Show how you would accomplish each of the following synthetic conversions.

a) Trans-but-2-ene$\to$trans-1,2-dimethylcyclopropane

b) Cyclopentene$\to$

c) Cyclohexanol$\to$

Carbene insertion reaction is inserting carbene into electron rich pi$\left(\text{C}=\text{C}\right)$ bond double bond of an alkene. This reaction is a concerted reaction that occurs in a single step only.

Trans-2-butene on reaction with methylene iodide, ${\text{CH}}_2{\text{I}}_2$ and zinc-copper couple, $\mathrm{Zn}-\mathrm{Cu}$ gives trans-cyclopropane as the product..This reaction is known as Simmons-Smith reaction. This reaction is stereospecific, which means trans-alkene will convert to trans-cyclopropane and cis-alkene will convert to cis-cyclopropane.

Sodium hydroxide, on reaction with methylene bromide produces carbene :${\text{CBr}}_2$, which is singlet carbine. This will then undergo insertion reaction at the double bond of cyclopentene and form bromocyclopropane. In the process, one bromide ion acts as a leaving group.

Cyclohexanol, on reaction with sulphuric acid followed by heating undergoes dehydration, that is, loss of water molecules. It produces cyclohexene as the product. Then, on further reaction with trichloromethane, ${\text{CHCl}}_3$and a base such as sodium hydroxide, $\text{NaOH}$, a singlet carbene is produced, that is, ${\text{CCl}}_2$, which undergoes insertion reaction at the double bond and forms chlorocyclopropane as the product with the loss of one chloride ion which acts as a leaving group.