Total Relative Rate Constant for the Reaction F + HCl → HF + Cl

 Question:

For the reaction F + HCl(ν) → HF (ν’) + Cl, the relative rate constants have been measured by J. L. Kirsch and J. C. Polanyi [J.Chem. Phys.57, 4498 (1972)] and are shown in the following table, where the rates are relative to the specific rate constant for ν = 0 and ν’ = 2 and are for a translational temperature of 1700 K.

Assuming a Boltzmann distribution of HCl levels at 1700 K ( ṽ_HCl = 2990 cm⁻¹ ), calculate the total (relative) rate constant for the reaction F + HCl → HF + Cl.

This is the problem 8.8 of the book “Chemical Kinetics and Reaction Dynamics, written by Paul L. Houston”.

Solution:
The total relative rate constant at a given temperature can be calculated as,

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