Formation of Mesitylene Through Various Organic Synthesis Routes

To determine which reaction(s) lead to the formation of $1,3,5$-trimethylbenzene (commonly known as mesitylene), let us analyze each option step-by-step:

1. Option (A):

   • Reaction: Acetone ($\text{CH}_3\text{COCH}_3$) treated with concentrated $\text{H}_2\text{SO}_4$ under heating ($\Delta$).
   • Mechanism: Concentrated $\text{H}_2\text{SO}_4$ acts as a dehydrating and acid-catalyzing agent. Three molecules of acetone undergo an acid-catalyzed intermolecular aldol condensation followed by dehydration: $3\,\text{CH}_3\text{COCH}_3 \xrightarrow{\text{Conc. }\text{H}_2\text{SO}_4,\,\Delta} 1,3,5\text{-trimethylbenzene} + 3\,\text{H}_2\text{O}$
   • Result: This is a classic and well-known synthetic method for preparing $1,3,5$-trimethylbenzene (mesitylene). Hence, Option (A) is correct.

2. Option (B):

   • Reaction: Propyne ($\text{CH}_3-\text{C}\equiv\text{CH}$) passed through a heated iron tube at $873\text{ K}$.
   • Mechanism: Cyclic trimerization of terminal alkynes occurs at high temperatures over transition-metal catalysts (such as an iron or copper tube). The cyclic trimerization of propyne yields a mixture of regioisomers: $3\,\text{CH}_3-\text{C}\equiv\text{CH} \xrightarrow[\text{873 K}]{\text{heated Fe tube}} 1,3,5\text{-trimethylbenzene (mesitylene)} + 1,2,4\text{-trimethylbenzene (pseudocumene)}$
   • Result: Since $1,3,5$-trimethylbenzene is formed as one of the products, Option (B) is correct.

3. Option (C):

   • Reaction: $1,3,5$-triacetylbenzene subjected to:
     1. $\text{Br}_2/\text{NaOH}$ (haloform reaction)
     2. $\text{H}_3\text{O}^+$ (acidification)
     3. Sodalime ($\text{NaOH} + \text{CaO}$), $\Delta$ (decarboxylation)
   • Mechanism:
     • In steps (1) and (2), the methyl ketone groups ($-\text{COCH}_3$) undergo the haloform reaction to form carboxylic acid groups ($-\text{COOH}$), giving benzene-$1,3,5$-tricarboxylic acid (trimesic acid): $\text{C}_6\text{H}_3(\text{COCH}_3)_3 \xrightarrow{1)\,\text{Br}_2,\,\text{NaOH},\; 2)\,\text{H}_3\text{O}^+} \text{C}_6\text{H}_3(\text{COOH})_3$
     • In step (3), heating trimesic acid with sodalime causes complete decarboxylation of all three carboxylic acid groups: $\text{C}_6\text{H}_3(\text{COOH})_3 \xrightarrow{\text{sodalime},\,\Delta} \text{C}_6\text{H}_6 \text{ (benzene)} + 3\,\text{CO}_2$
   • Result: The final product obtained is benzene, not $1,3,5$-trimethylbenzene. Hence, Option (C) is incorrect.

4. Option (D):

   • Reaction: Benzene-$1,3,5$-tricarbaldehyde treated with $\text{Zn/Hg}$ and concentrated $\text{HCl}$ (Clemmensen reduction).
   • Mechanism: The Clemmensen reduction selectively reduces carbonyl groups of aldehydes and ketones to methylene/methyl groups ($-\text{CHO} \to -\text{CH}_3$): $\text{C}_6\text{H}_3(\text{CHO})_3 \xrightarrow{\text{Zn/Hg, HCl}} \text{C}_6\text{H}_3(\text{CH}_3)_3 \text{ (}1,3,5\text{-trimethylbenzene)}$
   • Result: This directly produces $1,3,5$-trimethylbenzene. Hence, Option (D) is correct.

Therefore, the reactions that lead to the formation of $1,3,5$-trimethylbenzene are (A), (B), and (D).