Approximation of Alternating Melting Temperatures of Homologs Using Second-Order Recurrence Relations

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Abstract

The first-order recurrence relations A(nC + 1) = aA(nC) + b are applicable for approximation of variations of various properties of organic compounds (A) in homologous series, otherwise, depending on the number of carbon atoms in molecules, nC. However, they are unsuitable for approximation of melting temperatures (Tmel) because of the alteration of their values in homologues with even and odd number of carbon atoms in molecules for many series. It is confirmed that the solution of this problem is possible using the second-order recurrence relations, A(nC + 2) = aA(nC) + b. An explanation of this fact is proposed: the algebraic nonrecurrence solution of this recurrence equation, contains the denominator (–√а)nC, the sign of which is a function of parity or oddness of the number of carbon atoms in the molecule. Such kind of functions for characterization of alternating properties of homologues is proposed for the first time. It is shown that in order to achieve the greatest accuracy of approximation, preliminary statistical processing of Tmelt values from different sources with calculation of mean values, their standard deviations, and rejection of unreliable data is necessary. As an example of such processing, the example of T(fused) of n-alkancarboxylic acids with 0 ≤ nC ≤ 35 is considered in detail. The errors of the recurrence approximation of Tplavl homologues by the characterized method do not exceed the standard deviations of randomized interlaboratory data.

About the authors

I. G. Zenkevich

St. Petersburg State University, Institute of Chemistry

Email: izenkevich@yandex.ru
St. Petersburg, Russia

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