An unsaturated hydrocarbon 'X' gives white precipitate with Tollen's reagent. If X is gaseous in nature, the molecular formula of X is

Options

A. `C_(3)H_(6)`
B. `C_(2)H_(4)`
C. `C_(2)H_(2)`
D. `C_(4)H_(8)`

Explanation

To solve the problem, we need to identify the unsaturated hydrocarbon 'X' that gives a white precipitate with Tollen's reagent and is gaseous in nature. Let's break down the steps to arrive at the molecular formula of 'X'.

### Step 1: Understanding Unsaturated Hydrocarbons
Unsaturated hydrocarbons can be classified into two main categories: alkenes (which contain at least one double bond) and alkynes (which contain at least one triple bond).

**Hint:** Remember that alkenes have the general formula CnH2n, while alkynes have the general formula CnH2n-2.

### Step 2: Tollen's Reagent Reaction
Tollen's reagent is used to test for aldehydes. It produces a white precipitate of silver when it reacts with terminal alkynes (alkynes with a hydrogen atom attached to the carbon of the triple bond). Alkenes do not react with Tollen's reagent.

**Hint:** Identify the functional groups that react with Tollen's reagent.

### Step 3: Identifying the Type of Hydrocarbon
Since 'X' gives a white precipitate with Tollen's reagent, it must be a terminal alkyne. This indicates that 'X' has a triple bond and a hydrogen atom attached to one of the carbons of the triple bond.

**Hint:** Terminal alkynes are the only unsaturated hydrocarbons that will react positively with Tollen's reagent.

### Step 4: Determining the Molecular Formula
For a terminal alkyne, the general formula is CnH2n-2. Since 'X' is gaseous, we can consider small values of 'n'.

- For n = 2:
- Molecular formula = C2H2(2) - 2 = C2H2 (which is ethyne or acetylene)

- For n = 3:
- Molecular formula = C3H2(3) - 2 = C3H4 (which is propyne)

Since we are looking for a gaseous hydrocarbon that fits the criteria, C2H2 (ethyne) is the simplest and most likely candidate.

**Hint:** Check the molecular formulas of small alkynes to find the one that fits the criteria.

### Conclusion
The molecular formula of the unsaturated hydrocarbon 'X' that gives a white precipitate with Tollen's reagent and is gaseous in nature is **C2H2** (ethyne).

**Final Answer:** C2H2