# 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)

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.