# pKa explanation through empirical formula?

Suppose two compounds with, say, $\mathrm{p}K_{\mathrm{a}1}=2.8$ and $\mathrm{p}K_{\mathrm{a}2}=3.2$, and formulae $\ce{C_{$a$}H_{$b$}O_{$c$}}=\ce{C_{$p$}O_{$q$}(OH)_{$r$}}$ and $\ce{C_{$d$}H_{$e$}O_{$f$}}=\ce{C_{$u$}O_{$v$}(OH)_{$w$}}$, respectively, with given $abcdef$, $pqruvw$. Can we explain the above $\mathrm{p}K_\mathrm{a}$ with (ONLY) the knowledge of the given numbers of atoms of $\ce{C}$, $\ce{H}$ and $\ce{O}$ using the theory of Usanovich, and no knowledge of the internal chemical structure of the chemical bonds inside the two molecules?

No, nobody's theory (including Usanovich's) can explain $\ce{pK_{a}}$ differences based on molecular formula coefficients. This is best illustrated by the observation that even compounds with the same coefficients (same values for "abcdef") can have different $\ce{pK_{a}}$ values. For example, $\ce{C3H6O}$
\begin{aligned} \ce{&acetone &&pK_{a}=20}\\ \ce{&allyl~ alcohol &&pK_{a}=$15.5$}\\ \end{aligned}