REGRESSION ANALYSIS OF ISOBAR BOILING POINT OF WATER-ORGANIC BINARY MIXTURES

Abstract

We developed an algorithm for separating the non-stochastic contribution to the empirical dependence of the physicochemical properties of binary solutions on the concentrations of the components. The algorithm is based on the different behaviours of stochastic and deterministic coefficients of Fourier expansions.  It was proved that the isolation of a non-additive part of the dependence allows a quantitative description of the contribution of the solvating effects on the system’s energy. In addition, this isolation is necessary for the analytical continuation of the studied function in the formalized area of negative values of concentrations. It was proved that the suggested development allows separating the stochastic part of the empirical data. We determined the qualitative criteria for the separation of deterministic and stochastic Fourier harmonics.

We suggested an efficient three-parameter basis for the regressive description of the isobar of the boiling points of binary solutions. It was proved that the first component of the basis already describes the greater part of non-stochastic empirical information. We formulated a two-stage algorithm for the regressive description of the isobar of the boiling point of aqueous-organic solutions. That algorithm can reduce the amount of necessary empirical information. We also calculated the regression model coefficients for a number of solutions with practical relevance. For most of the investigated solutions, one component of the three-parameter basis fully describes the empirical information. For less than 20% of the studied solutions, the regression basis needs to be supplemented with Fourier harmonics. The number of such harmonics does not exceed two. It was proved that the relative error of the proposed algorithm does not exceed 2% and can be explained by experimental errors.