Find the hydrogen density of a hydrogen-helium mixture containing 50% helium (by volume).

Let’s write down given:

Mixture: H2 + He

ϕ (He) = 50% or 0.5

D mixture H2 -?

Solution:

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.