Question

Give the molecular formula of a hydrocarbon containing five carbon atoms that is (a) an alkane, (b) a cycloalkane, (c) an alkene, (d) an alkyne. Which are saturated and which are unsaturated hydrocarbons?

Short answer

The molecular formulas for the hydrocarbons with five carbon atoms are: (a) Alkane: \(C_5H_{12}\), (b) Cycloalkane: \(C_5H_{10}\), (c) Alkene: \(C_5H_{10}\), and (d) Alkyne: \(C_5H_8\). Alkanes and cycloalkanes are saturated hydrocarbons, while alkenes and alkynes are unsaturated hydrocarbons.

Step-by-step solution

Write the general molecular formula for each type of hydrocarbon

First, let's write down the general molecular formulas for these types of hydrocarbons: (a) Alkanes: \(C_nH_{2n+2}\) (b) Cycloalkanes: \(C_nH_{2n}\) (c) Alkenes: \(C_nH_{2n}\) (d) Alkynes: \(C_nH_{2n-2}\)

Replace the variables in the molecular formulas with the given number of carbon atoms

Now, let's replace "n" with the given number of carbon atoms, which is 5: (a) Alkane: \(C_5H_{2(5)+2} = C_5H_{12}\) (b) Cycloalkane: \(C_5H_{2(5)} = C_5H_{10}\) (c) Alkene: \(C_5H_{2(5)} = C_5H_{10}\) (d) Alkyne: \(C_5H_{2(5)-2} = C_5H_8\)

Identify the saturated and unsaturated hydrocarbons

(a) Alkane: \(C_5H_{12}\) and (b) Cycloalkane: \(C_5H_{10}\) are saturated hydrocarbons because they have single bonds between carbon atoms. (c) Alkene: \(C_5H_{10}\) and (d) Alkyne: \(C_5H_8\) are unsaturated hydrocarbons because they have carbon-carbon double bonds or triple bonds, respectively.

Key concepts

Alkanes

Alkanes are organic compounds composed entirely of single-bonded carbon and hydrogen atoms, with a general molecular formula of \(C_nH_{2n+2}\). This formula signifies that for each carbon atom in the molecule (symbolized by 'n'), there are two hydrogen atoms plus two additional hydrogens. For a hydrocarbon with five carbon atoms, the alkane formula is \(C_5H_{12}\), indicating a molecule of pentane, which is fully saturated due to the single bonds filling all available valence electrons of carbon. This saturation makes alkanes relatively unreactive.Saturated hydrocarbons, like alkanes, are essential in the energy sector as they are major components of fuels such as propane and butane.

Cycloalkanes

Cycloalkanes are another type of saturated hydrocarbons, but with carbon atoms arranged in rings. These compounds have two less hydrogen atoms than their non-cyclic counterparts because the ends of the chain are bonded to each other to form a cycle, leading to the general molecular formula \(C_nH_{2n}\). A five-carbon cycloalkane, therefore, has the molecular formula \(C_5H_{10}\), representing a compound called cyclopentane. Despite being saturated (all carbons are connected by single bonds), cycloalkanes can show different properties due to the ring strain — tension caused by the geometric constraints of the cyclic structure.

Alkenes

Alkenes are unsaturated hydrocarbons characterized by having at least one double bond between carbon atoms, which is reflected by their general formula \(C_nH_{2n}\). With five carbon atoms, the molecular formula for an alkene is \(C_5H_{10}\). The presence of a double bond in alkenes like pentene allows for isomerism, where molecules with the same formula can differ in the arrangement of the atoms, leading to variations in physical and chemical properties. The unsaturation (double bonds) in alkenes makes them more chemically reactive than alkanes and cycloalkanes.

Alkynes

Alkynes represent a group of hydrocarbons with at least one triple bond between two carbon atoms, denoted by the formula \(C_nH_{2n-2}\). Adhering to this formula, a five-carbon alkyne would have the molecular structure \(C_5H_8\) – known as pentyne. Analogous to alkenes, alkynes are also unsaturated but are even more reactive due to the higher energy and electron-rich triple bond. Alkynes have significant applications in organic synthesis and as intermediates in the preparation of various chemicals.

Saturated and Unsaturated Hydrocarbons

The classification into saturated and unsaturated hydrocarbons is essential when understanding the chemical behavior of these organic compounds. Saturated hydrocarbons, including alkanes and cycloalkanes, contain only single covalent bonds between carbon atoms, resulting in a stable and low-reactivity structure. In contrast, unsaturated hydrocarbons such as alkenes and alkynes possess carbon-carbon double or triple bonds, respectively. These multiple bonds introduce reactive sites into the molecules, making them more interactive and useful in polymerization processes and in making more complex chemical substances. Essentially, the saturation level indicates the hydrocarbon's bonding arrangement, which directly influences its chemical reactivity and practical applications.