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

Explanation

To find the value of \( n \) in the molecular formula \( O_n \) given that the vapor density is 24, we can follow these steps:

### Step 1: Understand the relationship between vapor density and molecular weight.
The molecular weight (M) of a gas can be calculated from its vapor density (VD) using the formula:
\[ M = 2 \times \text{VD} \]

### Step 2: Calculate the molecular weight using the given vapor density.
Given that the vapor density is 24, we can substitute this value into the formula:
\[ M = 2 \times 24 = 48 \text{ g/mol} \]

### Step 3: Relate the molecular weight to the molecular formula.
The molecular weight of the gas with the molecular formula \( O_n \) can be expressed as:
\[ M = n \times 16 \]
where 16 g/mol is the molecular weight of oxygen (O).

### Step 4: Set up the equation.
Now we can set the two expressions for molecular weight equal to each other:
\[ n \times 16 = 48 \]

### Step 5: Solve for \( n \).
To find \( n \), divide both sides of the equation by 16:
\[ n = \frac{48}{16} = 3 \]

### Conclusion:
Thus, the value of \( n \) is 3, which means the molecular formula of the gas is \( O_3 \) (ozone).

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