To solve the problem of identifying the general formula of alkenes, we need to review some fundamental chemistry concepts concerning hydrocarbons:

Alkenes are a class of hydrocarbons characterized by at least one carbon-carbon double bond. They are unsaturated hydrocarbons, meaning they have fewer hydrogen atoms attached compared to alkanes (which have only single bonds and are saturated).

The general molecular formula for alkenes is given by the expression:

C_nH_{2n}

Here's a step-by-step explanation for deriving this:

1. The simplest alkene is ethene (commonly known as ethylene), with the molecular formula C_2H_4. Following the formula C_nH_{2n}, for n=2, the number of hydrogens is 2 \times 2 = 4.
2. For a three-carbon alkene, propene, the formula is C_3H_6. Again, this matches the pattern C_nH_{2n}.
3. Continuing this pattern, for any alkene with 'n' carbon atoms, the number of hydrogen atoms will be '2n'. This results from the one double bond reducing the maximum number of hydrogen atoms by two compared to alkanes, which are fully saturated compounds.

Now let's evaluate the provided options against this understanding:

• C_nH_{2n-2}: This is the general formula for alkynes, not alkenes, as alkynes have a triple bond.
• C_nH_{2n+2}: This is the formula for alkanes, which are saturated hydrocarbons.
• C_nH_n: This is not a standard formula for any main class of hydrocarbons.
• C_nH_{2n}: The correct formula for alkenes, as explained.

Therefore, the correct answer is C_nH_{2n}. This formula represents the molecular structure of alkenes, consistent with their characteristic carbon-carbon double bond.