Question

Which of the following gases has the highest rate of diffusion?

• A. O\(_2\)
• B. CO\(_2\)
• C. H\(_2\)
• D. N\(_2\)

Hint:

To solve diffusion problems quickly, just remember: Lighter is Faster. You don't always need to calculate the square root; simply finding the gas with the lowest molecular weight will give you the answer!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Diffusion is the movement of gas molecules from an area of higher concentration to an area of lower concentration. According to Graham's Law of Diffusion, the rate at which a gas diffuses is inversely proportional to the square root of its molar mass.

Step 2: Key Formula or Approach
\[ \text{Rate} \propto \frac{1}{\sqrt{M}} \] Where \(M\) is the molar mass of the gas. The gas with the smallest molar mass will have the highest rate of diffusion.

Step 3: Detailed Explanation
Calculate the molar masses of the given gases:
• O\(_2\): \(16 \times 2 = 32 \text{ g/mol}\)
• CO\(_2\): \(12 + (16 \times 2) = 44 \text{ g/mol}\)
• H\(_2\): \(1 \times 2 = 2 \text{ g/mol}\)
• N\(_2\): \(14 \times 2 = 28 \text{ g/mol}\) Hydrogen (H\(_2\)) has the lowest molar mass (2 g/mol), which means its molecules are the lightest and travel the fastest.

Step 4: Final Answer
H\(_2\) has the highest rate of diffusion.