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I'm having some difficulty understanding how the pentahydrate of copper sulfate dissolves in water. I understand how polar molecules work, and how things dissolve in water, but I can't get my head around this in particular.

What happens to the water molecules in the pentahydrate? Does the copper sulfate split up at all? What makes the solution blue, if the solute is split?

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When copper(II) sulfate pentahydrade dissolves in water it actually just becomes further hydrated, in what is called an aquo complex (a coordination compound containing only water molecules as ligands). According to this Wikipedia article:

The pentahydrate ($\ce{CuSO4·5H2O}$), the most commonly encountered salt, is bright blue. It exothermically dissolves in water to give the aquo complex $\ce{[Cu(H2O)6]^2+}$, which has octahedral molecular geometry. The structure of the solid pentahydrate reveals a polymeric structure wherein copper is again octahedral but bound to four water ligands. The $\ce{Cu(II)(H2O)4}$ centers are interconnected by sulfate anions to form chains.

The aquo complex maintains the blue coloration that is present in the pentahydrate solid.

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