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I would like to know what min and max values of densities are achievable with water solutions.
There are some conditions:
1. Normal or close to normal temperature;
2. Non-radioactive solutions/components;
3. Acids are good as long as they can be safely contained.

Thanks for your help!

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Highest known is about 4.25 (all densities in g/cm${}^3$) at room temperature: http://en.wikipedia.org/wiki/Clerici_solution

If you're willing to allow heating it comes close to 5 because the solubility of the salts increases with temperature: http://books.google.com/books?id=kaa2qeFRXmUC&pg=PA99

My favorite runner-up is the Thoulet solution mentioned at http://en.wikipedia.org/wiki/Potassium_tetraiodomercurate(II) but it only reaches around 3.20.

Lowest would depend on what you mean by "water solution". If you mix a drop of water with a gallon of a very light liquid such as diethyl ether (which is not very miscible with water but does dissolve some -- hence the need to dry it in the lab over sodium or molecular sieves), then the answer is the density of the liquid (ether = 0.73). If water has to be the majority component I'd expect the minimum to be very close to the density of water, since mixtures tend to decrease a bit in volume. (The density of water is 1.0 at 4${}^\circ$, close to 1.0 at room temperature, 0.94 near the boiling point).

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