The study of carbon-containing compounds forms the basis of organic chemistry. Among these are hydrocarbons, molecules constructed solely from carbon and hydrogen atoms. Chemists utilize systematic approaches to organize these millions of unique molecules into manageable groups. One such organizational tool is the concept of the homologous series, which classifies compounds based on shared structural features and predictable properties. Understanding the general formula for a series is the first step in unlocking the chemical identity of all its members.
Defining a Homologous Series
A homologous series is a family of organic compounds that share a common relationship in their molecular structure. All members within one series are represented by the exact same algebraic general formula. This shared formula indicates that every molecule in the group possesses the same defining functional group, which dictates its chemical reactivity.
Successive members in a homologous series are differentiated by the consistent addition of one methylene group, which is a unit composed of one carbon and two hydrogen atoms (\(CH_2\)). For example, moving from the three-carbon propane to the four-carbon butane, the molecular mass increases by approximately 14 atomic mass units. Due to the presence of the same functional group, all compounds in the series exhibit highly similar chemical properties and undergo comparable types of reactions, such as addition reactions.
The physical properties of the compounds, such as melting points and boiling points, do not remain constant but instead change in a predictable, graded manner. As the carbon chain length increases, the molecular size and mass also increase, leading to a corresponding, gradual rise in boiling temperature. This systematic change helps chemists predict the physical characteristics of larger molecules within the series.
The General Formula for the Series Including Ethene
The specific homologous series that includes the two-carbon molecule known as ethene (\(C_2H_4\)) is formally called the Alkene series. This family of hydrocarbons is defined by the presence of at least one carbon-carbon double bond within the molecule’s structure. The general formula used to describe the composition of non-cyclic alkenes is \(C_nH_{2n}\).
In this formula, the letter ‘n’ represents the total number of carbon atoms present in the molecule’s principal chain. The number of hydrogen atoms is precisely determined by taking the carbon number ‘n’ and multiplying it by two, resulting in \(2n\) hydrogen atoms. This specific ratio of hydrogen to carbon is a direct result of the structural requirement of the double bond.
For example, to determine the chemical formula for the three-carbon alkene, propene, one substitutes the number three for ‘n’ in the general formula. The resulting formula becomes \(C_3H_{(2 \times 3)}\), which simplifies to \(C_3H_6\). This formula holds true for all straight-chain alkenes, provided ‘n’ is two or greater.
The doubling of the hydrogen count relative to the carbon count is necessary because the formation of one double bond effectively removes two hydrogen atoms compared to a fully saturated molecule. This simple algebraic formula efficiently captures the composition of every straight-chain and branched alkene, starting with \(n=2\) for ethene.
How the Formula Determines Molecular Structure
The general formula \(C_nH_{2n}\) indicates that all members of the Alkene series are categorized as unsaturated hydrocarbons. An unsaturated molecule does not contain the maximum possible number of hydrogen atoms for its carbon framework. This deficiency is compensated for by the presence of at least one carbon-carbon multiple bond.
The structural feature that defines this series is the double bond, which serves as the molecule’s functional group and the site of its chemical activity. Unlike single bonds, the double bond consists of a sigma bond and a pi bond, making it more accessible for reaction. Ethene, the simplest member, demonstrates this with its two carbon atoms sharing a double bond, resulting in a flat, trigonal planar geometry around each carbon.
This double bond gives alkenes their characteristic chemical behavior, allowing them to participate readily in addition reactions. During an addition reaction, the pi bond breaks, and the two carbon atoms bond with two new atoms or groups, converting the unsaturated alkene into a saturated product. The formula defines a class of compounds characterized by high chemical potential at the double bond site.