# Is the density of a two-component mixture always between the densities of its individual components?

There exist eutectic mixtures, in which the freezing point of the mixture is below those of either component of the mixture, i.e., the freezing point of the mixture is not intermediate between that of each component, but is instead lower than both.

Can the same occur for density? Are there mixtures of substances $$\ce{A}$$ and $$\ce{B}$$ such that either $$\rho_\mathrm{mix}$$ is greater than both $$\rho_\ce{A}$$ and $$\rho_\ce{B},$$ or $$\rho_\mathrm{mix}$$ is less than than both $$\rho_\ce{A}$$ and $$\rho_\ce{B}?$$

Or is the density of a two-component mixture always bracketed by (i.e., some intermediate value between) the densities of its individual components?

• May I ask why this question is being downvoted? It seems a relevant question to those exploring chemistry, though perhaps technically more in the realm of physics? – TheEnvironmentalist Jul 5 at 4:03
• The problem is how it's written. It wasn't sufficiently precise, plus you're not actually asking if density is additive. Densities are never simply additive, since density is an intensive property (like temperature -- you can see that temperature is not additive). You're asking whether the density of a 2-component mixture is always bracketed by (i.e., some intermediate value between) the densities of its individual components. I've edited your question to make it clearer. – theorist Jul 5 at 8:03
• Well, optical density can often be treated as additive for the non-reacting mix, but I see no reason why mass density must ever be additive. Maybe have a look at the Wikipedia page on intensive and extensive properties – andselisk Jul 5 at 8:58
• – Mithoron Jul 5 at 17:00
• @Mithoron Those answers all give examples of volume contraction, which is different from what's being asked. Volume contraction is a necessary but not sufficient criterion for the mixture to have a density that exceeds that of its individual components. Correspondingly, none of the volume contraction examples in those answers meet the OP's criterion: Ethanol-water solutions never have a density greater than that of pure water (engineeringtoolbox.com/…) and NaCl(aq) solutions never have a density greater than that of NaCl(s) (2.16 g/cm^3). – theorist Jul 5 at 22:47

No, there is no law that requires the density of a mixture to fall between the densities of pure components. It does so most of the time, but the exceptions are not unheard of. Here's one.

Water: density $$1.00\ \rm{g/cm^3}$$
Hydrazine: $$1.02\ \rm{g/cm^3}$$
Hydrazine hydrate: $$1.03\ \rm{g/cm^3}$$

So it goes.

• Any examples of the opposite, where the density of the mixture is lower than that of both the pure components? – theorist Jul 5 at 22:56
• Can't think of any, but there is no fundamental law forbidding that, either. – Ivan Neretin Jul 6 at 0:39
• Ethanol/benzene and ethanol/toluene: researchgate.net/figure/…. Benzene/m-xylene: ddbst.com/en/EED/VE/VE0%20Benzene%3Bm-Xylene.php. – peruca3d Jul 6 at 2:30
• Positive excess volume per se is not enough to ensure the condition in question. – Ivan Neretin Jul 8 at 17:07