I know I got this wrong, I guessed. But could someone show me how to do this? Ef

Question

I know I got this wrong, I guessed. But could someone show me how to do this?

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 results 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 lower average speed and molecular mass = 24 amu B) Unshaded molecules have lower average speed and molecular mass = 29 amu C) Unshaded molecules have higher average speed and molecular mass = 14 amu D) Unshaded molecules have higher average speed and molecular mass = 17 amu

Explanation / Answer

Rate of effusion is inversely proportional to molar mass . Hence

Rate of effusion of shaded gas / rate of effusion by unsahed gas = sqrt ( Molar mass of unshaded /Molar mass of shaded)

we see 5 shaded gas molecules effused while 6 unshaded molecules effused in given time. Hence rate of effusion of shaded = 5, while for unshaded = 6 . Substituting these in formula we get

( 5/6) = sqrt ( Molar mass of unshaded / 20)

Molar mass of unshaded = 20 x ( 5/6)^2

        = 13.89 = 14 amu   ( rounded value)

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