Proportionality between the extent of reaction and enthalpy

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The determination of kinetic parameters from thermal analysis studies (differential thermal analysis and differential scanning calorimetry) involves numerous assumptions. Seldom are these stated explicitly and hardly ever are they investigated. In this paper we are concerned with the assumption of a direct proportionality between the extent of reaction and the enthalpy change. It lies at the heart of obtaining the triplet of information: rate, temperature and extent of reaction, which is the starting point for kinetic investigations. Such an assumption must be made because the thermal analysis curve does not provide independent information about the relationship between extent of reaction and the enthalpy change. However, it is necessarily true only for certain ideal thermodynamic processes. The systems studied by thermal analysis seldom lend themselves to alternative methods of investigation. A recent investigation of the kinetics of the solid-state reaction between tungsten and potassium dichromate provided the opportunity for making a comparison between the use of thermal analysis and spectrophotometry for the determination of extent of reaction. The stoichiometry of the reaction can be represented by the equation [l] W + 2K,Cr,O, = WO, + 2K,CrO, + Cr,O,. The use of spectrophotometry to determine the extent of reaction has been based on the determination of the chromate ion [2]. The analysis is made complicated by the equilibrium established between dichromate and chromate ions in solution Cr,O;+ H,O = 2CrOi’ + 2H+. By working with alkaline solutions we have ensured that the equilibrium is displaced to the chromate ion. Thus for the stoichiometric reaction the amount of chromate ion determined will fall from four moles to two moles as the reaction proceeds to completion. The experiments were carried out using a mixture containing 50% tungsten and 50% potassium dichromate (by weight). This mixture contains a two-fold excess of tungsten. It was prepared by sieve-mixing the weighed components. The tungsten (Murex) had a particle size of 1.0 pm measured by the Fisher sub-sieve sizer. Potassium dichromate was ball-milled to a particle size of 6 pm.