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1 mol of Gas A (molar mass $= 64 g {mol}^{- 1}$ ) escapes from a container through a hole in 8 seconds. A mixture of 0.8 mol gas A and 0.2 mol gas B, escapes from an identical container through same hole (at same T and P) in 9 seconds. What is the molar mass of gas B?

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answer is 149.

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Detailed Solution

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For gaseous mixture 80% gas A and 20% gas B:
Average molar mass of mixture $(M_{mix}) = \frac{(0.8 \times 64) + (0.2 \times M_{0})}{1}$
$\frac{r_{A}}{r_{B}} = \sqrt{\frac{M_{mix}}{64}}$
$\frac{\frac{1}{8}}{1 / 9} = \sqrt{\frac{M_{mix}}{64}}$
$\frac{9}{8} \times \frac{9}{8} = \frac{M_{mix}}{64}$
$M_{mix} = 81$
So $81 = \frac{(0.8 \times 64) + (0.2 \times M_{0})}{1}$
$149 = M_{0}$

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