For the gas phase reaction

H + HBr [H-H-Br] H₂ + Br

the following data have been obtained.

Barrier height E_o (difference between zero point levels of activated complexes and reactants) = 4.65 kJ mol^-1.

HBr internuclear distance = 143.4 pm

HBr vibrational frequency = 2440 cm^-1

The activated H-H-Br complex is taken to be a linear molecule with

H-H distance = 162 pm

H-Br distance = 147 pm

The real vibrational frequencies in the activated state are 2290 cm^-1 and 465 cm^-1 (doubly degenerate). The fourth frequency corresponds to passage to products.

Using partition function theory, calculate the gas phase rate constant for this reaction. Briefly (less than 250 words!) compare your answer to the measured value of 2.0 x 10⁹ M^-1 s^-1.