The Pharmaceutics and Compounding Laboratory
Chemical Kinetics

Arrhenius Equation

When a new drug product is being formulated, it is desirable to determine the stability of the drug entity in the drug product so that a shelf life or expiration date may be assigned to the product. The shelf-life is the length of time required for the product potency to be reduced to some percentage of its original value. For most products, this is the T90 or time at which the product retains 90% of its original potency. Although the drug's stability at room temperature is of primary interest, a stability study at room temperature would take too long to be useful as a screening procedure for new formulations. Therefore, such screening studies are conducted at elevated temperatures in accordance with the Arrhenius equation:

where,

Kapp = the apparent rate constant for the reaction - A = the frequency factor - Ea = the activation energy for the reaction - R = the gas constant (1.987 cal./deg. mole) - T = absolute temperature (degrees Kelvin)

The Arrhenius equation can be rewritten as:

Again, an equation of the form y = mx + b is generated, indicating that a semi-log plot of Kapp vs. the reciprocal of the absolute temperature (1/T) should yield a straight line with a negative slope equal to -Ea/R. This line can be extrapolated to the value of 1/T that corresponds to room temperature and the predicted rate constant for the reaction at room temperature can be taken from the y- axis.

Although the degradation of aspirin in a solution buffered at pH = 7.5 occurs too slowly at room temperature to be adequately studied during one laboratory period, the reaction proceeds rapidly at temperatures of 50°C and above. The reaction will be conducted at approximately 55°, 60°, and 65°C.