Question

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

Short answer

The general formula for any cyclic alkene with one double bond is: \(C_nH_{2n-4}\).

Step-by-step solution

Identify the General Formula for an Alkene

Alkenes are unsaturated hydrocarbons with the general formula C𝑛H2𝑛. The 𝑛 represents the number of carbon atoms in the alkene and the 2𝑛 indicates twice the number of carbon atoms for hydrogen atoms. This general formula applies to both cyclic and non-cyclic (also known as acyclic) alkenes.

Adjust the Formula for Cyclic Alkenes

In a cyclic alkene, the carbon atoms are joined in a ring structure. A ring structure eliminates the need for the additional two hydrogen atoms found in non-cyclic alkenes. As a result, the general formula for a cyclic alkene will have two fewer hydrogen atoms than the general alkene formula. This results in the general formula for cyclic alkenes as C𝑛H2𝑛-2. Here, 𝑛 represents the number of carbon atoms in the cyclic alkene.

Account for the Double Bond

Cyclic alkenes contain at least one carbon-carbon double bond. Since the presence of a double bond means that a cyclic alkene has a double bond and a ring structure, we need to modify the general formula to properly represent this feature. The presence of a double bond reduces the hydrogen count by an additional 2 atoms. Thus, the general formula for a cyclic alkene with one double bond is C𝑛H2𝑛-4. The final general formula for any cyclic alkene with one double bond is: C𝑛H2𝑛-4.