Question #44394

Consider the following reaction sequences starting from phenol:

Reaction I: Phenol $\xrightarrow[125^\circ\text{C, 5 atm}]{\text{1. } NaOH, CO_2} \xrightarrow{\text{2. } H_3O^+} \mathbf{P}$ (Major Product)

Reaction II: Phenol $\xrightarrow[150^\circ\text{C, 5 atm}]{\text{1. } KOH, CO_2} \xrightarrow{\text{2. } H_3O^+} \mathbf{Q}$ (Major Product)

Let $c$ and $d$ be the position numbers of the carbon atoms attached to the $-COOH$ group in the aromatic rings of $\mathbf{P}$ and $\mathbf{Q}$ respectively, strictly assigning the carbon attached to the $-OH$ group as position 1.

When $\mathbf{P}$ and $\mathbf{Q}$ are treated separately with excess aqueous bromine ($Br_2/H_2O$), they undergo electrophilic aromatic substitution to form products $\mathbf{X}$ and $\mathbf{Y}$ respectively. Let $a$ and $b$ be the total number of bromine atoms present in one molecule of $\mathbf{X}$ and $\mathbf{Y}$ respectively.

Calculate the value of the expression: $(c \times d) + (a \times b)$.