36 ml of a gaseous mixture consisting of a gaseous organic compound A and just sufficient amount of oxygen required for complete combustion gives 16 ml of `CO_(2)`, 24 ml water vapour and 8 ml of `N_(2)`. The volumes are measured at same temperature and pressure.
Volume of `O_(2)` required for complete combustion

Options

A. 8 ml
B. 28 ml
C. 74 ml
D. 22 ml

Answer

To solve the problem, we need to determine the volume of oxygen required for the complete combustion of the gaseous organic compound A. We will use the information provided about the products formed during combustion and apply the principles of gas laws.

### Step-by-Step Solution:

1. **Identify the total volume of the gaseous mixture**:
The total volume of the gaseous mixture is given as 36 ml. This mixture consists of the organic compound A and the oxygen required for combustion.

2. **Identify the products of combustion**:
The combustion produces:
- 16 ml of CO₂ (carbon dioxide)
- 24 ml of H₂O (water vapor)
- 8 ml of N₂ (nitrogen)

3. **Write the balanced chemical equation**:
For the combustion of a hypothetical organic compound A (assumed to be C₂H₄N₂ for this example), the balanced equation can be written as:
\[ C_2H_4N_2 + 3O_2 \rightarrow 2CO_2 + 2H_2O + N_2 \]

4. **Set up the volume relationship using Gay-Lussac's law**:
According to Gay-Lussac's law, the volumes of gases involved in a reaction at constant temperature and pressure are in simple whole number ratios. From the balanced equation:
- 1 volume of C₂H₄N₂ reacts with 3 volumes of O₂ to produce 2 volumes of CO₂, 2 volumes of H₂O, and 1 volume of N₂.

5. **Calculate the volume of oxygen (O₂)**:
Let the volume of oxygen required for combustion be \( V \) ml. The volume of the organic compound A will then be \( 36 - V \) ml. According to the stoichiometry from the balanced equation:
\[ \frac{36 - V}{V} = \frac{1}{3} \]

6. **Cross-multiply and solve for V**:
\[ 3(36 - V) = V \]
\[ 108 - 3V = V \]
\[ 108 = 4V \]
\[ V = \frac{108}{4} = 27 \text{ ml} \]

7. **Conclusion**:
The volume of oxygen required for the complete combustion of the gaseous organic compound A is 27 ml.

### Final Answer:
The volume of O₂ required for complete combustion is **27 ml**.