Part 2 – Reaction rate constants with TST: rates

We can now insert our partition functions values in the expression for the rate constant at T=300K:

\sf k(T)= \sf \frac{k_BT}{h}\frac{Q^{\ddagger}(T)}{Q_R(T)}e^{-\beta E_a}

To find,

\sf k(T=300K)=  \sf \text{\sf 8.229957e+03 } cm^3 / molecule / s

Note that the overall reaction rate reactant partition function is taken as the product of each reactant partition function. This procedure can be repeated at each temperature to get a profile of the reaction rate constant as a function of temperature. Here is a plot in logarithmic scale where we compare our results (blue curve) to published results (red triangles)

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The main role of the temperature dependence is in the exponential, this is why we see a linear dependence of the logarithm of the rate. Further, as expected the rate increases as temperature rises (i.e in the limit of the x axis going to zero) and decreases at lower temperatures. When quantum effects are included, one might see a large change at low temperatures which is due to the presence of tunneling. Other differences arise from the fact that the rate as is comes from a static picture and no dynamics has been carried out.

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