 

This corresponds to parallel first-order decompositions of H2S+ and HS, or to parallel second-order reactions of HS and S with H30+. In the example of 4-aminosalicylic acid, fen2s [H2S+] represents a relatively small correction term [250]. In the cases of 4-aminobenzoic acid [78] and anthranilic acid [77], however, feH2s [H2S+] is the more important term at pH values below 4. Equation (68) is equivalent to the following equation for the dependence of the first-order rate coefficient on... 

Kinetic data for the thermal decomposition of benzoyl peroxide in various solvents are given in Table 70 according to rate law (1). Barnett and Vaughan assumed that, by employing low concentrations of peroxide, the observed rate coefficient was equivalent to the first order coefficient, k. In other instances styrene or iodine was used to trap radicals so that induced decomposition would be suppressed and thus the observed rate coefficient would correspond to kf <... 

Single concentration approach. An alternative, less rigorous, technique is to enploy kinetic data derived for a sin e chromophore concentration in combination with the unquenched lifetime Any attempt to derive equivalent rate coefficients in homopolymers must of necessity be confined to the less rigorous single concentration approach (2) This inevitably produces a pseudo first order koM terra which is... 

The rate coefficients for electron treinsfers of this type, reaction (10), are known to be high, of the order of 10 —10 1 mole sec . The position of the equilibrium will depend on the electron affinities of the two olefins. The electron affinity of naphthalene, for instance, is higher than that of styrene and considerable amounts of N should be present with equivalent quantities of the two hydrocarbons. The situation is more favourable for formation of styrene" if sodium biphenyl is used. The equilibrium will be grossly perturbed, however, by subsequent reaction of the M " species so that none is detectable by ESR measurements even with equimolar amounts of naphthalene" and styrene [86]. This follows because the M" species can dimerize... 

A more detailed analysis of the radical mechanisms has been presented . Generally, all three processes show first-order kinetics but Ej reactions do not exhibit an induction period and are unaffected by radical inhibitors such as nitric oxide, propene, cyclohexene or toluene. For the non-chain mechanism, the activation energy should be equivalent to the homolytic bond dissociation energy of the C-X bond and within experimental error this requirement is satisfied for the thermolysis of allyl bromide For the chain mechanism, a lower activation energy is postulated, hence its more frequent occurrence, as the observed rate coefficient is now a function of the rate coefficients for the individual steps. Most alkyl halides react by a mixture of chain and E, mechanisms, but the former can be suppressed by increasing the addition of an inhibitor until a constant rate is observed. Under these conditions a mass of reliable reproducible data has been compiled for Ej processes. Necessary conditions for this unimolecular mechanism are (a) first-order kinetics at high pressures, (b) Lindemann fall-off at low pressures, (c) the absence of induction periods and the lack of effect of inhibitors and d) the absence of stimulation of the reaction in the presence of atoms or radicals. 

If this reaction is carried out at a total pressure of 1 atm and at 700 K, [RH] 5i 10 molecules cm. Because of the high reactivity of CH3, one expects [RH]jj>[CH3], and if the conversion of azomethane is small [RH] will be nearly constant over the course of the reaction. The bimolecular rate of the reaction of CH3 with RH, r = A 2[CH3][RH], can be expressed as /t2[CH3], where k 2 — A 2[RH]. The apparent kinetic order of this reaction is then 1, and with a constant concentration folded into the rate coefficient, is spoken of as pseudo-first order. This two-step reaction sequence is now formally equivalent to A->B->C. Using data from the literature, — 10 to 10 ", and we expect the steady state ap-... 

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