A gas has molecular formula `O_(n)`. If its vapour density is 24, the value of n is ____________.

Explanation

To solve the problem, we need to determine the value of \( n \) in the molecular formula \( O_n \) given that the vapor density of the gas is 24.

### Step-by-Step Solution:

1. **Understanding Vapor Density**:
The vapor density (VD) of a gas is defined as the ratio of the molecular mass of the gas to the molecular mass of hydrogen. The formula for vapor density is:
\[ \text{Vapor Density} = \frac{\text{Molecular Mass of Gas}}{\text{Molecular Mass of Hydrogen}} \]

2. **Molecular Mass of Hydrogen**:
The molecular mass of hydrogen (H₂) is 2 g/mol.

3. **Setting Up the Equation**:
Given that the vapor density of the gas is 24, we can set up the equation:
\[ 24 = \frac{\text{Molecular Mass of Gas}}{2} \]

4. **Calculating Molecular Mass of the Gas**:
Rearranging the equation to find the molecular mass of the gas:
\[ \text{Molecular Mass of Gas} = 24 \times 2 = 48 \text{ g/mol} \]

5. **Relating Molecular Mass to the Formula**:
The molecular formula of the gas is \( O_n \). The molecular mass can also be expressed in terms of \( n \):
\[ \text{Molecular Mass of } O_n = n \times \text{Atomic Mass of Oxygen} \]
The atomic mass of oxygen (O) is approximately 16 g/mol. Therefore:
\[ \text{Molecular Mass of } O_n = n \times 16 \]

6. **Setting Up the Equation for n**:
Now, we can set the two expressions for molecular mass equal to each other:
\[ n \times 16 = 48 \]

7. **Solving for n**:
To find \( n \), divide both sides of the equation by 16:
\[ n = \frac{48}{16} = 3 \]

8. **Conclusion**:
The value of \( n \) is 3.

### Final Answer:
The value of \( n \) is **3**.