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This acidity is due to the stability of the resonance structures of the corresponding enolate ion that forms upon dissociation. When the hydroxide is able to subtract a hydrogen atom, a carbanion is formed. This carbanion is a very strong base and is able to attack the chlorine thus taking one of the chlorine atoms. The introduction of one chlorine atom catalyzes the attack of another hydroxide molecule on the remaining ?-hydrogens of the ketone. The subsequent attacks occur faster because with every introduction of a chlorine atom, the remaining hydrogens are more acidic because of the inductive effect of the halogens...
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