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Q.

An effusion experiment requires 40 s for a certain number of moles of a gas of unknown molar mass to pass through a small orifice into a vacuum. Under the same conditions, 16 s was required for the same number of moles of $O_{2}$ to effuse. What is the molar mass of the unknown gas ?

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a

5.1 g/mol

b

12.8 g/mol

c

80 g/mol

d

200 g/mol

answer is D.

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Detailed Solution

$\frac{t_{(gas)}}{t (O_{2})} = \sqrt{\frac{M_{(gas)}}{M (O_{2})}} \Rightarrow \frac{40}{16} = \sqrt{\frac{M_{(gas)}}{32}} \Rightarrow \frac{5}{2} = \sqrt{\frac{M_{(gas)}}{32}} \Rightarrow \frac{25}{4} = \frac{M_{(gas)}}{32} \Rightarrow M_{(gas)} = 200 g / mol$

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