Question

A gaseous mixture of He and O₂ is found to have a density of 0.518 gL^-1 at 25° C and 720 torr. The mass percent of helium in this mixture is ______.

Options

• 20.06

• 19.90

• 17.01

• 15.36

Answer 1

A gaseous mixture of He and O₂ is found to have a density of 0.518 gL^-1 at 25° C and 720 torr. The mass percent of helium in this mixture is 19.90.

Explanation:

Let the wt. of the mixture be 100 g and the wt. of He be x g

Then the number of moles He in the mixture = (100 - x g)

and the no. of moles of He in the mixture = `x/4`

And the no. of moles of O₂ in the mixture = `(100 - x)/4`

Now from PV = nRT = `w/"M"`RT

`=> "PV" = "dRT"/"M"`

`=> "M" = "dRT"/"P"`

`= (0.518 xx 0.0821 xx 298)/((720//760) xx 13.34)`

⇒ M = 3.34   ...(Average molecular wt.)

Now again from PV = nRT = `(w"RT")/"M"`

`=> "V" = (w"RT")/"PM"`

`=> "V" = (100 xx 0.0821 xx 298)/((720//760) xx 13.34)`

⇒ V = 193.56 L

Now again from PV = nRT

`=> 720/760 xx 193.56`

`= (x/4 + (100 - x)/32) xx 0.0821 xx 298`

`=> 7.496 = x/4 + (100 - x)/32`

⇒ 239.88 = 8x + 100 - x

⇒ 139.88 = 7x

⇒ x = 19.9

Hence the mass % of He in the mixture = 19.9%.