Step 1: Understanding the Concept:
Vapour density of a gas is defined as the ratio of the mass of a certain volume of the gas to the mass of the same volume of hydrogen gas under identical conditions of temperature and pressure.
Step 2: Key Formula or Approach:
Based on Avogadro's hypothesis, this ratio simplifies to the ratio of their molar masses.
Since the molar mass of hydrogen (\(\text{H}_2\)) is approximately \(2 \text{ g/mol}\), vapour density is related to the molar mass of a gas by the formula:
\[ \text{Vapour Density} = \frac{\text{Molar Mass}}{2} \]
Step 3: Detailed Explanation:
First, find the molar mass of oxygen gas (\(\text{O}_2\)).
The atomic mass of an oxygen (\(\text{O}\)) atom is \(16 \text{ u}\).
Since oxygen gas is diatomic (\(\text{O}_2\)), its molar mass is:
\[ \text{Molar Mass of } \text{O}_2 = 2 \times 16 = 32 \text{ g/mol} \]
Now, apply the formula to calculate the vapour density:
\[ \text{Vapour Density} = \frac{32}{2} = 16 \]
Note that vapour density is a unitless quantity as it is a relative ratio.
Step 4: Final Answer:
The vapour density of \(\text{O}_2\) gas is 16.