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Therefore,

Intercept at log(1 + t) = 0 is -2.55. From equation (4.70),

Intercept = log k0 - log

form of equation (4.66):

log kt = -2.08 + [74 680/(2.303 x 8.314)] x [(1/285.5) - (1/293)] = -2.08 + 0.3497 = -1.730

and where the final term on the right of equation (4.70) is neglected. Therefore, log k0 = -2.55 + log 2.95 = -2.08

That is, the rate constant at temperature T0 (12.5°C) is 0.0083 h-1.

The rate constant at 20°C may then be calculated from the Arrhenius equation in the kt = 1.86 x 10 h-1 The rate constant at 20°C is thus 0.0186 h-1.

The advantages of this method over the conventional method of stability testing are that (a) the data required to calculate the stability are obtained in a single one-day experiment rather than from a series of experiments which may last for several weeks; (b) no preliminary experiments are required to determine the optimum temperatures for the accelerated storage test; and (c) the linearity of the plot of log f (c) against log(1 + t) confirms that

Figure 4.18 Example 4.10: accelerated storage plot for the decomposition of riboflavin in 0.05 mol dm-3 NaOH using data from reference 29.

Figure 4.18 Example 4.10: accelerated storage plot for the decomposition of riboflavin in 0.05 mol dm-3 NaOH using data from reference 29.

the correct order of reaction has been assumed.

Several improvements on the original non-isothermal stability testing methods have been suggested. Rather than subjecting the drug formulation to a predetermined fixed time-temperature profile, the temperature may be changed during the course of the experiment at a rate consistent with the analytical results from the experiment. 30 The resultant time-temperature data are fitted to a polynomial expression of sufficient degree to describe the changes. This relationship and the experimental data are then combined and utilised to compute a series of degradation pathways corresponding to a series of values of activation energy. The curves are matched with the experimental analytical data to obtain the correct activation energy for the reaction. Using this activation energy and the analytical data, the reaction rate and stability may be calculated. Computational procedures whereby the activation energy and frequency factor of the Arrhenius equation may be determined from simple nonisothermal experiments with a fixed temperature-time profile have been described.31,32

An improvement in the design of stability tests which avoids the difficulties inherent in the nonlinear curve-fitting procedures outlined above has been suggested. 33 The experimental procedure involves changing the temperature of the samples being studied until degradation is rapid enough to proceed at a convenient rate for isothermal studies to be carried out. The analytical information obtained during the nonisothermal and isothermal portions of the experiment is utilised in calculating the activation energy and determining the order of reaction and the reaction rate and predicting stability at any required temperature.

Although accelerated storage testing has proved invaluable in the development of stable formulations, it is important that we consider some of the limitations of this technique. We must take care that the order of reaction is not different at the higher temperatures from that which occurs at room temperature. There are several cases where this might be so. For example, with complex decomposition processes involving parallel or consecutive reactions, there may be a change in the relative contributions of the component reactions as the temperature is increased.

### Suspensions

One complication which arises when we are carrying out stability testing of suspensions is the changes in the solubility of the suspended drug with increase in temperature. With suspensions, the concentration of the drug in solution usually remains constant because, as the decomposition reaction proceeds, more of the drug dissolves to keep the solution saturated. As we have seen, this situation usually leads to zero-order release kinetics. If the actual decomposition of dissolved drug is firstorder, then we can express the decrease of concentration, c, with time, t, as

where k0 = k15 and S is the solubility of the drug.

The problem that arises with these systems is that an increase of temperature causes not only the usual increase in rate constant but also an increase in solubility. Application of the Arrhenius equation to the data involves the measurement of the changes in solubility of the drug over the temperature range involved. An alternative method which does not necessitate the determination of solubility uses the relationship between solubility and temperature:

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