Does copper hydroxide dissolve in water?

Copper metal doesn’t dissolve in water (salty or not) as the metal. However, exposure of the metal to air and then to water results in an interesting oxide layer on the surface of copper. The first few atom thickness is the dull reddish brown copper(I) oxide and this exists in an equilibrium with the outer oxide layer of black copper(II) oxide. As the outer oxide thickens, so too does the inner oxide. Even the outer oxide is very thin - too thin for the black of the oxide to be noticed other than by a dulling or darkening of the surface - that is, it is not thick enough to be opaque.

This oxide layer does dissolve in water to a slight extent giving rise to copper ions in the water. The extent of solubility is both temperature and pH dependent but at 25 degC and a pH=7, you are probably looking at the concentration of a saturated solution in the region of 10(-7) moles/dm^3.

Eventually an equilibrium is set up which balances the rate of growth of thickness of the oxide with the rate of dissolution to give a steady state for the given situation. The rate of dissolution increases with flow (turbulent more so than laminar in a pipe), changes in pH and temperature.

This small amount of copper is responsible for the antifouling properties of copper based alloys in marine environments since the copper is toxic to algae and organisms such as barnacles and shellfish that may try to attach themselves inside the piping and which would otherwise block pipes of, say, pumps and cooling condensers for marine steam turbines (as found in ships and coastal power stations).

This is also why we should not drink water from hot water tanks at home (higher concentrations of copper from the hot water can be toxic to humans, too) and why it is a good idea to run water that has been standing in copper pipes for a minute or so if the water has been standing in the pipes for several hours.

You specifically ask about the influence of salt on solubility. In the case of a copper surface that is continually wet (say a tank that is not emptied and refilled) the concentration of chloride ions in the water is (in my opinion) unlikely to increase solubility of the copper significantly, however, if the tank is repeatedly emptied and the salt water left to evaporate, the concentration of chloride ions would increase as water evaporates and the pH would decrease* making the copper(II) ions more likely to dissolve (acid + metal oxide) and the solubility of the copper would increase due to various chloro copper complex formation as opposed to the simple aqua copper complexes that would normally be found in aqueous solution. This may be evidenced by a blue deposit forming where salt water drops have evaporated slowly. Once the tank or pipe is refilled, then the deposits would dissolve, flow of water would remove these deposits and the protective oxide layer would be re-established eventually.

Note * NaCl at typical concentrations is pH neutral, however as NaCl solution evaporates, the solubility of all of the species must be considered:

Ions present = Na^(+), Cl^(-), H^(+) and OH^(-)

This means we have, in effect HCl and NaOH present, too.

The solubility of NaOH is high, but less than that of HCl, so a point is reached where NaOH is precipitated (common ion effect) thereby removing OH^(-) ions and leaving an excess of H(+) which, in turn, reduces the pH aiding the formation of copper chloro complexes as well as copper (II) chloride.

I do not believe that this would happen at the concentration of sea water but may, I expect if boiling, concentrated NaCl solution was used and certainly if the water could evaporate (or the pH of the solution was to be reduced or the chloride ion concentration was to be increased in some other way).

At 25C the Solubility Product of Cu(OH)2 in water is 22.2×10^20. Therefore, it is not considered soluble in water. Add a few drops of ammonium hydroxide and it will dissolve promptly, imparting the solution a beautiful color.