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Question 5.17: A flammable gas made up only of carbon and hydrogen is found...

A flammable gas made up only of carbon and hydrogen is found to effuse through a porous barrier in 1.50 min. Under the same conditions of temperature and pressure, it takes an equal volume of bromine vapor 4.73 min to effuse through the same barrier. Calculate the molar mass of the unknown gas, and suggest what this gas might be.

Strategy The rate of effusion is the number of molecules passing through a porous barrier in a given time. The longer the time it takes, the slower is the rate. Therefore, the rate is inversely proportional to the time required for effusion. Equation (5.17) can now be written as  r_{1}/r_{2}=t_{1}/t_{2}=\sqrt{ℳ_{2}/ℳ_{1} }   where t_{1}   and   t_{2}  are the times for effusion for gases 1 and 2, respectively.

\frac{r_1}{r_2}=\sqrt{\frac{ℳ_2}{ℳ_1}}     (5.17)

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