In the pharmaceutical industry, close attention must be paid to drug purity, quality, stability, and safety. Pharmaceutical compounds often have several different structural forms with different molecular shapes. These compounds are also susceptible to thermal degradation, to the pickup and retention of water, and to photodecomposition. One of the best methods to characterize pharmaceuticals from raw product to finished product stage is thermal analysis. The following questions deal with applications of thermal analysis methods to pharmaceuticals.

(a) Determining the purity of drugs is one of the most important tests done by the pharmaceutical industry. One such test is based on a determination of the melting point of the drug of interest by DSC and the following relationship from thermodynamics:

where X1 is the mole fraction of the drug whose purity is being determined, ?Ht is the enthalpy of fusion, R is the gas constant, and T is temperature. From this equation, derive the following modified van't Hoff equation:

where / is the fraction of sample melting at temperature T, T0 is the melting point of the pure drug, and X02 is the mole fraction of the impurity in the original compound.
Hint: Assume the drug is close to pure so that In Xl can be approximated by

As the temperature is increased toward the true melting point T0, the mole fraction in the liquid state X2 is constantly reduced according to

(b) The fraction/can be found from A/AT, where A is the area of the melting endotherm up to temperature T and AT is the total area of the melting endotherm. By dividing the endotherm into partial melting areas, the fraction f can be determined at various temperatures. Rearrange the modified van't Hoff equation to give the melting temperature T as a function of I/f Show that a plot of T versus I/f should be linear with an intercept of T0 and a slope of -RT0X2/?Ht. If the heat of fusion is known, X2 can be determined.

(c) Look up the article by H. Staub and W. Perron, Anal. Chem., 1974,46,128. Give some of the limitations of the DSC approach to impurity determinations. Describe the "step heating" method used by the authors. How does this differ from normal DSC?

(d) Which type of DSC, power compensated or heat flux, would be most useful in determining purity? Why?

(e) What thermal analysis technique would be suitable for characterizing and quantifying the moisture content in a pharmaceutical sample? Why?

(f) Describe how thermal analysis could be used to determine the degree of hydration of a pharmaceutical compound.

(g) When heated, many pharmaceutical materials show a variety of thermal events, including melting, transitions to glassy states, moisture loss, thermal relaxation, and in some cases, decomposition. How could irreversible kinetic events be distinguished from reversible heat flow events?

(h) Describe how microthermal analysis might be useful in studies of pharmaceutical materials. Consider problems such as polymorphic forms, impurities, and identification of glassy states in your answe