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 \(C_nH_{2n-2}\).

Step-by-step solution

Understand cyclic alkenes

A cyclic alkene is a hydrocarbon molecule with a ring structure, containing a double bond between two carbon atoms. Cyclic alkenes are unsaturated, meaning they have the ability to form more bonds with other atoms because of the presence of the double bond.

Identify hydrocarbon formula

A hydrocarbon is a compound that consists of only hydrogen and carbon atoms. The general formula of a hydrocarbon is C_nH_m, where n represents the number of carbon atoms and m represents the number of hydrogen atoms.

Determine general formula for cyclic alkene with one double bond

For a cyclic alkene with one double bond, we first need to determine the number of carbon atoms in the molecule. Each carbon atom in a cyclic alkene contributes two hydrogen atoms, except for the two carbon atoms with a double bond. These two carbon atoms, with the double bond, contribute one hydrogen atom each to the compound. To create a general formula, we can represent the number of carbon atoms by the variable n. For the hydrogen atoms in the molecule with no double bond, there are 2(n-2) hydrogen atoms, and for the hydrogen atoms in the two carbon atoms with a double bond, there are 2 hydrogen atoms. Adding these two terms together gives the total number of hydrogen atoms: 2(n-2) + 2.

Simplify general formula

Combining the expressions for carbon and hydrogen atoms from step 3, we obtain the general formula for a cyclic alkene with one double bond: C_nH_{2(n - 2) + 2} Simplifying the formula: C_nH_{2n - 4 + 2} C_nH_{2n - 2} So, the general formula for any cyclic alkene with one double bond is \(C_nH_{2n-2}\).