When and Why is there an effect of concentration of OH ions

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Solution

He is talking about dissociated H+/OH-. Consider, for example, a NaOH (strong base) aqueous solution: You have a dissociation of Na+ and OH- ions. Of course, the OH- ions give the solution its basicity.

By increasing the dilution of the solution, the concentration of dissociated OH- anions decreases, and thus the basicity of the solution decreases.

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