Arrhenius Equation.

The most satisfactory method for expressing the influence of temperature on reaction velocity is the quantitative relation proposed by Arrhenius.

K=Se -Ha/RT
Where,
K= Specific rate of degradation
R= Gas Constant (1.987 calories degree -1 mole-1).
T= Absolute Temperature.
S= Frequency factor
The constant of integration in the Arrhenius equation has been designated as the frequency factor.This is the frequency of collisions which can be expected between the reacting molecules for a given reaction.
Logarithmically it may be expressed as follows:
delta Ha
lnK= ------------+ lnS
RT
Converting to log10 deltaHa 1
log K= --------- x----- + log S
2.303 R

Where S can be considered as a constant delta Ha is the heat of activation.
Higher the value for the heat of activation the more the stability is temperature dependent

Rate Constant.

Arithmetic plots representing the change in absorbance vs time are linear,indicating that color loss is following zero order reaction.The slopes of these lines are obtained and are indicative of the rate of change of color with time.Most suitable example is the pH dependency of the hydrolysis of methyl DL-alpha-phenyl-2-piperidyl acetate at 80 degree C which shows the pH at which the maximum hydrolysis can be affected.
In order for rate constants or velocity of degradation to be of use in the formulation of pharmaceutical products,it is necessary to evaluate the temperature dependency of the reaction. This permits the prediction of the stability of the product at ordinary shelf temperature from data obtained under exaggerated conditions of testing.According to the rule of thumb method the rate of reaction was said to be double for each 10 degree C rise in temperature.Although the rule may serve as a fairly accurate method to estimate for certain preparations,it is not generally applicable therefore,to assign an overall factor for influence of temperature on the acceleration of the reaction is unwise.Some deterioration reactions are not measurably influenced over 10 degrees C temperature range,while other undergo rapid degradative changes.The recommended procedure is to set up a planned schedule of accelerated tests for each formulation in order to ascertain the temperature dependency of the chemical changes in the product undergoing evaluation.

Rate Determination Step.

It can be made applicable to exaggerate test conditions of short duration provided the function can be linearised in accordance with chemical kinetic reaction orders.Example of color stability of a multidose sulfonamide preparation can be done by observing the plot of the logarithms of the rate of decrease in absorbance of extracted color per hour against the reciprocal of absolute temperature. By the use of colorimetric measurements of the sample subjected to thermally accelerated degradation, it is possible to predict the color stability of the preparation at room temperature.

From the information on chemical kinetics it is possible to accurately study the degradation of an active drug in solution, as well as determine the mechanism responsible for the degradation.A more complicated situation arises when an attempt is made to study stability of one or more drugs in liquid pharmaceutical dosage forms.Because of the multiplicity of ingredients in most pharmaceutical formulations,there exists the possibility of of interactions that take place, as well as each ingredient having different degradative characteristics.The ideal situation should be to study the degradation pattern of each in mixture individually. This of course is difficult,time consuming and expensive to accomplish.Fortunately it is not necessary for the purpose of stability prediction to determine the mechanism of degradation,since generally it is possible to evaluate the stability of any component of a pharmaceutical preparation by determining some property of the degradation as a function of time.