Question

A mixture of two gases is contained in a vessel. The gas 1 is monoatomic and gas 2 is diatomic and the ratio of their molecular masses $M₁/M₂ = 1/4$. What is the ratio of root mean square speeds of the molecules of two gases?

• A. 2
• B. 4
• C. 8
• D. 16

Hint:

$vᵣms \propto 1/\sqrtM$ at constant temperature.

Answer 1

The Correct Option is A

Step 1: $vᵣms = \sqrt\frac3RTM}$. For same temperature, $vᵣms \propto \frac1\sqrtM}$.

Step 2: $\fracv₁v₂ = \sqrt\fracM₂M₁ = \sqrt4 = 2$.