Page 171 - Introduction to chemical reaction engineering and kinetics

6.8 Problems for Chapter 6 153

constant value of fa (0.31 in problem 6-4), tfA (tat above) is a linear function of l/c~~, from
the slope and intercept of which ki and km can be determined. Compare the values with those
obtained in problem 6-4.
6-6 (a) Is the experimental quantity EA in the Arrhenius equation intensive or extensive? Does its
numerical value depend on the way in which the stoichiometry of reaction is expressed (cf.
AH of reaction)?
(b) The dimensions of EA are energy mol-‘. To what does “mol” refer?
6-7 The isomerization of cyclopropane to propylene has Arrhenius parameters A = 1.6 X 1015 s-l
andEA = 270kJmoll’.
(a) Calculate the entropy of activation, AS”*/J mol-’ K-l, at 500 K.
(b) Comment on the answer in (a) in comparison with the “expected” result for a unimolecular
reaction.
(c) Calculate the enthalpy of activation, AH”*/kJ mol-‘, at 500 K.

6-8 Rowley and Steiner (195 1) have obtained the result

k = Aexp(-EAIRT) = 3.0 x lO’exp(-115,00O/RT),

where A is in L mole1 s-l and EA is in J mol-‘, for the rate constant for the reaction

C2H4 + C4H6 + C6Hto (cyclohexene).

(a) Calculate the entropy of activation for this reaction at 800 K.
(b) Comment on the answer in (a) in comparison with the “expected” result for a bimolecular
reaction.
(c) Calculate the entbalpy of activation in k.I mol-‘.
6-9 (a) If the Arrhenius parameters for the gas-phase reaction

H CHO
CH2 = CH-CH = CH2 + CHz = CH-CHO +

are A = 1.5 X lo6 L mol-’ s-l and EA = 82.8 k.I mol-‘, calculate, at 500 K,
(i) the entropy of activation (AS”*/J mol-’ K-l), and
(ii) the enthalpy of activation (AH”t/k.I mol-‘).
(b) Comment on the value of AS”” calculated.
(c) Corresponding to the value of AS”* calculated in (a) for the transition state theory, would
you expect the value of the steric factor p in the simple collision theory to be = 1, > 1, or
< l? Explain briefly-detailed calculations or proofs are not necessary.
6-10 Show that, for the bimolecular reaction A + B -+ P, where A and B are hard spheres, kTsT is
given by the same result as kSCT, equation 6.4-17. A and B contain no internal modes, and the
transition state is the configuration in which A and B are touching (at distance dm between
centers). The partition functions for the reactants contain only translational modes (one factor
in Qr for each reactant), while the transition state has one translation mode and two rotational
modes. The moment of inertia (I in Table 6.2) of the transition state (the two spheres touching)
is pdh, where p is reduced mass (equation 6.4-6).