The general formula for alkenes is given by the expression $C_nH_{2n}$.

Alkenes are a specific class of hydrocarbons, meaning they are composed solely of hydrogen and carbon atoms. In this formula, the variable $n$ denotes the number of carbon atoms present in the molecule. For alkenes, the number of hydrogen atoms is always twice the number of carbon atoms, which is why the formula is expressed as $C_nH_{2n}$.

This relationship arises because alkenes are classified as unsaturated hydrocarbons. Unsaturated hydrocarbons contain at least one carbon-carbon double bond, which limits the number of hydrogen atoms that can be bonded to the carbon atoms. For instance, ethene, the simplest alkene, consists of two carbon atoms and four hydrogen atoms, conforming to the formula $C_nH_{2n}$.

The existence of the double bond imparts distinct chemical properties to alkenes, including their capacity to undergo addition reactions. This reactivity is due to the nature of the double bond, which allows other atoms or groups of atoms to attach themselves across it.

In summary, the general formula $C_nH_{2n}$ succinctly illustrates the relationship between the number of carbon and hydrogen atoms in any alkene molecule. It highlights the characteristic property of alkenes as unsaturated hydrocarbons featuring a carbon-carbon double bond.