Question

Which of the following relations is correct regarding rate of diffusion of a gas?

• A. directly proportional to its density
• B. directly proportional to its molecular mass
• C. directly proportional to the square of its molecular mass
• D. inversely proportional to the square root of its molecular mass

Hint:

Graham's law says the rate of diffusion is inversely proportional to the square root of the molar mass.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Graham's law of diffusion states that at constant temperature and pressure, \(r\propto\dfrac{1}{\sqrt{d}}\), where \(d\) is the density.

Step 2: Link with molar mass
Density is proportional to molar mass at the same conditions, so \(r\propto\dfrac{1}{\sqrt{M}}\).

Step 3: Conclusion
The rate of diffusion is inversely proportional to the square root of the molecular mass. Lighter gases diffuse faster.

Final Answer:
The rate of diffusion is inversely proportional to the square root of the molecular mass. \[ \boxed{\text{(D) }\text{inversely proportional to the square root of its molecular mass}} \]