Answer to Question #195814 in Molecular Physics | Thermodynamics for Muzk

Question

Heliox, a breathing gas composed of a mixture of helium (He) and oxygen (O₂), is used medically for treatment in acute asthma. In medicine heliox may refer to a mixture of 21% O2 (the same as air) and 79% He. Calculate the average molar mass and density of heliox at pressure Patm = 100 kPa and room temperature t = 22°C. The molar mass of oxygen is po 16 and helium He = 4 g/mole.

Answer 1

Solution.

$m(O_2)=0.21m;$

$m(He)=0.79m;$

$P_{atm}=100\sdot10^3Pa;$

$T=295K;$

$M(O_2)=32\sdot10^{-3}kg/mol;$

$M(He)=4\sdot10^{-3}kg/mol;$

$\nu=\nu(O_2)+\nu(He);$

$\nu=\dfrac{0.21m}{32\sdot10^{-3}}+\dfrac{0.79m}{4\sdot10^{-3}}=\dfrac{6,53m}{32\sdot10^{-3}}=2.04\sdot10^2(mol);$

$\nu=\dfrac{m}{M}\implies M=\dfrac{m}{\nu};$

$M=\dfrac{m}{2.04\sdot10^2}=5\sdot10^{-3}(kg/mol);$

$PV=\dfrac{m}{M}RT; P=\dfrac{\rho}{M}RT\implies \rho=\dfrac{PM}{RT};$

$\rho=\dfrac{100\sdot10^3\sdot5\sdot10^{-3}}{8.31\sdot295}=2.04(kg/m^3);$

Answer:$M ​ =5⋅10^ {−3} (kg/mol);$

$\rho=2.04(kg/m^3).$