One volume of a gaseous organic compound of C, H and N on combustion produced 2 volumes of `CO_(2)`, 3.5 volumes of `H_(2)O` vapour and 0.5 volume of `N_(2)` under identical conditions of temperature and pressure. The molecular formula of the compound is

Options

A. `C_(2)H_(7)N`
B. `C_(4)H_(14)N_(2)`
C. `C_(2)H_(7)N_(2)`
D. `C_(4)H_(14)N_(4)`

Answer

To determine the molecular formula of the gaseous organic compound containing carbon (C), hydrogen (H), and nitrogen (N) based on the combustion products, we can follow these steps:

### Step 1: Analyze the combustion products
From the problem, we know that:
- 1 volume of the organic compound produces 2 volumes of CO₂.
- 1 volume of the organic compound produces 3.5 volumes of H₂O.
- 1 volume of the organic compound produces 0.5 volumes of N₂.

### Step 2: Determine the number of moles of each element
- **Carbon (C)**: Each mole of CO₂ contains 1 mole of carbon. Since 2 volumes of CO₂ are produced, this means:
\[ \text{Moles of C} = 2 \text{ moles} \]

- **Hydrogen (H)**: Each mole of H₂O contains 2 moles of hydrogen. Since 3.5 volumes of H₂O are produced, this means:
\[ \text{Moles of H} = 3.5 \times 2 = 7 \text{ moles} \]

- **Nitrogen (N)**: Each mole of N₂ contains 2 moles of nitrogen. Since 0.5 volumes of N₂ are produced, this means:
\[ \text{Moles of N} = 0.5 \times 2 = 1 \text{ mole} \]

### Step 3: Write the empirical formula
Now that we have the moles of each element, we can write the empirical formula based on the ratio of the number of moles:
- C: 2
- H: 7
- N: 1

Thus, the empirical formula of the compound is:
\[ \text{C}_2\text{H}_7\text{N} \]

### Step 4: Determine the molecular formula
Since we are given that the compound is a gaseous organic compound and we have derived the empirical formula, we can conclude that the molecular formula is the same as the empirical formula in this case (assuming no additional information about molecular weight is provided).

### Final Answer
The molecular formula of the compound is:
\[ \text{C}_2\text{H}_7\text{N} \]

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