Question #44383

Consider the following aromatic carboxylic acids (typical products of Kolbe-Schmitt type reactions): I. \ce{2-Hydroxybenzoic acid} II. \ce{2,4-Dihydroxybenzoic acid} III. \ce{2,4,6-Trihydroxybenzoic acid} IV. \ce{2,6-Dihydroxybenzoic acid} V. \ce{3-Hydroxybenzoic acid}

These acids undergo acid-catalyzed decarboxylation via an $S_E2$ mechanism (electrophilic attack of $H^+$ at the ipso-carbon). Let $N$ be the rank of \ce{2,4-Dihydroxybenzoic acid} when the above acids are arranged in decreasing order of their decarboxylation rate (i.e., Rank 1 = fastest). Let $M$ be the total number of oxygen atoms in the most reactive acid among the given list. Let $P$ be the number of $\pi$ electrons delocalized in the arenium ion (Wheland intermediate) formed during the rate-determining step of this decarboxylation. Calculate the value of $(N \times P) + M$.