Stability of Drugs and Dosage Forms Sumie Yoshioka

36 Chapter 2 • Chemical Stability of Drug Substances
Figure 5. Free-energy diagram showing reactants proceeding to products through a transition state or activated
complex.
(2.7)
where ∆G ‡ , ∆S‡, and ∆H‡ are the free energy, entropy, and enthalpy of activation, respectively.
∆G ‡ is the difference in free energy between the reactant state and the activated
complex, as shown in Fig. 5. The term κ is the Boltzmann constant, h is the Planck constant,
and Tis the temperature in degrees kelvin.
In descriptive terms, Eq. (2.7) essentially suggests that for chemical reaction to occur,
molecules must first collide. The term κ T/h represents a so-called universal collision number.
Not only must the molecules collide, but they must collide with sufficient overall free energy
for rearrangement of the molecules to occur. The term e -
−−∆G‡ /RT represents the fraction of
molecules colliding with sufficient energy to overcome the free-energy barrier to reaction.
This free-energy barrier is made up of both an enthalpic term (∆H ‡ ) and an entropic term
(∆S‡).
Other kinetic theories, such as the collision theory, were proposed earlier. In the collision
theory, proposed by Lewis, the reaction rate, v, was given by
where Z is the collision frequency, R is the gas constant, and E is the activation energy.
Thereafter, Eyring developed the theory of absolute reaction rates by introducing the concept
of the formation and breakdown of an activated complex. This so-called transition-state
model, defined by the reaction illustrated in Fig. 5, is represented by
where Q A , Q B , and Q ‡ are the partition functions of A, B, and the activated complex,
respectively, and E 0 is the energy required for the formation of 1 mol of the activated complex
at 0°K. Replacing partition functions in Eq. (2.9) by thermodynamic functions yields Eq.
(2.7).
Because chemical reaction rates depend not only on the concentrations (more accurately,
the activities) of participating species but also on temperature and the free energy of
(2.8)
(2.9)