Effusion of a 1:1 mixture of two gases,represented by unshaded and shaded spheres in the diagram below,through a small pinhole produces the result shown below.The shaded spheres have a molecular mass of 20 amu.Which gas molecules have the higher average speed and what is the molecular mass of the unshaded molecules?
A)Unshaded molecules have higher average speed and molecular mass = 14 amu.
B)Unshaded molecules have higher average speed and molecular mass = 17 amu.
C)Unshaded molecules have lower average speed and molecular mass = 24 amu.
D)Unshaded molecules have lower average speed and molecular mass = 29 amu.

Question

Effusion of a 1:1 mixture of two gases,represented by unshaded and shaded spheres in the diagram below,through a small pinhole produces the result shown below.The shaded spheres have a molecular mass of 20 amu.Which gas molecules have the higher average speed and what is the molecular mass of the unshaded molecules? 
A)Unshaded molecules have higher average speed and molecular mass = 14 amu. 
B)Unshaded molecules have higher average speed and molecular mass = 17 amu. 
C)Unshaded molecules have lower average speed and molecular mass = 24 amu. 
D)Unshaded molecules have lower average speed and molecular mass = 29 amu.

Quizplus · Accepted Answer

The rate of effusion is inversely proportional to the square root of the molecular mass. Since both gases have the same initial pressure and volume, the gas with the lower molecular mass (unshaded) will have a higher average speed. Let the molecular mass of the unshaded gas be x. Then we can set up the following equation:

√(20) / √x = 1

Solving for x, we get:

x = (√20)² = 20

Therefore, the molecular mass of the unshaded gas is 20 amu, which corresponds to neon. The shaded gas is oxygen, with a molecular mass of 32 amu. Thus, the unshaded gas has a lower molecular mass and therefore a higher average speed.

Effusion of a 1:1 Mixture of Two Gases,represented by Unshaded