Question

Give the molecular formula of a hydrocarbon containing five carben atoms that is (a) an alkane, (b) a cycloalkane, (c) an alkene

Short answer

a) Alkane: \(C_5H_{12}\) b) Cycloalkane: \(C_5H_{10}\) c) Alkene: \(C_5H_{8}\)

Step-by-step solution

Identify general molecular formulas

The general molecular formulas for the three types of hydrocarbons are as follows: - Alkanes: \(C_nH_{2n+2}\) - Cycloalkanes: \(C_nH_{2n}\) - Alkenes: \(C_nH_{2n-2}\) where \(n\) represents the number of carbon atoms in the hydrocarbon.

Determine the molecular formula for an alkane with five carbon atoms

We will use the general molecular formula for alkanes, \(C_nH_{2n+2}\), and substitute \(n=5\) to find the specific molecular formula: Molecular formula = \(C_5H_{2(5)+2}\) = \(C_5H_{12}\) So, the molecular formula of an alkane containing five carbon atoms is \(C_5H_{12}\).

Determine the molecular formula for a cycloalkane with five carbon atoms

We will use the general molecular formula for cycloalkanes, \(C_nH_{2n}\), and substitute \(n=5\) to find the specific molecular formula: Molecular formula = \(C_5H_{2(5)}\) = \(C_5H_{10}\) So, the molecular formula of a cycloalkane containing five carbon atoms is \(C_5H_{10}\).

Determine the molecular formula for an alkene with five carbon atoms

We will use the general molecular formula for alkenes, \(C_nH_{2n-2}\), and substitute \(n=5\) to find the specific molecular formula: Molecular formula = \(C_5H_{2(5)-2}\) = \(C_5H_{8}\) So, the molecular formula of an alkene containing five carbon atoms is \(C_5H_{8}\). #Results# The molecular formulas for a hydrocarbon containing five carbon atoms are: a) Alkane: \(C_5H_{12}\) b) Cycloalkane: \(C_5H_{10}\) c) Alkene: \(C_5H_{8}\)

Key concepts

Alkane Molecular Formula

When we refer to alkanes, we're discussing a family of hydrocarbons that follow a specific pattern in their molecular structure. Alkanes are the simplest form of hydrocarbons, characterized by a fully saturated chain; in other words, the carbon atoms within the chain are connected by single bonds, and each carbon atom has the maximum number of hydrogen atoms attached.

The general molecular formula for alkanes is represented as \(C_nH_{2n+2}\). Each carbon atom in the chain dictates how many hydrogen atoms will be present. For an alkane with five carbon atoms (\(n=5\)), the molecular formula becomes \(C_5H_{12}\), which indicates a chain of five carbon atoms, each bonded to hydrogen to fulfill the valency, resulting in a total of twelve hydrogen atoms.

Cycloalkane Molecular Formula

Cycloalkanes bring a twist to the structure of hydrocarbons by forming cyclic compounds. Unlike their straight-chain relatives, cycloalkanes have their carbon atoms connected in a loop.

This closed-loop structure impacts the molecular formula. While still maintaining single bonds, cycloalkanes have two fewer hydrogen atoms than the corresponding linear alkanes because the end carbons in a straight chain alkane that would've held additional hydrogens are now bonded to each other to form the ring. For this reason, the molecular formula for cycloalkanes is described as \(C_nH_{2n}\). For a cycloalkane with five carbon atoms, this formula simplifies to \(C_5H_{10}\), indicating that the five carbon atoms form a ring, each bound to two hydrogen atoms.

Alkene Molecular Formula

Alkenes form another significant class of hydrocarbons characterized by the presence of at least one carbon-carbon double bond. This unsaturation alters the hydrocarbon's molecular formula as double bonds decrease the number of hydrogen atoms that can attach to the carbon chain.

The general molecular formula for alkenes is represented as \(C_nH_{2n-2}\). Following this pattern, an alkene with five carbon atoms, which incorporates one double bond, would have a molecular formula \(C_5H_{8}\). It's important to note that with alkene structures, the position of the double bond also plays a significant role in the properties and nomenclature of the compound.

Hydrocarbon Chain

The backbone of hydrocarbon molecules is known as the hydrocarbon chain. It's a sequence of carbon atoms bonded together, either in a linear or cyclic form, and hydrogen atoms fill in the remaining bonds. The type of bonding (single, double, or triple) within the chain is what distinguishes different classes of hydrocarbons - alkanes having single bonds, alkenes with at least one double bond, and alkynes that are not covered here but are characterized by triple bonds.

These chains can vary in length and structure, leading to a vast diversity of hydrocarbon compounds. The length and arrangement of the hydrocarbon chain are decisive for the physical and chemical properties of the substance, including boiling points, melting points, and reactivity.

Carbon Atoms in Hydrocarbons

The role of carbon atoms in hydrocarbons is fundamental. Carbon, due to its ability to form four covalent bonds, acts as a versatile building block that can create chains and rings of varying lengths and complexities.

In a hydrocarbon molecule, the number of carbon atoms is denoted by the letter 'n', and this number is crucial when determining the compound's molecular formula. For instance, in the context of our examples with five carbon atoms, the number of carbon atoms directly affects the number of hydrogen atoms in alkanes (\(2n+2\)), cycloalkanes (\(2n\)), and alkenes (\(2n-2\)). The versatility of carbon allows for an immense variety of hydrocarbons, both in terms of structure and function, which is why they are the fundamental basis for all organic chemistry.