If the Density of a Mixture of Helium and Oxygen gasses in 25 degrees Celcious temperature , 8.314x10^5 Pa , is 0.835 g/dm^-3 , Find the Percentage of mass of Helium included in the mixture?
[ R.A.M {He=4 , O=16}

Question

If the Density of a Mixture of Helium and Oxygen gasses in 25 degrees Celcious temperature , 8.314x10^5 Pa  , is 0.835 g/dm^-3  , Find the Percentage of mass of Helium included in the mixture?
[ R.A.M {He=4  , O=16}

aaronq · Answer

use: PV=nRT, sub in $n=\dfrac{m}M{}$ and $d=\dfrac{m}{V}$ and isolate for M, which is the average of the molar masses of the gases.

(1) $M_{ave}=\dfrac{dRT}{P}$

The $M_{ave}$ is made up of the molar mass and % abundance of each gas.

(2) $M_{ave}=M_{He}*\%He+M_{O_2}*\%O_2$ 

Their percentages equal 100%, so 1

(3) $\%He+\%O_2=1$

plug numbers given in the question into (1), $M_{ave}=29.944~g/mol$

combine (2) and (3), plug in molar masses, solve for %He

$M_{ave}=M_{He}*\%He+M_{O_2}*(1-\%He)=29.944~g/mol$

$\%He=0.0734=\color{red}{7.34\%}$ which is the mass percent of He of the mixture.