Question #44944

An aqueous solution of 4-methylbenzenediazonium chloride ($0.10\text{ M}$) is prepared at $273\text{ K}$ in dilute $\ce{HCl}$. The thermal decomposition of this diazonium salt to 4-methylphenol and $\ce{N2(g)}$ proceeds via an $\text{S}_\text{N}1$ mechanism. The first-order rate constant for this decomposition is $k = 6.93 \times 10^{-2}\text{ min}^{-1}$ at $298\text{ K}$.

During a synthesis protocol, the cooling bath fails, and the acidic reaction mixture is inadvertently exposed to $298\text{ K}$ for exactly 20 minutes. The mixture is then rapidly quenched to $273\text{ K}$, and an excess of alkaline naphthalen-2-ol ($\beta$-naphthol) is immediately added to achieve complete electrophilic aromatic substitution.

Assuming no volume change and quantitative coupling of the surviving diazonium ions, identify the major organic products in the final mixture (excluding unreacted naphthalen-2-ol) and their exact molar ratio. (Given: $\ln 2 = 0.693$)