Discuss how you can determine which of the following compounds might be alkanes, cycloalkanes, alkenes, or alkynes, without drawing their formulas: (a) \(\mathrm{C}_{6} \mathrm{H}_{12}\) (b) \(\mathrm{C}_{4} \mathrm{H}_{6}\) (c) \(\mathrm{C}_{5} \mathrm{H}_{12}\) (d) \(\mathrm{C}_{7} \mathrm{H}_{14}\) (e) \(\mathrm{C}_{3} \mathrm{H}_{4}\)

Alkanes are the simplest type of hydrocarbons that consist only of carbon (C) and hydrogen (H) atoms with single covalent bonds between the carbon atoms. They follow a general formula of ewline C_nH_{2n+2}ewline where n represents the number of carbon atoms. Because of the single bonded structure, alkanes are known to be saturated hydrocarbons. This means they have the maximum number of hydrogen atoms possible for the given number of carbon atoms.

Due to their structure, alkanes are not highly reactive and have relatively low chemical reactivity, which makes them quite stable. The names of alkanes end with the suffix '-ane', and they are often used as a reference point for identifying other types of hydrocarbons.

Cycloalkanes, as the prefix 'cyclo-' implies, are alkanes that form a closed ring structure. Unlike straight-chain alkanes, cycloalkanes have a general formula of ewline C_nH_{2n} ewline which reflects the fact that they have two fewer hydrogen atoms than their straight-chain alkane counterparts with the same number of carbon atoms. This is because each end of an alkane chain would normally have three hydrogen atoms, but when the ends join to form a ring, each end loses a hydrogen atom.

Cycloalkanes share similar properties with alkanes, such as being saturated hydrocarbons. However, due to the ring structure, they may have different physical properties and slightly higher reactivities than linear alkanes.

Alkenes are unsaturated hydrocarbons that contain at least one double bond between two carbon atoms. Their general formula is given by ewline C_nH_{2n} ewline which is the same as cycloalkanes but differs by their structure. Because the presence of a double bond means that two hydrogen atoms are missing compared to an alkane. The existence of this double bond introduces the possibility of geometrical isomerism and gives alkenes their characteristic reactivity, enabling them to participate in addition reactions. These reactions make alkenes much more reactive than alkanes. The naming of alkenes follows the suffix '-ene' to indicate the presence of at least one double bond.

Alkynes are another category of unsaturated hydrocarbons distinguished by the presence of a triple bond between two carbon atoms. Their general formula is ewline C_nH_{2n-2} ewline and represents the fact that they have two fewer hydrogen atoms than the alkenes for the same number of carbon atoms. The triple bond presents significant chemical reactivity and can undergo addition reactions similar to those of alkenes, but with the added complexity provided by the triple bond's reactivity. Alkynes are denoted by the suffix '-yne' to indicate the presence of this triple bond.

Alkynes, like alkenes, can form isomers. Due to the linear nature of the triple bond, alkynes are less likely than alkenes to form structural isomers but can form isomers based on the position of the triple bond within the molecule.

The general formula for hydrocarbons is an essential concept for determining the type of hydrocarbon based on its molecular formula. In this context, a molecular formula represents the actual number of carbon and hydrogen atoms in a molecule. For saturated alkanes, the formula is ewline C_nH_{2n+2} ewline reflecting a molecule with no double or triple bonds. As we have seen, the formula changes for unsaturated hydrocarbons, such as alkenes and alkynes, due to the presence of double or triple bonds.When analyzing a molecular formula, like those given in the original exercise, identifying if the hydrocarbon is an alkane, cycloalkane, alkene, or alkyne, often involves comparing the number of hydrogens to carbons. If the hydrogens are less than double the number of carbons plus two, the hydrocarbon is unsaturated. If not, it potentially is a saturated alkane or a ring structure like a cycloalkane, requiring further analysis to confirm.