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If the ion came from a strong acid or strong base, it will not affect the ph since the conjugates of these acids and bases are weak. Conjugates of weak acids and bases will affect the ph since they'll be strong acid and bases.
The ability of an ion to change the pH of the solution depends on what it is a conjugate of. If you have a strong acid and a weak base, the base will be protonated and the resulting compound will have be a strong conjugate acid so the salt solution will be acidic. For example, if we titrate a strong acid with a weak base like NH3, the salt will contain NH4 which can further dissociate into NH3 and H, thus making the salt solution acidic. So we can conclude that titrations of strong acids and weak bases yield acidic salt solutions , and titrations of weak acids and strong bases yield basic solutions. The strength of the acid and base will play a role in the neutralization process as the pH of the solution depends on the dissociation of acids and bases and how well they provide hydrogen or hydroxide ions to the solution.
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