`(A)underset(250^@C)overset(Al_2O_3)to(B)underset((ii)AgOH)overset(HI)to( C)underset(150^@C)overset(Al_2O_3)to(B)underset((ii)H_2O_2, OH^(-))overset((i)B_2H_6)to(A)`
In the above reaction sequence (A) and ( C) are isomers.Molecular formula of B is `C_5H_10`.which can also be obtained form the product of the reaction with `CH_3CH_2MgBr` and `(CH_3)_2CO` are followed by acidification.
Identify the structure of B

Options

A. `(CH_3)_2-CH-CH=CH_2`
B. `CH_3-undersetunderset(CH_3)(|)oversetoverset(CH_3)(|)C-C=CH_2`
C. `(CH_3)_2CH=CHCH_3`
D. `CH_2-CH-undersetunderset(CH_3)(|)CH-CH_3`

Explanation

To identify the structure of compound B in the given reaction sequence, we will follow a systematic approach based on the information provided.

### Step-by-Step Solution:

1. **Understanding the Molecular Formula**:
- The molecular formula of compound B is given as C₅H₁₀. This indicates that B is likely an alkene or a cyclic compound due to the unsaturation.

**Hint**: Consider the degree of unsaturation in the molecular formula to determine the possible structures.

2. **Formation of Compound B**:
- Compound B can be obtained from the reaction of a Grignard reagent (C₂H₅MgBr) with a ketone (specifically, (CH₃)₂CO, which is acetone).
- The reaction with the Grignard reagent will yield a tertiary alcohol after acidification.

**Hint**: Recall that Grignard reagents add to carbonyl groups, forming alcohols upon hydrolysis.

3. **Identifying the Structure of B**:
- The tertiary alcohol formed from the reaction is likely to be 2-pentanol (C₅H₁₂O) after acidification.
- Upon dehydration of 2-pentanol, we can form the alkene, which is 2-pentene or 3-pentene.

**Hint**: Consider the possible isomeric forms of pentene that could arise from dehydration.

4. **Reaction of B with HI and AgOH**:
- When B (the alkene) reacts with HI, it will undergo hydrohalogenation to form a tertiary alcohol.
- The subsequent reaction with AgOH will lead to the formation of a silver salt of the alcohol.

**Hint**: Hydrohalogenation typically leads to Markovnikov addition, favoring the formation of more stable carbocations.

5. **Formation of Compound C**:
- The tertiary alcohol formed from B will be compound C. Since A and C are isomers, we can infer that A is likely a secondary alcohol that can convert to B through dehydration.

**Hint**: Isomerism can involve structural differences such as chain branching or functional group positioning.

6. **Identifying Compound A**:
- Since A is a secondary alcohol, it could be 3-pentanol. This aligns with the reaction sequence where A converts to B through dehydration.

**Hint**: Verify that the structures of A and C are indeed isomers by checking their connectivity.

7. **Final Structure of B**:
- Based on the above deductions, compound B is likely 2-pentene or 3-pentene, which corresponds to the molecular formula C₅H₁₀.

**Hint**: Draw the structures of 2-pentene and 3-pentene to confirm they match the molecular formula.

### Conclusion:
The structure of compound B is either **2-pentene (C₅H₁₀)** or **3-pentene (C₅H₁₀)**, which can be derived from the reactions described in the sequence.