(a) Can \(\mathrm{C}_{6} \mathrm{H}_{12}\) be a saturated hydrocarbon? (b) Are all molecules containing a benzene ring unsaturated?

A saturated hydrocarbon is a hydrocarbon where all carbon atoms are bonded with single bonds, and there are no double or triple bonds between carbon atoms. Saturated hydrocarbons are also called alkanes, and their general formula is \(C_nH_{2n+2}\). An unsaturated hydrocarbon, on the other hand, contains at least one double bond or triple bond between carbon atoms. If there is a double bond, the compound is called an alkene and follows the general formula \(C_nH_{2n}\). If there is a triple bond, the compound is an alkyne with the general formula \(C_nH_{2n-2}\).

In this part, we have to determine whether the given compound \(\mathrm{C}_{6} \mathrm{H}_{12}\) is a saturated hydrocarbon or not. To do this, let's compare the given compound to the general formulas for saturated and unsaturated hydrocarbons. We have a hydrocarbon with 6 carbon atoms and 12 hydrogen atoms, so its formula can be written as: \(C_6H_{12}\) Now let's compare it with the general formula of alkanes (saturated hydrocarbons), which is \(C_nH_{2n+2}\). Plugging n=6 (the given number of carbon atoms) into the alkane formula gives: \(C_6H_{2(6)+2} = C_6H_{14}\) Since \(C_6H_{12}\) is not equal to \(C_6H_{14}\), it cannot be a saturated hydrocarbon. Thus, the answer to part (a) is no, \(\mathrm{C}_{6} \mathrm{H}_{12}\) cannot be a saturated hydrocarbon.

For this part, we need to discuss whether all molecules containing a benzene ring are unsaturated. A benzene ring is a hexagonal ring structure with alternating single and double bonds between adjacent carbon atoms. A molecule containing a benzene ring is considered unsaturated because of the presence of the double bonds between some of its carbon atoms. While the benzene ring may be a part of a larger molecular structure, the presence of these double bonds makes the entire molecule unsaturated. Hence, the answer to part (b) is yes, all molecules containing a benzene ring are considered unsaturated.