What is the difference in the molecular formula of the two successive members in a homologous family ?

Answer

To determine the difference in the molecular formula of two successive members in a homologous family, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Homologous Series**:
- A homologous series is a group of organic compounds that have the same functional group and similar chemical properties but differ by a constant unit.

2. **Identify the General Formula**:
- For alkanes (a common example of a homologous series), the general formula is given as \( C_nH_{2n+2} \), where \( n \) is the number of carbon atoms.

3. **Determine Successive Members**:
- The simplest alkane is methane (\( CH_4 \)), which corresponds to \( n = 1 \).
- The next member in the series is ethane (\( C_2H_6 \)), corresponding to \( n = 2 \).
- The third member is propane (\( C_3H_8 \)), corresponding to \( n = 3 \).

4. **Calculate the Molecular Formula for Successive Members**:
- For \( n = 1 \):
- Methane: \( C_1H_{2(1)+2} = CH_4 \)
- For \( n = 2 \):
- Ethane: \( C_2H_{2(2)+2} = C_2H_6 \)
- For \( n = 3 \):
- Propane: \( C_3H_{2(3)+2} = C_3H_8 \)

5. **Identify the Difference in Molecular Formula**:
- The difference between successive members (e.g., from methane to ethane) can be calculated:
- Ethane (\( C_2H_6 \)) - Methane (\( CH_4 \)) = \( (C_2 - C_1) + (H_6 - H_4) = CH_2 \)
- Thus, the difference in molecular formula between two successive members in a homologous series is \( CH_2 \).

### Final Answer:
The difference in the molecular formula of two successive members in a homologous family is \( CH_2 \).