3.5 The rate constant based on
The observed reaction rate constant cannot explain the relationship
between the reaction rate and sulfuric acid concentration very well.
Therefore, it is necessary to study the rate constant based on .
Extensive studies have shown that the rate-determining step for
homogeneous aromatic nitration in mixed acids is the attack of nitrate
ions on the aromatics, and the reaction rate can be expressed by the
concentration of CB and nitronium
ions as follows:3,32
where is the observed rate constant expressed for , and is the
concentration.
Based on the Brønsted-Bjerrum rate law (transition-state
theory),33,34 the nitration rate can be expressed as
follows:
where k * is the rate constant based on and ,
and are the activity coefficients for CB, nitronium ions and the
transition-state intermediate, respectively.
The value of the activity coefficient is not easy to obtain. To
calculate the pK a of weak bases in a study of acid-base
equilibrium, Marziano et al.26,34 introduced the
activity coefficient function M c to describe the
change in the activity coefficient with acid strength:
where n is a thermodynamic parameter related to the type of
aromatic compounds. The M c for sulfuric acid
represents a general scale describing its acidity, and its value depends
only on the concentration of sulfuric acid at a given temperature.
Therefore, the value corresponding to describes the variation in the
activity coefficient ratio of Equation (12) as a function of the
sulfuric acid concentration, and the effective concentration of the
reactant is taken into consideration.
Combining Equations (7) and (13), the relationship betweenk * and k obs can be
expressed as follows:
Taking the logarithm of Equation (14), we obtain:
Therefore, taking as the ordinate and M c as the
abscissa, the values of n and k * can be
obtained by the slope and intercept of the resulting straight line.
However, before this can be done, the values ofM c and need to be determined.