A compound X `(C_5H_8)` reacts with ammoniacal `AgNO_3` to give a white precipitate, and on oxidation with hot alkaline `KMnO_4` gives the acid, `(CH_3)_2CHCOOH`. Therefore , X is

Options

A. `CH_2=CHCH=CHCH_3`
B. `CH_3(CH_2)_2C-=CH`
C. `(CH_3)_2CH-C-=CH`
D. `(CH_3)_2C=C=CH`

Explanation

To determine the identity of compound X `(C_5H_8)`, we can analyze the information given in the question step by step.

### Step 1: Analyze the molecular formula
The compound X has the molecular formula `C_5H_8`. This indicates that it is likely an unsaturated hydrocarbon, possibly an alkene or a cycloalkane.

**Hint:** Unsaturated hydrocarbons have fewer hydrogen atoms than their saturated counterparts, which can lead to reactions with reagents like ammoniacal AgNO₃.

### Step 2: Reaction with ammoniacal AgNO₃
The compound reacts with ammoniacal `AgNO₃` to produce a white precipitate. This reaction typically indicates the presence of a terminal alkyne or an alkene that can form a silver complex.

**Hint:** Look for functional groups that can react with silver nitrate, such as terminal alkynes, which yield silver acetylide precipitate.

### Step 3: Oxidation with hot alkaline KMnO₄
The compound X is oxidized with hot alkaline `KMnO₄`, resulting in the formation of `(CH₃)₂CHCOOH`, which is 2-methylbutanoic acid. This suggests that the compound X must have a structure that can be oxidized to yield this carboxylic acid.

**Hint:** Consider how the structure of X can be transformed into the given acid through oxidation. This often involves breaking double bonds or adding functional groups.

### Step 4: Identify possible structures for X
Given that X is `C_5H_8` and can produce a carboxylic acid upon oxidation, we can deduce that X is likely a branched alkene or alkyne. The structure of `(CH₃)₂CHCOOH` suggests that the precursor compound X could be 3-methyl-1-butene or a similar structure.

**Hint:** Draw possible structures for X that fit the criteria of `C_5H_8` and can produce `(CH₃)₂CHCOOH` upon oxidation.

### Step 5: Confirm the identity of X
After considering the possible structures, we can conclude that compound X is likely 3-methyl-1-butene. This compound fits the molecular formula `C_5H_8`, can react with ammoniacal AgNO₃ to give a white precipitate, and can be oxidized to form the carboxylic acid `(CH₃)₂CHCOOH`.

**Hint:** Verify the structure by checking if it meets all the conditions provided in the question.

### Final Answer
Thus, the compound X is **3-methyl-1-butene**.