The density of a gaseous mixture containing H₂ and O₂ at 27 ^oC and 760 Torr is 0.50 g L^-1. The amount fraction of He in the mixture is

Since $\rho =pM/RT,$ we have $M_{\mathrm{av}}=\frac{\rho RT}{p}=\frac{\left(0.50 \mathrm{g} {\mathrm{L}}^{-1}\right)\left(0.082 \mathrm{L} \mathrm{atm} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}\right)(300 \mathrm{K})}{(1 \mathrm{atm})}=12.3 \mathrm{g} {\mathrm{mol}}^{-1}$

If x is the amount fraction of helium in the mixture, then

$M_{\mathrm{av}}=x M_{{\mathrm{H}}_2}+(1-x)M_{{\mathrm{O}}_2}=M_{{\mathrm{O}}_2}+\left(M_{{\mathrm{H}}_2}-M_{{\mathrm{O}}_2}\right)x$  or

$x=\frac{M_{\mathrm{av}}-M_{{\mathrm{O}}_2}}{M_{{\mathrm{H}}_2}-M_{{\mathrm{O}}_2}}=\frac{12.3 \mathrm{g} {\mathrm{mol}}^{-1}-32 \mathrm{g} {\mathrm{mol}}^{-1}}{2 \mathrm{g} {\mathrm{mol}}^{-1}-32 \mathrm{g} {\mathrm{mol}}^{-1}}=0.66$