The yield of alkyl bromide obtained as a result of heating the dry silver salt of carboxyic acid with bromine what will be the order of formation w.r.t. alkyl bromide

Options

A. `1^(@) gt 3^(@) gt 2^(@)` bromides
B. `1^(@)gt2^(@) gt 3^(@)` bromides
C. `3^(@) gt 2^(@) gt1^(@)` bromides
D. `3^(@) gt 2^(@) gt 1^(@)` bromides

Answer

To determine the order of formation of alkyl bromides when heating the dry silver salt of carboxylic acid with bromine, we will analyze the reaction mechanism and the stability of the intermediates involved.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
- The reaction involves the dry silver salt of a carboxylic acid reacting with bromine (Br2).
- This reaction is known as the **Hunsdiecker reaction**, which results in the formation of alkyl bromides (RBr).

2. **Mechanism of the Reaction**:
- The silver salt of the carboxylic acid can be represented as RCOOAg.
- When it reacts with Br2, an acyl hypobromite intermediate is formed:
\[ RCOOAg + Br2 \rightarrow RCOOBr + AgBr \]
- This intermediate undergoes homolytic cleavage, resulting in the formation of radicals:
\[ RCOOBr \rightarrow R\cdot + Br\cdot + CO2 \]
- The R radical then combines with the Br radical to form the alkyl bromide:
\[ R\cdot + Br\cdot \rightarrow RBr \]

3. **Stability of Radicals**:
- The stability of the radicals formed during the reaction plays a crucial role in determining the yield of the alkyl bromides.
- The order of stability for alkyl radicals is:
- **Tertiary (3°) > Secondary (2°) > Primary (1°) > Methyl (0°)**
- However, in this reaction, the formation of the alkyl bromide is influenced by the stability of the radical intermediates.

4. **Order of Formation**:
- The yield of alkyl bromides is influenced by the ease of radical formation and the stability of the resulting alkyl radical.
- Due to the nature of the reaction, the order of formation of alkyl bromides is:
- **Primary > Secondary > Tertiary**
- This is because primary radicals are less sterically hindered and can stabilize better compared to secondary and tertiary radicals in this specific reaction context.

5. **Conclusion**:
- Therefore, the order of formation of alkyl bromides when heating the dry silver salt of carboxylic acid with bromine is:
- **Primary > Secondary > Tertiary**