Randomisation rate constants

Fig. 4. Hydrogen isotope exchange between C6H and C6D6. Correlation of randomisation rate constant kF, with percentage d-character of the metallic bonds (4). 

These values of the first and second order randomisation rate constants do not seem unreasonable. The values for /ij are about the same for both molecules, and are close to the generally accepted estimate of around 10 s" for intramolecular randomisation processes [82.T]. No previous estimates have been made for second order randomisation rate constants, but it seems plausible that they might increase with increasing state density, as we find here the density of states near threshold is about six or seven times greater in the deuteriated as opposed to the normal methyl... 

Fig. 7.4. Fall-off curves for the thermal isomerisation of perdeuteriomethyl isocyanide at 230.4°C. The points represent the direct fall-off measurements of Schneider Rabinovitch [63.S1] for this reaction. The dashed line is the standard strong collision fall-off calculation. The solid line includes both first order and second order randomisation effects, with r,= = i.30x lO Torr s ,/ii =5.0x 10 s and r2 = 3.0 x 10 Torr s .The dotted curve shows the result of using the same randomisation rate constants as were used in the preceding diagram.

There is no reason why the randomisation rate p, should not be regarded as being different for each grain, but in all the numerical experiments I have conducted so far, I have taken it to be constant for a given molecule also, it is clearly an approximation to regard p in equation (7.1), or p, in equation (7.2), as strict exponential decay rates, but the error in so doing is, I hope, small. 

Fig. 7.5. Kinetic isotope effect kn/k for CHjNC and CDjNC thermal isomerisations as a function of pressure at 230.4°C. The points represent two sets of ratio measurements made by Schneider Rabinovitch [63.S1]. The dashed line uses the standard strong collision fall-off calculation for each molecule, whereas the solid line allows for reactant state randomisation with the rate constants used in Figures 7.3 and 7.4 respectively.

We conclude that randomisation of the product states is a vital part of any isomerisation reaction. This being the case, then we may also conclude that at such time in the future when we can calculate rate constants with sufficient confidence, the rates of thermoneutral isomerisations will need to be reduced by a factor of about two compared with the rates of strongly exothermic isomerisations. 

If the more general form, equation (7.2), for p including both first and second order randomisation, is used and the analytic form, equation (7.7), is used to calculate the rate constants, the results found from the separable approximation in Figures 13-1.5 are recovered unaltered. 

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