Page 160 - Introduction to chemical reaction engineering and kinetics

142 Chapter 6: Fundamentals of Reaction Rates

Table 6.1 Expected (approximate) values of AS”’
for different values of molecularity (m) at 500 K

Comparing equations 6.5-13 and 3.1-8, we obtain
1 A = (kBTlh)eAso”Rem (6.5-14)

or

AS”* = R[ln(Ahlk,T) - m] (6.5-15) 1

= 8.314(-23.76 + In A - In T - m) J mol-i K-i (6.515a)

on substitution of numerical values for the constants.
From equation 6.515a and typical experimental values of A, we may estimate ex-
pected values for AS”‘. The results are summarized in Table 6.1.

If the Arrhenius parameters for the gas-phase unimolecular decomposition of ethyl chlo-
ride (C,H,Cl) to ethylene (C,H,) and HCl are A = 4 x 1014 s-l and EA = 254 kJ mol-‘,
calculate the entropy of activation (AS’S /J mol-1 K-l), the enthalpy of activation (AH”’
/J mol-‘), and the Gibbs energy of activation (AGO* /J mol-‘) at 500 K. Comment on the
value of AS’S in relation to the normally “expected” value for a unimolecular reaction.

SOLUTION

From equation 6.5-15,

8.314[(
ASot = l?(lng -m)

= In 4 x 1014 x 6.626 x 1O-34
1.381 x 10-23 x 500

= 22 J mol-’ K-’

From equation 6.5-12,

AH@ = EA - mRT
= 254,000 - 1(8.314)500
= 250,000 J mol-’