Hinshelwood’s treatment

In Hinshelwood s treatment, the molecule A is allowed to acquire an amount of energy El at an enhanced rate. The rate at which A converts to A is independent of that energy. Let us take the expression for first order rate constant given by Lindemann s theory, i.e. 

However, the following difficulties still remain, which could not be explained on the basis of Hinshelwood s treatment. 

In case of Hinshelwood s modification both k2 and (k lk ) have been treated as independent of E, i.e. amount of energy in the energized molecule. In Hishelwood s treatment the critical energy El is involved, not E. ... 

The first of the shortcomings of the Lindemann theory—underestimating the excitation rate constant ke—was addressed by Hinshelwood [176]. His treatment showed that ke can be much larger than predicted by simple collision theory when the energy transfer into the internal (i.e., vibrational) degrees of freedom is taken into account. As we will see, some of the assumptions introduced in Hinshelwood s model are still overly simplistic. However, these assumptions allowed further analytical treatment of the problem in an era long before detailed numerical solution was possible. 

An important consequence of the Hinshelwood-Lindemann treatment is that the probability to find AB at the energy E depends now on the number of oscillators, s, or in other words on the size of the reacting... 

More sophisticated treatments of Lindemann s scheme by Lindemann— Hinshelwood, Rice—Ramsperger—Kassel (RRK) and finally Rice— Ramsperger—Kassel—Marcus (RRKM) have essentially been aimed at re-interpreting rate coefficients of the Lindemann scheme. RRK(M) theories are extensively used for interpreting very-low-pressure pyrolysis experiments [62, 63]. 

This treatment is called the Lindemann-Hinshelwood theory. Although the treatment of Hinshelwood was successful in reproducing the experimental values of high-pressure limit rate constants k o, the theory stUl has one defect, that the values of s necessary to explain the experimental values differ largely from the acmal number of vibrational freedom and there is a large discrepancy of with experimental values in the fall-off region. 

In spite of the progress that the treatment of Hinshelwood has brought to the field, some difficulties remain. One that persisted was the reciprocal dependence of l/k versus the reciprocal of concentration, which as we have seen is not found at high pressures. However, there are other problems, such as the fact that the number of degrees of freedom required to reproduce experimental data is one-half of the total number of vibrational modes. Also, according to eq. (8.23), one would also expect a strong temperature dependence of the preexponential factor, especially for large values of s. There is no experimental evidence for this prediction. 

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