An effusion experiment requires `40 s` of a certain number of moles of a gas of unknown molar mass to pass through a small orifice into a vaccum. 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?

Options

A. `5.1 g//mol`
B. `12.8 g//mol`
C. `80 g//mol`
D. `200 g//mol`

Answer

D

Explanation

`(t_((gas)))/(t(O_(2)))=sqrt(M_((gas))/(M_((O_(2)))))`
`implies(40)/(16)=sqrt(M_((gas))/(32))`
`implies (5)/(2)=sqrt(M_((gas))/(32))implies (25)/(4) =(M_((gas)))/(32)`
`implies M_(gas)= 200 g// mol`