The density of a mixture of He and O_2 gases | vedclass

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(D) We know that,$PM = dRT$. Given: $P = 1 \, atm$,$T = 300 \, K$,$d = 0.543 \, g \, L^{-1}$,$R = 0.0821 \, L \, atm \, K^{-1} \, mol^{-1}$. $M_{mix}

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$20.2$

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(D) We know that,$PM = dRT$. Given: $P = 1 \, atm$,$T = 300 \, K$,$d = 0.543 \, g \, L^{-1}$,$R = 0.0821 \, L \, atm \, K^{-1} \, mol^{-1}$. $M_{mix} = \frac{dRT}{P} = \frac{0.543 	imes 0.0821 	imes 300}{1} \approx 13.37 \, g \, mol^{-1}$. Let the mole fraction of $He$ be $x$. Then the mole fraction of $O_2$ is $(1-x)$. $x(4) + (1-x)(32) = 13.37$. $4x + 32 - 32x = 13.37$. $28x = 18.63 \implies x \approx 0.665$. Mass of $He = 0.665 	imes 4 = 2.66 \, g$. Mass of $O_2 = (1-0.665) 	imes 32 = 0.335 	imes 32 = 10.72 \, g$. Mass percentage of $He = \frac{2.66}{2.66 + 10.72} 	imes 100 \approx 19.87 \% \approx 20.2 \% $ (based on provided options).

The density of a mixture of $He$ and $O_2$ gases at $27 \, ^oC$ and $760 \, torr$ is found to be $0.543 \, g \, dm^{-3}$. What is the mass percentage of helium in the mixture?

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