How can I estimate the density of a liquid mixture (e. g. liquid air?)

What is the density of liquid air at its highest temperature? Sue Kamal

I can give you a quick back-of-the-envelope estimate, but I don't have that data.

Cryogenic properties of gases, taken from the CRC Handbook of Chemistry and Physics
Gas	Density, kg/m³	Boiling point at 1 atm, K
O₂	1142	90.18
N₂	804	77.35
Ar	1390	87.45

The highest temperature for liquid air is the boiling point for nitrogen gas. If I assume that liquid air is an "ideal solution" (that is, all the molecules in the mixture interact the same way, whether they're oxygen, nitrogen, or argon), I can write density of liquid air = 0.78084 × density of nitrogen + 0.20946 × density of oxygen + 0.00934 × density of argon

where the fractions are the volume fractions of each component in pure, dry air. (They don't add up to 1 because I'm ignoring all the trace gases, including CO₂, to keep things simple). If I further assume that the densities of liquid oxygen and liquid argon aren't much different at the boiling point of nitrogen then they are at their own boiling points, I can write the density of liquid air at the boiling point of nitrogen as (0.78084 × 804 kg/m³) + (0.20946 × 1142 kg/m³) + (0.00934 × 1390 kg/m³) = 880 kg/m³ or a bit less dense than water is around room temperature.

Author: Fred Senese senese@antoine.frostburg.edu

General Chemistry Online! How can I estimate the density of a liquid mixture (e. g. liquid air?)