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When a salt dissociates, the cation and anion can form a weak acid/base when it reacts with water. For example, when NaCl dissociates, it forms Na+ and Cl-. Na+ reacts with H2O to form NaOH, a strong base. Since it is a strong base, NaOH will fully dissociate in water again to reform Na+ and OH-, thus not affecting the pH. Cl- will also react with H2O to form HCl, a strong acid. Since it is a strong acid, it will fully dissociate in water to reform H3O+ and Cl-, thus not affecting the pH. The pH will only be affected when a salt dissociates and the result acid/base formed is weak. For example, is NH4Cl is dissociated, it will form NH4+ and Cl-. NH4+ will react with water to form H3O+ and NH3. Since NH3 is a weak base, it will not fully dissociate. And since this reaction forms H3O+, it will result in the solution becoming more acidic. The Cl- does not affect the solution for the same reasons as mentioned above.
Salts usually only affect pH if they are weak rather than strong. Strong acids and bases can disassociate totally, and they wont affect the pH, while a weak one will only disassociate partially, meaning that the concentration of H30+ or OH- molecules will increase or decrease depending on the compound. this causes a change in pH.
If the salt in question was formed by a strong acid and strong base, then it will be a neutral salt (i.e. HCL + NaOH => H2O + NaCl), however if a weak acid or a weak base was used, then the resulting salt will be an acidic salt or a basic salt, respectively.
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