Step 1: Understanding the Concept:
The rate of diffusion of a gas refers to how fast the gas molecules spread out into the available space. According to Graham's Law of Effusion/Diffusion, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
Step 2: Key Formula or Approach:
Graham's Law:
\[ r \propto \frac{1}{\sqrt{M}} \]
where $r$ is the rate of diffusion and $M$ is the molar mass of the gas. This implies that the gas with the lowest molar mass will have the highest rate of diffusion.
Step 3: Detailed Explanation:
Let's calculate the molar masses of the given gases:
1. $\text{O}_2$: $2 \times 16 = 32 \, \text{g/mol}$
2. $\text{CO}_2$: $12 + (2 \times 16) = 44 \, \text{g/mol}$
3. $\text{H}_2$: $2 \times 1 = 2 \, \text{g/mol}$
4. $\text{N}_2$: $2 \times 14 = 28 \, \text{g/mol}$
Comparing the molar masses:
\[ M(\text{H}_2)<M(\text{N}_2)<M(\text{O}_2)<M(\text{CO}_2) \]
Since Hydrogen ($\text{H}_2$) has the smallest molar mass ($2 \, \text{g/mol}$), it will have the highest rate of diffusion.
Step 4: Final Answer:
$\text{H}_2$ has the highest rate of diffusion. The correct option is (C).