Effusion of a 1:1 mixture of two gases, represented by unshaded and shaded spher

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 32 amu. Which gas molecules have the higher average speed and what is the molecular mass of the unshaded molecules? Unshaded molecules have higher average speed and molecular mass = 14 amu Unshaded molecules have higher average speed and molecular mass = 21 amu Unshaded molecules have lower average speed and molecular mass = 48 amu Unshaded molecules have lower average speed and molecular mass = 72 amu

Explanation / Answer

r1 / r2 = sqrt ( M2 / M1)

where 1 denotes shaded molecule and 2 denotes unshaded molecule

r1 = 3/2 r2 because all the molecules of 1 are effused but two molecules of 2 remain so effusion rate order is 3/2

3/2 = sqrt( M2 / M1)

9 / 4 = M2 / 32

M2 = 72 amu

Unshaded molecules have lower average speed because molecular mass is more

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