Rate coefficients and constants

Rai D, Zachara JM. 1984. Chemical attenuation rates, coefficients, and constants in leachate migration. Volume 1 A critical Review. Electric Power Research Institute, Palo Alto, CA. 

For 4-nitrophenol (studied in the range 1.4-10 M nitric acid) the first-order rate coefficients (at constant nitrous acid concentration) decrease approximately 50 % as the nitric acid concentration is increased from 2 M to 5 M but increase considerably as it is further increased to 10 M the increase is greater the lower the fixed concentration of nitrous acid and is attributed to the catalysed reaction. The rate decrease was attributed to superimposition upon the normal catalysis noted above for 4-chloroanisole of the effect of lowering of the concentration of the highly reactive phenoxide ion as the acidity was increased. In 10 M nitric acid the anti-catalysed reaction was again observed. 

Since there is inherent in reactions which give low selectivities, the possibility that non-competitive conditions are responsible, Olah and Overchuck359 have measured directly the rates of benzylation, isopropylation, and fer/.-butylation of benzene and toluene with aluminium and stannic chlorides in nitromethane at 25 °C. Apparent second-order rate coefficients were obtained (assuming that the concentration of catalyst remains constant), but it must be admitted that the kinetic plots showed considerable departure from second-order behaviour. The observed rate coefficients and kreh values determined by the competition method are given in Table 88, which seems to clearly indicate that the competitive ex-... 

With a view to determining the equilibrium constant for the isomerisation, the rates of reduction of an equilibrium mixture of cis- and rra/i5-Co(NH3)4(OH2)N3 with Fe have been measured by Haim S . At Fe concentrations above 1.5 X 10 M the reaction with Fe is too rapid for equilibrium to be established between cis and trans isomers, and two rates are observed. For Fe concentrations below 1 X lO M, however, equilibrium between cis and trans forms is maintained and only one rate is observed. Detailed analysis of the rate data yields the individual rate coefficients for the reduction of the trans and cis isomers by Fe (24 l.mole sec and 0.355 l.mole .sec ) as well as the rate coefficient and equilibrium constant for the cw to trans isomerisation (1.42 x 10 sec and 0.22, respectively). All these results apply at perchlorate concentrations of 0.50 M and at 25 °C. Rate coefficients for the reduction of various azidoammine-cobalt(lll) complexes are collected in Table 12. Haim discusses the implications of these results on the basis that all these systems make use of azide bridges. The effect of substitution in Co(III) by a non-bridging ligand is remarkable in terms of reactivity towards Fe . The order of reactivity, trans-Co(NH3)4(OH2)N3 + > rra/is-Co(NH3)4(N3)2" > Co(NH3)sN3 +, is at va-... 

The first evidence that two step proton transfer from a hydrogen-bonded acid could occur consisted of Eigen plots for proton removal by buffer bases. The demonstration of a change in the rate-limiting step as in (30) and (31) provides even more clear evidence and permits the calculation of the rate coefficients and equilibrium constant for opening of the hydrogen bond. 

Luke, W.T., Dickerson, R.R., and Nunnermacker, L.J. Direct measurements of the photolysis rate coefficients and Henry s law constants of several alkyl nitrates, J. Geophys. Res., 94(D12) 14905-14921, 1989. 

When the reaction temperature does not change with time, the rate coefficients remain constant, so that separation of the variables and integration gives... 

From the preceding equations it can be seen that the rate coefficients and the equilibrium constant are related. Recall from thermodynamics that... 

The backward reaction rate coefficient can be calculated from the forward reaction rate coefficient and the exchange equilibrium constant. 

Growth of isolated nuclei at an electrode surface is eventually limited when they start to coalesce due to their number and size and the size of the electrode area. Analysis of the overlap problem can be performed by use of the Avrami theorem [152] and leads to maxima in the current—time curves at constant potential. Potentiostatic conditions are convenient for the study of these phenomena because electrochemical rate coefficients and surface concentration conditions are well controlled. 

The first term on the right-hand side describes [C4H9](f) at the source entrance, here due to pseudo-first-order decay in the reactor with a time constant r, which is the reciprocal of the pseudo-first-order rate coefficient, and the second term is the exit response where tp is the effusion time constant. The solution of this equation is... 

We now introduce notations for the equilibrium constants of the reactions (11.1) and (11.2), connect them with the rate coefficients and write down the expressions for the equilibrium constants at high temperature 14... 

We neglect the term K3NO compared with K202 in the denominator15 and use the relation between the rate coefficients and the equilibrium constants finally we assume that the concentration of atomic oxygen is determined by the dissociation equilibrium of molecular oxygen... 

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