Spectrophotometric determination of dissociation constants for propionic acid and 2,5-dinitrophenol at elevated temperatures

Using the temperature dependence of pK_a for acetic acid, the pK_a for 2,5-dinitrophenol have been spectrophotometrically determined in acetate buffer at elevated temperatures under the saturation vapor pressures. For 2,5-dinitrophenol $$pK_a = - 33.206 + 2106.7/T + 5.495\ln T$$ where T is in Kelvin. Similarly, pK_a values of propionic acid were obtained at temperatures from 25°C to 175°C producing $$pK_a = - 43.703 + 2128.6/T + 7.2686\ln T$$ From this result, several thermodynamic functions of propionic acid were calculated and compared with those obtained from emf measurement.     

A remark on nilpotent Lie Algebras

Letf(n) denoted the number of essential parameters which are needed to classifyn-dimensional nilpotent Lie Algebras over the complex number field. Then $f(2n) \geqslant \tfrac{{n(n2 - 7)}}{6} - 2$ .