The term in the brackets of eq (33.31) is the rotational partition function of the activated complex. The moment of inertia I is given by
r 2 where r is the "bond length" of the activated complex and
= mAm B / ( mA +mB ) is the reduced mass. Substituting the values of qA, qB and qC in equations (33.27) and (33.28), we get
k2 =
(kBT /
h)(RT /p0)NA ( 2 I kBT / 2 ) e
(33.33)
Canceling RT / p0 and V 0m ( which are equal ) and substituting the values of 0A, 0B and 0C, we get
k 2 = NA (8 kBT /
) 1/ 2 ( r 2 ) e
(33.34)
If we identify the reaction cross section
as r 2, this equation, (33.32) is identical to the equation derived using a simple collision theory of lecture 32. It is indeed remarkable that two very different theories give the same result! Does it mean that this result is more "correct" than the result that is usually obtained from a single theory ? While it would be tempting to say yes, what this means is that we have captured some of the essential features relevant in the dynamics of chemical reactions. Further improvements will come when we consider the cross sections of each of the states of the reacting species and also when we remove the requirement that C is not in equilibrium with A and B. In the next section, we relate k2 to the activation parameters for the reaction.
r 2 where r is the "bond length" of the activated complex and
= mAm B / ( mA +mB ) is the reduced mass. Substituting the values of qA, qB and qC in equations (33.27) and (33.28), we get 
(kBT /
h)(RT /p0)NA 
( 2 I kBT / 
2 ) e
0A, 
, we get 
) 1/ 2 ( 
r 2 ) e 
as 
