A confused student was doing an isomer problem and listed the following six names as different structural isomers of \(\mathrm{C}_{7} \mathrm{H}_{16}\) a. 1 -sec-butylpropane b. 4 -methylhexane c. 2 -ethylpentane d. 1 -ethyl-1-methylbutane e. 3 -methylhexane f. 4 -ethylpentane How many different structural isomers are actually present in these six names?

Structural isomers are molecules with the same molecular formula but have a different arrangement of atoms. They have the same number of atoms of each element but are connected in a different order. In this problem, all the molecules have the molecular formula of \(\mathrm{C}_{7} \mathrm{H}_{16}\), and we need to figure out if they have different structures.

Before we begin, let's familiarize ourselves with the prefixes used in naming hydrocarbons: Methyl - CH3 Ethyl - CH2CH3 Propyl - CH2CH2CH3 Butyl - CH2CH2CH2CH3 Pentyl - CH2CH2CH2CH2CH3 Now, let's draw the structures of the given hydrocarbons: a. 1-sec-butylpropane - sec-butyl: (CH3)2CHCH2 - propane: CH3CH2CH3 b. 4-methylhexane - methyl: CH3 - hexane: CH3(CH2)4CH3 c. 2-ethylpentane - ethyl: CH2CH3 - pentane: CH3(CH2)3CH3 d. 1-ethyl-1-methylbutane - ethyl: CH2CH3 - methyl: CH3 - butane: CH3(CH2)2CH3 e. 3-methylhexane - methyl: CH3 - hexane: CH3(CH2)4CH3 f. 4-ethylpentane - ethyl: CH2CH3 - pentane: CH3(CH2)3CH3

Now that we have drawn the structures of the given hydrocarbons, let's identify which of them are different structural isomers: a. 1-sec-butylpropane: - Structure: (CH3)2CHCH2CH2CH2CH3 , a different structure. b. 4-methylhexane: - Structure: CH3CH2CH2CH(CH3)CH2CH3, a different structure. c. 2-ethylpentane: - Structure: CH3CH(CH2CH3)CH2CH2CH3, a different structure. d. 1-ethyl-1-methylbutane: - Structure: CH3CH2CH(CH3)CH2CH3, this structure is the same as 2-ethylpentane (c). e. 3-methylhexane: - Structure: CH3CH2CH(CH3)CH2CH2CH3, a different structure. f. 4-ethylpentane: - Structure: CH3CH2CH2CH(CH2CH3)CH3, a different structure. Looking at the structures, we can see that there are 5 different structural isomers present in these six names (excluding the repeat of 1-ethyl-1-methylbutane, which is the same as 2-ethylpentane).