In the reaction
`H_(3)C-overset(Br)overset(|)CH-CH_(2)-Brunderset((ii)C_(2)H_(5)Br)overset((i)"X mole "NaNH_(2))toCH_(2)-C-=C-C_(2)H_(5)`
The value of [X] is:

Options

A. One
B. Two
C. Three
D. Four

Answer

To solve the problem, we need to analyze the reaction step by step, focusing on the role of sodium amide (NaNH2) in the elimination of bromine and the formation of a triple bond.

### Step-by-Step Solution:

1. **Identify the Starting Material**:
The starting material is 1,2-dibromoethane (H₃C-CHBr-CH₂-Br). This compound has two bromine atoms attached to adjacent carbon atoms.

2. **First Reaction with NaNH2**:
- When we add 1 mole of NaNH2, it acts as a strong base.
- It will deprotonate the hydrogen from the beta carbon (the carbon adjacent to the one with the bromine).
- This results in the formation of an alkene (CH₃-CH=CH₂) as the bromine leaves, forming NaBr.

3. **Formation of Alkene**:
- After the first reaction, we have CH₃-CH=CH₂ and NaBr.
- The alkene can be represented as CH₃-CH=CH₂.

4. **Second Reaction with NaNH2**:
- We need to add another mole of NaNH2 to the alkene to convert it into a terminal alkyne.
- NaNH2 will again remove a hydrogen from the beta carbon of the alkene, leading to the formation of a triple bond (C≡C).
- This results in the formation of CH₃-C≡C-H.

5. **Final Reaction with C₂H₅Br**:
- Now, we want to introduce the ethyl group (C₂H₅) by adding C₂H₅Br.
- We need to add one more mole of NaNH2 to deprotonate the terminal hydrogen of the alkyne (CH₃-C≡C-H), leading to the formation of a carbanion (CH₃-C≡C⁻).
- This carbanion will then react with C₂H₅Br, resulting in the final product CH₃-C≡C-C₂H₅.

6. **Count the Moles of NaNH2**:
- We used 1 mole of NaNH2 for the first elimination (from 1,2-dibromoethane to alkene).
- We used another mole of NaNH2 for the second elimination (from alkene to alkyne).
- We used a third mole of NaNH2 to deprotonate the terminal alkyne before adding C₂H₅Br.
- Therefore, the total number of moles of NaNH2 used is 3.

### Conclusion:
The value of [X] is 3.