Properties and Reactions of By Product in Cumene Process

To determine the correct statements, let us trace the series of chemical reactions given in the problem step-by-step:

1. Identification of Compound $\mathbf{P}$

In the industrial preparation of phenol via the cumene process, $iso$-propylbenzene (cumene) reacts with oxygen ($\text{O}_2$) to form cumene hydroperoxide. Subsequent treatment with aqueous acid ($\text{H}_3\text{O}^+$) results in the rearrangement and cleavage to produce phenol ($\text{C}_6\text{H}_5\text{OH}$) and acetone ($\text{CH}_3\text{COCH}_3$) as a by-product. $\text{C}_6\text{H}_5\text{CH(CH}_3)_2 + \text{O}_2 \longrightarrow \text{C}_6\text{H}_5\text{C(CH}_3)_2\text{OOH} \xrightarrow{\text{H}_3\text{O}^+} \text{C}_6\text{H}_5\text{OH} + \underbrace{\text{CH}_3\text{COCH}_3}_{\text{By-product }\mathbf{P}}$

Thus, compound $\mathbf{P}$ is acetone ($\text{CH}_3\text{COCH}_3$).

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2. Identification of Compound $\mathbf{Q}$

Reaction of acetone ($\mathbf{P}$) with $3$ equivalents of $\text{Cl}_2$ leads to the replacement of three $\alpha$-hydrogen atoms on one methyl group by chlorine atoms: $\text{CH}_3\text{COCH}_3 + 3\text{Cl}_2 \longrightarrow \underbrace{\text{CCl}_3\text{COCH}_3}_{\mathbf{Q}} + 3\text{HCl}$

Thus, compound $\mathbf{Q}$ is 1,1,1-trichloroacetone ($\text{CCl}_3\text{COCH}_3$).

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3. Identification of Compounds $\mathbf{R}$ and $\mathbf{S}$

Treatment of 1,1,1-trichloroacetone ($\mathbf{Q}$) with calcium hydroxide ($\text{Ca(OH)}_2$) causes base-catalyzed nucleophilic cleavage (haloform reaction mechanism): $2\text{CCl}_3\text{COCH}_3 + \text{Ca(OH)}_2 \longrightarrow 2\underbrace{\text{CHCl}_3}_{\mathbf{R}} + \underbrace{(\text{CH}_3\text{COO})_2\text{Ca}}_{\mathbf{S}}$

Thus,

• Compound $\mathbf{R}$ is chloroform ($\text{CHCl}_3$).
• Calcium salt $\mathbf{S}$ is calcium acetate ($(\text{CH}_3\text{COO})_2\text{Ca}$).

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4. Analysis of Options

• Option (A): Reaction of acetone ($\mathbf{P}$) with chloroform ($\mathbf{R}$) in the presence of a strong base like $\text{KOH}$ is a nucleophilic addition reaction leading to the formation of chloretone ($1,1,1\text{-trichloro-2-methylpropan-2-ol}$): $\text{CH}_3\text{COCH}_3 + \text{CHCl}_3 \xrightarrow{\text{KOH}} (\text{CH}_3)_2\text{C(OH)CCl}_3$ This matches the structure given in option (A). Hence, Option (A) is correct.

• Option (B): Chloroform ($\mathbf{R} = \text{CHCl}_3$), in the presence of air ($\text{O}_2$) and light, undergoes slow oxidation to form phosgene gas ($\text{COCl}_2$): $2\text{CHCl}_3 + \text{O}_2 \xrightarrow{h\nu} 2\text{COCl}_2 + 2\text{HCl}$ Hence, Option (B) is correct.

• Option (C): When 1,1,1-trichloroacetone ($\mathbf{Q}$) is treated with aqueous $\text{NaOH}$, it undergoes haloform cleavage to yield sodium acetate and chloroform: $\text{CCl}_3\text{COCH}_3 + \text{NaOH} \longrightarrow \text{CH}_3\text{COONa} + \text{CHCl}_3$ It does not form $\text{Cl}_3\text{CCH}_2\text{OH}$ and $\text{Cl}_3\text{CCOONa}$ (which are Cannizzaro reaction products of chloral, $\text{CCl}_3\text{CHO}$). Hence, Option (C) is incorrect.

• Option (D): Dry distillation (heating) of calcium acetate ($\mathbf{S}$) yields acetone ($\mathbf{P}$) and calcium carbonate: $(\text{CH}_3\text{COO})_2\text{Ca} \xrightarrow{\Delta} \underbrace{\text{CH}_3\text{COCH}_3}_{\mathbf{P}} + \text{CaCO}_3$ Hence, Option (D) is correct.

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Conclusion

The correct options are A, B, and D.