(a) Write the major product in the following reaction (the reactant is the six-membered ring with one C=C double bond shown in the figure below): \( \text{ring} + \mathrm{Br_2} \xrightarrow{\text{heat}} \; ? \)
(b) Define Racemic mixture.
(c) p-dichlorobenzene has a higher melting point as compared to its ortho and meta isomers. Why?
Show Hint
Br2 adds across the C=C bond of cyclohexene to give 1,2-dibromocyclohexane. A racemic mixture is a 50:50 mix of d and l forms. The para isomer is symmetrical and packs better in the crystal.
Step 1: Read the three parts. Part (a) asks for a product. Part (b) asks for a definition. Part (c) asks for a reason. Each part carries 1 mark.
Step 2: Part (a), cyclohexene with bromine. The reactant is cyclohexene, a six-membered ring with one C=C bond. Bromine adds across a double bond. The pi bond opens, and one Br goes on each carbon of the former double bond. This is electrophilic addition through a cyclic bromonium ion. The second bromide attacks from the opposite face, so the two Br atoms end up trans. \[ \text{cyclohexene} + \mathrm{Br_2} \longrightarrow \textit{trans}\text{-1,2-dibromocyclohexane} \] The product is a ring of six carbons with one Br on each of two adjacent carbons.
Step 2b: Part (b), racemic mixture. A racemic mixture is an equimolar (50:50) mixture of the two enantiomers, one dextrorotatory (d) and one laevorotatory (l). The rotation caused by one is cancelled exactly by the other. So the mixture is optically inactive. This is called external compensation.
Step 3: Part (c), melting points of the dichlorobenzenes. The para isomer is highly symmetrical. Its molecules pack closely and neatly in the crystal lattice. Close packing gives stronger intermolecular forces in the solid. The ortho and meta isomers are less symmetrical and fit poorly into the lattice. So they need less energy to melt. Hence p-dichlorobenzene melts at a higher temperature (about 323 K) than the ortho (256 K) and meta (249 K) isomers.
Final Answer: (a) trans-1,2-dibromocyclohexane. (b) An equimolar mixture of d and l enantiomers, which is optically inactive. (c) The para isomer is symmetrical, packs better in the crystal and has stronger lattice forces. \[ \boxed{\text{1,2-dibromocyclohexane}} \]
