The question asks which compound does not undergo an addition reaction. To answer this, let's first understand the nature of each compound listed in the options:
- \(C_4H_8\): This compound is an alkene. Alkenes have a carbon-carbon double bond (C=C), which is reactive and can readily undergo addition reactions.
- \(C_2H_2\): This compound is acetylene, an alkyne. Alkynes have a carbon-carbon triple bond (C≡C), which can also react through addition reactions.
- \(C_3H_8\): This compound is propane, an alkane. Alkanes have only single bonds (C-C) and are generally saturated hydrocarbons. Alkanes do not have double or triple bonds, so they do not typically undergo addition reactions.
- \(C_2H_4\): This compound is ethylene, another alkene, similar to \(C_4H_8\), with the presence of a C=C double bond that can participate in addition reactions.
Since addition reactions typically occur at sites of unsaturation such as double or triple bonds, the compound \(C_3H_8\) (propane), which is fully saturated, does not undergo addition reactions.
Thus, the correct answer is Option C: \(C_3H_8\).