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If a species is more predominant that means that is the majority in the solution. For an acidic solution, the predominant species will be charged and for a basic solution, the predominant species is neutral.
For weak bases and acids they exist in an equilibrium with an equilibrium constant Ka (acid dissociation constant). So only a certain amount of protons or hydroxide are dissociated out. This concentration determines the pH, the negative log of [H+] or [OH-]. pKa is the negative log of Ka which is also dependent on [H+] or [OH-]. This means if pH is greater than pKa then there is more "stuff" on the side with [H+] and [OH-], so predominant species is charged. But is pH is less than pKa, at that time there is less [H+] or [OH-] than there should be at equilibrium, so there is more "stuff" on the side without [H+] and [OH-] which is the neutral side.
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