Stability of Drugs and Dosage Forms Sumie Yoshioka

62 Chapter 2 • chemical Stability of Drug Substances
indicated in Eq. (2.71). Observed linear Arrhenius plots can be explained by the much larger
temperature dependency of the exponential term in Eq. (2.70) as compared to that of A. In
theory, however, Arrhenius plots should not be linear.
E a = ∆ H ‡ +RT (2.71)
Nevertheless, Arrhenius plots have been traditionally used to describe the temperature
dependency for various chemical reactions by regarding A and E a as independent of
temperature. A prerequisite for the application of Eq. (2.70) [and Eq. (2.7)] is that the
degradation mechanism does not change in the temperature range of interest. E a values of
about 10-30 kca/mol (40-130 kJ/mol) are generally observed in the degradation of drug
substances. Table 4 shows E a values for degradation of representative drug substances. The
values of E a are presented in units of calories per mole rather than kilojoules per mole
because those were the units reported in the original reference sources (1 kcal/mol = 4.18
kJ/mol).
As an alternative to Arrhenius plots, the data can be fitted to the Eyring equations:
(2.72)
(2.73)
A plot of In k/T versus 1/T is linear. Thus, plots of either k versus 1/T or k/T versus 1/T are
usually plotted by taking either the natural logarithm (In) or the logarithm to the base 10
(log) of k. The slopes of plots of log k or log k/T versus 1/T are –E a /2.303RT and
–∆ H ‡ /2.303 RT, respectively.
Temperature is obviously an important parameter because most reactions proceed faster
at elevated temperatures than at lower temperatures. The terms E a and∆ H ‡ are a measure of
how sensitive the degradation rate of a drug is to temperature changes. Table 5 shows the
effect of a 10°C change in temperature on the rate constant. If the E a for a degradation process
is only 10 kcal/mol, this temperature change results in only a 1.76-fold change in drug
reactivity. However, if the E a is 30 kcal/mol, a 10°C increase in temperature results in about
a 5.5-fold increase in the degradation rate.
2.2.4.2. Quantitation of the Temperature Dependency of Degradation Rate Constants
Estimation of an appropriate rate or rate constant for drug degradation is an important
step in predicting the stability of pharmaceuticals. Knowing how such a rate or rate constant
changes with temperature in a quantitative way may allow one to predict the stability at other
temperatures. Even if a rate or rate constant cannot be estimated by fitting the data to a
theoretical or empirical equation, constants such as time required for 10% degradation (t 90 )
can be utilized instead of rate constants. Stability prediction is possible, for example, from
the relationship between the reciprocal of t 90 and temperature.
In the previous section, the Arrhenius equation was described. The Arrhenius equation
was applied to the prediction of drug degradation in the 1940s and 1950s. Taking the
logarithm of both sides of Eq. (2.70) yields
(2.74)