Rate coefficient, definitions

By using the natural logarithm of the reaction rate coefficient definition [10.42], we have ... 

This is the situation exploited by the so-called isolation method to detennine the order of the reaction with respect to each species (see chapter B2.1). It should be stressed that the rate coefficient k in (A3,4,10) depends upon the definition of the in the stoichiometric equation. It is a conventionally defined quantity to within multiplication of the stoichiometric equation by an arbitrary factor (similar to reaction enthalpy). 

Before discussing such theories, it is appropriate to refer to features of the reaction rate coefficient, k. As pointed out in Sect. 3, this may be a compound term containing contributions from both nucleation and growth processes. Furthermore, alternative definitions may be possible, illustrated, for example, by reference to the power law a1/n = kt or a = k tn so that k = A exp(-E/RT) or k = n nAn exp(—nE/RT). Measured magnitudes of A and E will depend, therefore, on the form of rate expression used to find k. However, provided k values are expressed in the same units, the magnitude of the measured value of E is relatively insensitive to the particular rate expression used to determine those rate coefficients. In the integral forms of equations listed in Table 5, units are all (time) 1. Alternative definitions of the type... 

The definitions of the reaction rate coefficients by Ganguly (1982) differ from those in Table 2-1. The difference is explained in Box 2-3. 

The reaction rate coefficients in the above equations may be related to reaction rates per pair of particles 2/, in nuclear physics (e.g., Fowler et al., 1975 Harris et al., 1983) by k = Xj/(1 + 5/ ), where 8 = 0 except for i= , for which 5/ = 1. That is, for Reactions 2-145 and 2-147 in which two identical particles collide to react, the definition of k is half of defined by nuclear physicists and for reactions in which different particles collide, the definition of k is the same as Xij. The reaction rate coefficients depend on temperature in a complicated way (Table 2-3) and may be calculated as the average value of the product of relative velocity times cross section. The concentrations of the intermediate species can be derived as follows. From Equation 2-155, 145 [ H] = ki4e[ H]pH]. That is. 

Note. The unit of k is based on time (s) and concentration (mol/cmi). The reaction rate coefficients as a function of temperature are from Fowler et al. (1975) and Harris et al. (1983). Note that for Reactions 2-145 and 2-147, the definition of k is consistent with chemists definition used in this book and is half of Xij defined by nuclear physicists. That is, k = Xij/(l + 8j,), where Xi, is the reaction rates per pair of particles, and 5 , = 0 except for i=j for which 5 , = 1. The concentration unit is not converted to mol/L. 

It is noteworthy that the form of the rate (r = / (state of the system) does not actually depend on our choice of reaction rate definition. Only the rate coefficients and their dimensions change with each rate definition (Levenspiel, 1972). 

This discussion highlights the difficulty of deciding at what separation A and B form an encounter pair and then whether this reacts or separates. Noyes [5] and Wilemski and Fixman [51] have taken the encounter distance to be that separation which, if reduced slightly, will lead to reaction. Where these authors disagree is that Noyes [5] only allows reaction to occur in a very narrow range of separation distances about R (which is the usual assumption) and Wilemski and Fixman [51] assume that any separation distance less than the encounter distance, R, can lead to reaction between A and B and that A and B can diffuse through each other till their centres of mass coincide (Chap. 9, Sect. 4). Neither assumption is good, but the differences in predicted rate coefficients are so small that an experimental test of these theories could not be definitive. 

Using the definition or rs3 = 3/4irp,the rate coefficient can be identified as... 

Thus, firstly, the choice of the pure solvent as the reference state for the definition of activities of solutes in fact impairs a fair comparison of the activity of dilute solutes such as general adds to the activity of the solvent itself. Secondly, the observed first-order rate constants k or k0 for the reaction of a solute with the solvent water are usually converted to second-order rate constants by division through the concentration of water, h2o = oA iho, for a comparison with the second-order rate coefficients HA. Again, it is questionable whether the formal h2o coefficients so calculated may be compared with truly bimolecular rate constants kUA for the reactions with dilute general acids HA. It is then no surprise that the values for the rate coefficients determined for the catalytic activity of solvent-derived acids scatter rather widely, often by one or two orders of magnitude, from the regression lines of general adds.74... 

A kinetic analysis of the results, based on (17) and its O+OH analog, is in satisfactory agreement with observations on a wide variety of flames. These flames are relatively cool, and the concentrations of H and OH exceed their equilibrium values even in the burned gases, so that the observed sodium emission is definitely chemiluminescent. The third order rate coefficients for excitation by H+H and H+OH are estimated to be 8 x 109 and 2x 1010 l2.mole-2.sec-1, corresponding to an efficiency near unity per triple collision. The possible importance of mechanisms of the type (14,15) has not been carefully studied. 

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