A mixture of helium and neon gases has a density of 0.2460 g/L at 35.2°C and 288 torr. What is the mole fraction of neon in this mixture?

We know the volume of one mole of gas at 273 K and 760 Torr is 22.4 L. Using

(PV) / T = constant

We can calculate the volume of the gasses at the given conditions:

(P₁V₁) / T₁ = (P₂V₂) / T₂

(760 * 22.4) / 273 = (288 V₂) / 308.2

V₂ = 66.7 L

Mass of He: 4

Mass of Ne: 20

Fraction of Ne: x

Fraction of He: 1 - x

avg density = (∑ (component fraction * component mass)) / volume

0.2460 = (20x + 4 (1 - x)) / 66.7

x = 0.775