Question

Give the general formula for any cyclic alkene, that is, a cyclic hydrocarbon with one double bond.

Short answer

The general molecular formula for cyclic alkenes is \(C_nH_n\), where n represents the number of carbon atoms in the ring.

Step-by-step solution

Understanding the structure of cyclic alkenes

Cyclic alkenes are ring-shaped molecules formed by carbon atoms with one carbon-carbon double bond in the ring structure. These hydrocarbons contain only hydrogen and carbon atoms, and they follow the general rule of having adjacent carbon atoms connected by alternating single and double bonds.

Analyzing the simplest cyclic alkene

The simplest possible cyclic alkene is cyclopropene, which has three carbon atoms in the ring. Cyclopropene has one double bond between two carbon atoms and a single bond connecting the remaining carbon atom. Each carbon atom also has a hydrogen atom bonded to it. The molecular formula for cyclopropene is \(C_3H_4\).

Deriving the general formula for cyclic alkenes

Let's use "n" to represent the number of carbon atoms in the ring. Each carbon atom has two hydrogen atoms bonded to it, with the exception of those connected by the double bond. The two carbon atoms connected by the double bond have only one hydrogen atom bonded to each. So, for a cyclic alkene with n carbon atoms, there will be: - n carbon atoms - (n - 2) hydrogen atoms from the carbon atoms connected by single bonds - 2 hydrogen atoms from the carbon atoms connected by the double bond This results in a total of (n - 2) + 2 = n hydrogen atoms in the molecule. Therefore, the general molecular formula for cyclic alkenes is \(C_nH_n\), where n represents the number of carbon atoms in the ring.