Write the net ionic equation for the equilibrium that is established when potassium hypochlorite is dissolved in water.

Potassium hypochlorite when dissolved in water would dissociate into ions namely the potassium ions and the hypochlorite ions. Furthermore, hypochlorite ions would interact with water molecules and would decompose further. The dissociation reactions are as follows:

KClO <=> K+ + ClO-
ClO- + H2O <=> HOCl + OH-

Adding the two reactions, would give

KClO + ClO- + H2O = K+ + HOCl + OH- + ClO- 

The two ClO- ions in both sides would cancel giving us the net ionic equation:

KClO + H2O = K+ + HOCl + OH-