Homologous Series of Chemical Compounds in Three-component Systems (Aa+ – Bb+ – Cc–) and (Zn2+ - Ge4+ - P3-) in Generalized Form

Abstract

For the first time, a method for calculating formulas of homologous series of chemical compounds of the systems (A^a+ – B^b+ – C^c–) and {Zn²⁺ – Ge⁴⁺ – P^3–} in a generalized form is presented. The calculation is confirmed by the literature experimentally obtained compounds: thirteen compounds of the system (N^a+ – Ti⁴⁺ – O^2–), seven – systems (Li⁺ – Ti⁴⁺ – O^2–), five – systems (K⁺ – V5^a+ –  – O^2–), eight – systems (Ba²⁺ – Cu²⁺ – O^2*). Homological series in (A^a+ – B^b+ – C^c–) have the following generalized form: A_{{t – k·r + nr – r)bc}B_racC_{{t – k·r + nr)ab} and A_tbcB_{{r – k·t + nt – t}acC (r – k·t + nt)ab}.
In (Zn²⁺ – Ge⁴⁺ – P^3–) systems for the m-group the formulas of homologous series, that develops towards Ge₃P₄, have the following generalized form: Zn_6tGe_{(6r – 6kt + 6n – 6t)}P_{(8r – 8kt + 8n)}  and for αm-homologous series – Zn₆Ge_3nP_{4(n + 1)}. A method for calculating formulas of homologous series of chemical compounds in a generalized form can be used for any system of chemical elements.