Understanding Homologous Series and General Formulas

A homologous series is a series of compounds with the same general formula, usually varying by a single parameter such as the length of a carbon chain. Members of a homologous series have similar chemical properties due to the presence of the same functional group, and their physical properties show a gradual change with increasing molecular mass.

In organic chemistry, alkanes, alkenes, and alkynes are common examples of homologous series based on hydrocarbons.

General Formulas for Hydrocarbon Homologous Series

Each homologous series can be represented by a unique general formula that relates the number of carbon atoms (n) to the number of hydrogen atoms. Let's look at the standard, correct general formulas:

• Alkanes: These are saturated hydrocarbons containing only single bonds. The general formula is \(\text{C}_n\text{H}_{2n+2}\), where n >= 1. Examples: Methane (\(\text{CH}_4\), n=1), Ethane (\(\text{C}_2\text{H}_6\), n=2).
• Alkenes: These are unsaturated hydrocarbons containing at least one carbon-carbon double bond. The general formula is \(\text{C}_n\text{H}_{2n}\), where n >= 2. Examples: Ethene (\(\text{C}_2\text{H}_4\), n=2), Propene (\(\text{C}_3\text{H}_6\), n=3).
• Alkynes: These are unsaturated hydrocarbons containing at least one carbon-carbon triple bond. The general formula is \(\text{C}_n\text{H}_{2n-2}\), where n >= 2. Examples: Ethyne (\(\text{C}_2\text{H}_2\), n=2), Propyne (\(\text{C}_3\text{H}_4\), n=3).

Analyzing the Given Formulas

The question provides several formulas and asks to choose the INCORRECT one among the options. Let's compare the given formulas with the standard correct ones:

Evaluating the Options

The options present combinations or single formulas. We need to find the option that contains a formula identified as incorrect for its stated homologous series.

• Option 1: Alkane - \(\text{C}_n\text{H}_{2n+2}\) and Alkyne - \(\text{C}_n\text{H}_{2n-2}\). Both formulas are correct for their respective series. This option is not the answer.
• Option 2: Alkene - \(\text{C}_n\text{H}_{2n+3}\). The standard formula for Alkene is \(\text{C}_n\text{H}_{2n}\). The formula \(\text{C}_n\text{H}_{2n+3}\) is incorrect for an alkene. This option contains an incorrect formula.
• Option 3: Alkane - \(\text{C}_n\text{H}_{2n+2}\). This formula is correct for an alkane. This option is not the answer.
• Option 4: Alkyne - \(\text{C}_n\text{H}_{2n-2}\). This formula is correct for an alkyne. This option is not the answer.

Based on the analysis, the formula Alkene - \(\text{C}_n\text{H}_{2n+3}\) is indeed incorrect. The formula \(\text{C}_n\text{H}_{2n+1}\) given in the question stem for Alkene is also incorrect (it represents an alkyl group), but option 2 specifically highlights \(\text{C}_n\text{H}_{2n+3}\) as the formula to consider, and it is definitively incorrect for an alkene.

Conclusion

The question asks for the INCORRECT formula. Comparing the options to the standard general formulas for homologous series, the formula \(\text{C}_n\text{H}_{2n+3}\) given for an Alkene in option 2 is incorrect. The correct general formula for an alkene is \(\text{C}_n\text{H}_{2n}\).

Revision Table: Homologous Series Formulas

Additional Information on Homologous Series

Besides alkanes, alkenes, and alkynes, other classes of organic compounds also form homologous series based on their functional groups. For example:

• Alcohols: General formula \(\text{C}_n\text{H}_{2n+1}\text{OH}\) (or \(\text{C}_n\text{H}_{2n+2}\text{O}\)). Examples: Methanol (\(\text{CH}_3\text{OH}\)), Ethanol (\(\text{C}_2\text{H}_5\text{OH}\)).
• Carboxylic Acids: General formula \(\text{C}_n\text{H}_{2n+1}\text{COOH}\) (or \(\text{C}_n\text{H}_{2n+2}\text{O}_2\)). Examples: Methanoic acid (\(\text{HCOOH}\)), Ethanoic acid (\(\text{CH}_3\text{COOH}\)). Note that for carboxylic acids, 'n' often represents the number of carbon atoms in the alkyl chain attached to the COOH group, so the total carbons would be n+1. A more general formula considering total carbons could be \(\text{C}_k\text{H}_{2k}\text{O}_2\) where k >= 1.

Each successive member in a homologous series differs by a \(\text{-CH}_2\text{-}\) group. This difference in molecular structure leads to a predictable change in physical properties like boiling point, melting point, and density as the molecular mass increases.