Question

Which of the following gases will have the highest rate of diffusion at the same temperature and pressure?

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

Hint:

Graham’s law of diffusion states that lighter gases (with lower molar masses) diffuse faster than heavier gases at the same temperature and pressure.

Answer 1

The Correct Option is A

Step 1: Understand Graham's Law of Diffusion. According to Graham's law, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass: \[ \text{Rate} \propto \frac{1}{\sqrt{M}} \] where \( M \) is the molar mass of the gas. Step 2: Compare the molar masses of the gases. - The molar mass of \( \text{H}_2 \) is \( 2 \, \text{g/mol} \). - The molar mass of \( \text{O}_2 \) is \( 32 \, \text{g/mol} \). - The molar mass of \( \text{N}_2 \) is \( 28 \, \text{g/mol} \). - The molar mass of \( \text{CO}_2 \) is \( 44 \, \text{g/mol} \). Step 3: Determine the rate of diffusion. Since the rate of diffusion is inversely proportional to the square root of the molar mass, the gas with the lowest molar mass will diffuse the fastest. Among the given gases, \( \text{H}_2 \) has the lowest molar mass, so it will have the highest rate of diffusion. Answer: Therefore, \( \text{H}_2 \) will have the highest rate of diffusion.