Let’s write down given:
Mixture: H2 + He
ϕ (He) = 50% or 0.5
D mixture H2 -?
1) Let’s say we have 44.8 liters of gas mixture.
2) Find the volume of helium and hydrogen in the mixture:
V (He) = 44.8 l * 0.5 = 22.4 l.
V (H2) = 44.8 L – 22.4 L = 22.4 L
3) Calculate the masses of gases:
m = V / Vm * M
M (H2) = 2 g / mol
M (He) = 4 g / mol
m (H2) = 22.4 l / 22.4 l / mol * 2 g / mol
m (H2) = 2 g
m (He) = 22.4 l / 22.4 l / mol * 4g / mol
m (He) = 4 g
4) Find the mass of the mixture of gases and their mass fractions in it:
m (mixture) = 2 g + 4 g = 6 g;
w (He) = 4 g * 100% / 6 g = 0.667% or 0.667
w (H2) = 2g * 100% / 6g = 33.3% or 0.333
5) Calculate the molar mass of the mixture and its density in terms of hydrogen:
M (mixture) = w (H2) * M (H2) + w (He) * M (He)
M (mixture) = 0.333 * 2 g / mol + 0.667 * 4 g / mol = 3.334 g / mol
D mixture H2 = 3.334 g / mol / 2 g / mol = 1.667
Answer: the density of the mixture for hydrogen is 1.667.
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