Alkane obtained by the decarboxylation of fatty acid contains

Options

A. One carbon atom more than the acid
B. One carbon atom less than the acid
C. Same number of carbon atoms as the cid
D. Two carbon atoms less than the acid

Answer

To solve the question regarding the alkane obtained by the decarboxylation of a fatty acid, we need to understand the process of decarboxylation and its impact on the carbon count of the resulting alkane. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Understanding Decarboxylation**:
- Decarboxylation is a chemical reaction that involves the removal of a carboxyl group (-COOH) from a fatty acid. This process typically results in the release of carbon dioxide (CO2).

2. **Identify the Structure of Fatty Acid**:
- Fatty acids have the general formula R-COOH, where R represents a hydrocarbon chain. The number of carbon atoms in the fatty acid is represented by the length of the R group plus one carbon from the carboxyl group.

3. **Reaction with Soda Lime**:
- When a fatty acid reacts with soda lime (a mixture of sodium hydroxide and calcium oxide), the sodium salt of the fatty acid is formed. The reaction can be summarized as:
\[ R-COONa + NaOH \xrightarrow{\text{CaO}} R-H + Na2CO3 \]
- Here, R-H represents the alkane formed after decarboxylation.

4. **Carbon Count Analysis**:
- In the fatty acid R-COOH, there are "n" carbon atoms (where n is the number of carbon atoms in R plus one from the -COOH group).
- After decarboxylation, one carbon atom (from the carboxyl group) is removed, resulting in the alkane R-H, which contains "n-1" carbon atoms.

5. **Conclusion**:
- Therefore, the alkane obtained by the decarboxylation of a fatty acid contains one carbon atom less than that of the original fatty acid.

### Final Answer:
The alkane obtained by the decarboxylation of a fatty acid contains **one carbon atom less than that of the acid**.

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