Question

It takes 192 sec for an unknown gas to diffuse through a porous wall and 84 sec for N₂ gas to effuse at the same temperature and pressure. What is the molar mass of the unknown gas?

Answer 1

`γ_"unknown"/γ_("N"_2) = ("t"_("N"_2))/("t"_"unknown") = sqrt(("M"_("N"_2))/("M"_"unknown"))`

`(84  "sec")/(192  "sec") = sqrt((28  "g mol"^-1)/"M"_"unknown")`

On squaring both sides and rearranging

`((84  "sec")/(192  "sec"))^2 = (28  "g mol"^-1)/"M"_"unknown"`

`"M"_"unknown" = 28  "g mol"^-1 xx ((192  "sec")/(84  "sec"))^2`

`"M"_"unknown"` = 146 g mol⁻¹