Module 7 : Theories of Reaction Rates
Lecture 33 : Transition State Theory
 

Problems

33.1) Distinguish between K and K that have been described in this lecture.


33.2) Rate constant are often expressed as empirical equations. For a reaction A + B AB, the rate
 
constant in the vicinity of 298K is given by k2 = 10 13 exp (-7000 K / T) L mol -1 s -1, where T is the absolute temperature. Using the activated complex theory expression, evaluate the energy and entropy of activation for this reaction.
 
33.3) Distinguish between Ea and H.
 
33.4) At 300 K and low pressures, the preexponential factor for the decomposition of ozone is 1013. If the
 
activation energy is 10 kJ/mol, calculate H, S and G. (Equate 1013 exp(-Ea / RT) to the transition state theory expression to get G. Take appropriate derivatives to obtain the other parameters).
 
34.5)
Consider two reactions, one between atoms, A + B AB and another, between non-linear molecules, XY3 + WZ2 Products. Even if the activation energies for both reactions are the same, the second reaction is generally slower. One rationalization of this is through the P factor. Can you give a reasoning using partition functions? Assume all translational partition functions here to be 10 27 and all vibrational partition functions to be 1 and all rotational partition functions to be 50.
   
 
34.6)
Draw an energy level diagram involving two activated complexes during the course of the reaction and a relatively stable intermediate separating these two activated complexes.
 
34.7)
Through this problem, let us study the kinetic isotope effect. The potential energy for the breaking of C- H bond and C- D bond is shown below.(D = Deuterium or 2 H). E1, the activation energy for breaking the C- H bond is smaller than E2 (the activation energy for breaking the C- D bond) because of the larger mass of D. In terms of vibrational frequencies of C-H and C-D, the energy difference is
  E2 - E1 = NA [ 1/2 h (C-H) - 1/2 h (C-D)]
  = 1/2 NA k f 1/2[ CH-1/2 - CD-1/2]
 
where NA = Avogaro number, kf, the force constant for the bond and CH and CD are the reduced masses for the CH & CD species.The ratio of the dissociation rates for the two bonds is k (C-D) / k (C- H) = e where = (CH-1/2 - CD-1/2) kf 1/2 / 2 kBT Since CD > CH, > 0 and C-H bond cleavage is faster than CD bond cleavage. Calculate this ratio by substituting all the values in the equation above. kf =
 
If D is replaced by Tritium (3H) what is the kinetic isotope effect? In water, if 16O is replaced by 18O, what is the kinetic isotope effect (i.e., the rate alteration due to isotopic substitution)?