Abstract
For the first time, a method for calculating formulas of homologous series of chemical compounds of the systems (Aa+ – Bb+ – Cc–) and {Zn2+ – Ge4+ – P3–} in a generalized form is presented. The calculation is confirmed by the literature experimentally obtained compounds: thirteen compounds of the system (Na+ – Ti4+ – O2–), seven – systems (Li+ – Ti4+ – O2–), five – systems (K+ – V5a+ – – O2–), eight – systems (Ba2+ – Cu2+ – O2*). Homological series in (Aa+ – Bb+ – Cc–) have the following generalized form: A{t – k·r + nr – r)bcBracC{t – k·r + nr)ab and AtbcB{r – k·t + nt – t}acC (r – k·t + nt)ab.
In (Zn2+ – Ge4+ – P3–) systems for the m-group the formulas of homologous series, that develops towards Ge3P4, have the following generalized form: Zn6tGe(6r – 6kt + 6n – 6t)P(8r – 8kt + 8n) and for αm-homologous series – Zn6Ge3nP4(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.
![System (Aa+ – Bb+ – Cc–): αp-HS (AcCa direction) and αm-HS (BcCb direction). αp-HS: (p. 1 = TChCln(bas) = 1 = [AbcBacCab]abc+), (p. 2 = TCCn(bas) = 1 = AbcBacC2ab) (p. 3 = TwChCln(bas) = 1 = [AbcBac]2abc+), (p. 4 = TChCln = 2 = [A2bcBacC2ab]abc+), (p. 5 = TCCn = 2 = A2bcBacC3ab, (p. 6 = TwChCln = 2 = [A2bcBac]3abc+); αm-HS: (p. 1 = TChCln(bas) = 1 = [AbcBacCab]abc+), (p. 2 = TCCn(bas) = 1 = AbcBacC2ab), (p. 3 = TwChCln(bas) = 1 = [AbcBac]2abc+), (p. 7 = TChCln = 2 = [AbcB2acC2ab]abc+), (p. 8 = TCCn = 2 = AbcB2acC3ab, (p. 9 = TwChCln = 2 = [AbcB2ac]3abc+).](https://www.igminresearch.es/articles/figures/igmin117/igmin117.g001.png)
![System (Aa+ – Bb+ – Cc–): p-group HS (AcCa direction). (p. 10 = TCCn(bas) = 1 = AtbcBracC(t + r)ab), (p. 11 = TChCln(bas) = 1 = [AtbcBracCt ab]rabc+), (p. 12 = TwChCln(bas) = 1 = [AtbcBrac](t + r)abc+), (p. 13 = TChCln = 2 = [A(t + r)bcBracC(t + r)ab]rabc+), (p. 14 = TCCn = 2 = A(t + r)bcBracC(t + 2r)ab, (p. 15 = TwChCln = 2 = [A(t + r)bcBrac](t + 2r)abc+), (p. 16 = TChCln = 3 = A(t + 2r)bcBracC(t +2 r)ab]rabc+), (p. 17 = TCCn = 3 = A(t + 2r)bcBracC(t + 3r)ab, (p. 18 = TwChCln = 3 = [A(t + 2r)bcBrac](t + 3r)abc+).](https://www.igminresearch.es/articles/figures/igmin117/igmin117.g002.png)
![System (Aa+ – Bb+ – Cc–): m-group HS (BcCb direction). (p. 19 = TCCn(bas) = 1 = AtbcBracC(t + r)ab), (p. 20 = TChCln(bas) = 1 = [AtbcBracCrab]tabc+), (p. 21 = TwChCln(bas) = 1 = [AtbcBrac](t + r)abc+), (p. 22 = TChCln = 2 = [AtbcB(t + r)acC(t + r)ab]tabc+),(p. 23 = TCCn = 2 = AtbcB(t + r)acC(2t + r)ab, (p. 24 = TwChCln = 2 = [AtbcB(t + r)ac](2t + r)abc+), (p. 25 = TChCln = 3 = [AtbcB(2t + r)acC(2t + r)ab]tabc+), (p. 26 = TCCn = 3 = AtbcB(2t + r)acC(3t + r)ab, (p. 27 = TwChCln = 3 = [AtbcB(2t + r)ac](3t + r)abc+).](https://www.igminresearch.es/articles/figures/igmin117/igmin117.g003.png)
