Understanding Homologous Series and Atomic Mass Difference

In organic chemistry, 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 and show a gradual change in physical properties as the series progresses.

Difference Between Subsequent Members

Subsequent or successive members of a homologous series typically differ by a single repeating unit. For many common homologous series like alkanes, alkenes, alkynes, alcohols, carboxylic acids, etc., this repeating unit is a methylene group, which has the chemical formula \(\text{CH}_2\).

For example, consider the alkane series:

• Methane: \(\text{CH}_4\)
• Ethane: \(\text{C}_2\text{H}_6\)
• Propane: \(\text{C}_3\text{H}_8\)
• Butane: \(\text{C}_4\text{H}_{10}\)

The difference between ethane (\(\text{C}_2\text{H}_6\)) and methane (\(\text{CH}_4\)) is \(\text{C}_2\text{H}_6 - \text{CH}_4 = \text{CH}_2\). Similarly, the difference between propane (\(\text{C}_3\text{H}_8\)) and ethane (\(\text{C}_2\text{H}_6\)) is \(\text{C}_3\text{H}_8 - \text{C}_2\text{H}_6 = \text{CH}_2\). This difference is consistently a \(\text{CH}_2\) group for subsequent members in this series.

Calculating the Atomic Mass Difference

To find the difference in atomic mass units between subsequent members of a homologous series that differ by a \(\text{CH}_2\) group, we need to calculate the atomic mass of the \(\text{CH}_2\) group.

The approximate atomic masses of the elements are:

• Carbon (\(\text{C}\)): Approximately 12 atomic mass units (amu)
• Hydrogen (\(\text{H}\)): Approximately 1 atomic mass unit (amu)

The \(\text{CH}_2\) group contains one carbon atom and two hydrogen atoms. Therefore, the total atomic mass of the \(\text{CH}_2\) group is:

Atomic mass of \(\text{CH}_2\) = (Atomic mass of C) + 2 × (Atomic mass of H)

Atomic mass of \(\text{CH}_2\) = \(12 \text{ amu} + 2 \times 1 \text{ amu}\)

Atomic mass of \(\text{CH}_2\) = \(12 \text{ amu} + 2 \text{ amu}\)

Atomic mass of \(\text{CH}_2\) = \(14 \text{ amu}\)

Thus, subsequent members of a homologous series that differ by a \(\text{CH}_2\) unit differ by 14 atomic mass units.

Relating to the Options

The question asks by how many atomic mass units subsequent members of homologous series differ. Based on our calculation, the difference is 14 atomic mass units.

Looking at the provided options:

• 26 amu
• 32 amu
• 20 amu
• 14 amu

The value we calculated matches one of the options.

The difference in atomic mass between consecutive members of a homologous series is 14 atomic mass units, corresponding to the mass of a \(\text{CH}_2\) group.

Revision Table: Homologous Series Key Points

Additional Information on Homologous Series

While the \(\text{CH}_2\) difference is the most common, homologous series are defined by a repeating unit that leads to a gradual change in properties. Here are some examples:

• Alkanes: General formula \(\text{C}_n\text{H}_{2n+2}\). Members differ by \(\text{CH}_2\). Examples: \(\text{CH}_4\), \(\text{C}_2\text{H}_6\), \(\text{C}_3\text{H}_8\).
• Alkenes (with one double bond): General formula \(\text{C}_n\text{H}_{2n}\) (for n >= 2). Members differ by \(\text{CH}_2\). Examples: \(\text{C}_2\text{H}_4\), \(\text{C}_3\text{H}_6\), \(\text{C}_4\text{H}_8\).
• Alkynes (with one triple bond): General formula \(\text{C}_n\text{H}_{2n-2}\) (for n >= 2). Members differ by \(\text{CH}_2\). Examples: \(\text{C}_2\text{H}_2\), \(\text{C}_3\text{H}_4\), \(\text{C}_4\text{H}_6\).
• Alcohols (with one -OH group): General formula \(\text{C}_n\text{H}_{2n+1}\text{OH}\) or \(\text{C}_n\text{H}_{2n+2}\text{O}\). Members differ by \(\text{CH}_2\). Examples: \(\text{CH}_3\text{OH}\), \(\text{C}_2\text{H}_5\text{OH}\), \(\text{C}_3\text{H}_7\text{OH}\).

In all these common examples, the step-wise increase in the carbon chain length by one carbon atom and two hydrogen atoms results in the consistent 14 amu mass difference between subsequent members.