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The extent of solubility ranges widely, from infinitely soluble (without limit, i.e. miscible [2]) such as ethanol in water, to essentially insoluble, such as titanium dioxide in water. A number of other descriptive terms are also used to qualify the extent of solubility for a given application.
The following chart shows the solubility of various ionic compounds in water at 1 atm pressure and room temperature (approx. 25 °C, 298.15 K). "Soluble" means the ionic compound doesn't precipitate, while "slightly soluble" and "insoluble" mean that a solid will precipitate; "slightly soluble" compounds like calcium sulfate may require heat to precipitate.
In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose derived series terminates in the trivial subgroup .
The tables below provides information on the variation of solubility of different substances (mostly inorganic compounds) in water with temperature, at one atmosphere pressure.
For an infinite group, a "small neighborhood" is taken to be a finitely generated subgroup. An infinite group is said to be locally P if every finitely generated subgroup is P. For instance, a group is locally finite if every finitely generated subgroup is finite, and a group is locally soluble if every finitely generated subgroup is soluble.
In particular, all solubility parameter-based theories have a fundamental limitation that they apply only to associated solutions (i.e., they can only predict positive deviations from Raoult's law): they cannot account for negative deviations from Raoult's law that result from effects such as solvation (often important in water-soluble polymers ...
In mathematics, in the field of group theory, a metanilpotent group is a group that is nilpotent by nilpotent. In other words, it has a normal nilpotent subgroup such that the quotient group is also nilpotent.
Every infinite direct sum of finite groups is locally finite (Robinson 1996, p. 443) (Although the direct product may not be.) The Prüfer groups are locally finite abelian groups; Every Hamiltonian group is locally finite; Every periodic solvable group is locally finite (Dixon 1994, Prop. 1.1.5). Every subgroup of a locally finite group is ...