Aspirin is the trade name for acetylsalicylic acid. In a solution of sodium hydroxide the acid will be convereted to its sodium salt which is soluble. It could be recovered from the solution by adding acid to neutralise the sodium hydroxide and regenerate the free acid form which would again be mostly insoluble. In plain water the aspirin is unchanged and remains largely insoluble, only 1g dissolves in 100g of water at 37'C.
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Sodium acetylsalicylic acid is more soluble in water than acetylsalicylic acid because it dissociates into ions (Na+ and the acetylsalicylate anion) which then attract water molecules to form solvation sheaths around them. Source: Heinemann Chemistry 2
if you look up the sturcutre of aspirin it consits of aromatic rings which are really stable and not very acidic even though they contain dicarboxylic acid groups. Hydrochloric acid (HCL) it acid solution, so it hydrogens would H-bond with oxygen from aspirin but not aromatic side of molecule so that why it insoluble in HCL.