Lindemann plot, curvature

Thus the Lindemann theory predicts that a plot of l/kUni versus 1 /[M] should yield a straight line. Experimental data consistently shows downward curvature at high pressure (small values of 1/ [M]) in plots of this type. The predicted v-intercept (1 /kam) is too large (i.e., the theory underpredicts the extrapolated infinite-pressure rate constant kUni,oo)- This is the second general breakdown of the Lindemann theory that motivated further theoretical analysis. 

The simple model outlined in the previous section would require that be a linear function of [M]". In fact, such plots of experimental data show marked curvature. The simple scheme fails because the mean time for decomposition of X decreases with its energy. In Kassel s theory [3], the Lindemann scheme is taken to be valid for a small energy range and ft, and fe3 are evaluated as a function of energy. 

There is no reason for this expression to be consistent with the Lindemann straight line plot, but it is instructive to examine the physical reasons for the curvature. The low pressure limit is the same as in the Lindemann-Hinshelwood theory because the rate determining step is activation, which is dealt with in the same way in the two theories. This can be seen by taking the low pressure limit of Eq. (21). 

For the Lindemann approach the rates k and k would be independent of energy. In terms of ideal gas law one would have [D]/[S] = d// s[M] = RTkjk P and one should expect a linear relation of [D]/[S] versus P. This is not verified the plot has a pronounced downward curvature. The rate of decomposition should increase with an increase in the vibrational energy. 

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