For questions related to the solubility of compounds in various solvents, especially in water. Do not confuse with [solutions] or [aqueous-solution].
A chemical compound is "soluble", simply, if it will dissolve in a specified solvent and, all other things being equal, remain in this solution indefinitely. A solid compound that will not dissolve in a particular solvent is "insoluble" in that solvent; a liquid which will not mix with a solvent to form a homogeneous solution is "immiscible" with that solvent. Solvents are important in chemistry as a basic environment in which to mix reactants; solvents can catalyze or deter reactions, as compared to simply combining the non-dissolved reactants.
A compound "dissolves" when the attraction between molecules of the compound (known as the "solute") are broken by the introduction of the solvent, freeing individual molecules (or in the case of ionic salts, individual ions) which then disperse and remain mixed with the solvent's molecules. Compounds that, at least at some level, retain these bonds between ions or molecules do not dissolve; they may form tiny, even invisible particles, but at the molecular level there are clear regions dominated by either solvent or solute. Eventually, the compound will separate and settle either to the top or bottom of the container depending on the relative weight and density of the compound compared to the solvent. These "heterogeneous" mixtures are typically called "suspensions" when mixing a solid with water, or "emulsions" when mixing an oil with water.
The most common solvent for which solubility is data is widely available is water, as it is a fundamental, abundant, non-toxic polar solvent that can be used for a variety of reactions. Other common solvents used in conditions near room temperature and pressure include hydrocarbons, such as relatively light alkanes and aromatics, and their derivatives such as alcohols, aldehydes, ketones, esters, and ethers.
Solvents are typically classified as either polar or nonpolar, but polarity can be described using many criteria and is relative. A polar solvent has a molecular structure that produces a partial positive and negative charge at different atoms of the molecule. Water is one such molecule because its highly polar bonds create charge separation. Polar solvents typically work by "pulling apart" weaker bonds, such as some hydrogen and ionic bonds found in organic compounds and salts, respectively. It is not successful in solvating all of these, however; oils and waxes, for example, are defined in part by their immiscibility in water.
A nonpolar solvent has no localized partial charge and usually works instead by breaking and reforming hydrogen bonds between molecules of the solute. Most of these are organic hydrocarbon derivatives, with alcohols such as methanol, ethanol, and phenol being a primary subcategory and ketones such as acetone and methyl ethyl ketone commonly seen in everyday use. These typically work well to dissolve other hydrocarbons, and are also used as solvents for certain compounds which react strongly with water.