In an experiment `100 mL` of hydrogen take 5 second and 100 mL of an unknown gas take 20 seconds to diffuse through a porous membrane. Determine the density of the unknown gas relative to that of hydrogen.

Answer

16 times

Explanation

Rate of diffusion of hydrogen `(r_(H_(2))) = (100)/(5) = 20 mL s^(-1)`
Rate of diffusion of unknown gas `(r_("gas")) = (100)/(5) = 5 mL s^(-1)`
By applying Graham's Law of diffusion :
`(r_(H_(2)))/(r_("gas"))=sqrt((d_(("gas")))/(d_((H_(2)))))` or `sqrt((d_(("gas")))/(d_((H_(2))))) = ((20 mL s^(-1)))/((5mL s^(-1))) =4`.
Squaring both sides : `(d_("gas"))/(d_(H_(2))) = 16. d_(("gas")) = 16 d_((H_(2))`