Liquid-State Physical Chemistry: Fundamentals, Modeling, and Applications (2013)
14. Some Special Topics: Reactions in Solutions
14.5. Reaction Control
In TST, the reaction rate is given in terms of the molarity of the components. The conventional way of introducing medium effects is to realize that the molarity is the activity aX divided by the activity coefficient γX, and to replace the molarities cX in the TST expression accordingly.
In Section 14.2 we derived for the reaction A + BC ↔ (ABC)‡
(14.50) 
Here, the equilibrium constant K‡ is not the true equilibrium constant 
using activities aX, but the corresponding expression using molarities cX. In many cases we have an elementary reaction of the type
For a bimolecular reaction the true equilibrium constant and rate constant are then
(14.51) 
while we used
(14.52) 
For a unimolecular reaction, similarly kA/kA,0 = γA/γ‡, and if the structure of the activated complex is not too different from the reactant we have approximately kA/kA,0 = 1. This is, for example, the case for the decomposition of N2O5 in various solvents. Data for the decomposition of N2O5 at 20 °C are listed in Table 14.1; these data show that the pre-exponential factor and activation energy are approximately constant over the range of solvents indicated.
Table 14.1 Pre-exponential factor and activation energy (Eq. 14.10) for the decomposition of N2O5 at 20 °C.a)
|
Solvent |
lnA (l mol−1 s−1) |
Eact (J mol−1) |
|
Gas phase |
31.4 |
103.4 |
|
Nitromethane |
31.0 |
102.6 |
|
Bromine |
30.5 |
100.5 |
|
Pentachlorethane |
32.2 |
104.7 |
|
Carbon tetrachloride |
30.8 |
100.9 |
|
Ethylene chloride |
31.3 |
102.2 |
|
Chloroform |
31.8 |
103.0 |
|
Ethylidine chloride |
32.5 |
104.3 |
|
Nitrogen tetraoxide |
32.7 |
104.7 |
|
Propylene dichloride |
34.8b) |
117.2 |
|
Nitric acid |
34.0b) |
118.5 |
a) Data from Ref. [11].
b) Data at 45 °C.
Similar measurements in propylene dichloride and nitric acid showed relatively low rate constants, while the activation energies were relatively high. This suggests the formation of a complex between the reactant and solvent. Another example is the dimerization of cyclopentadiene (C5H6 to C10H12). At 50 °C the rate constant is 6 × 10−6 l mol−1 s−1 for the gas phase, while the rate constants were 6 × 10−6, 10 × 10−6 and 20 × 10−6 l mol−1 s−1 for the solvents CS2, C6H6, and C2H5OH, respectively. However, in many cases there is a significant influence of the solvent. For different types of solution we have discussed expressions for the activity coefficients, and we will discuss their effect on the reaction rates in the next sections.