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Is it necessary for an acid to have pH less than 7? If no, please elaborate with examples.

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Yes, the pH will be less than 7.

Remember that the pH of 7 in neutral water comes from its autodissociation. That autoionization diminishes when we add an acid or a base, but it does not disappear immediately. If the acid or base is very weak, you may still have much of the solvated proton/hydroxide ion concentration comes from water rather than acid/base dissociation.

If you have an acid that appears to be generating less than $10^{-6}$ mol/l solvated protons from the acid, or a base generating less than $10^{-6}$ mol/l hydroxide ions, then water autodissociation remains appreciable. You then need to look at both water dissociation and acid or base dissociation. When you do, you properly get pH below 7 for an acid, or above 7 for a base.

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    $\begingroup$ Neutrality doesn't necessarily mean that pH = 7. Neutral water at 25 degrees Celsius has a pH of 7, yes. The pH of neutral water will vary with temperature. The only requirement for neutrality is that [H+] = [OH-]. $\endgroup$ – Dissenter Jun 6 '16 at 5:36
  • $\begingroup$ I know. But usually these problems are posed in the context of ambient conditions. Regardless of the temperature or exact dissociation product, the point that we may need to be ready to consider solvent autodissociation as well as acjd/base dissociation stands. A practical example is the very slight acid hydrolysis of magnesium salts and maybe even calcium salts of strong acids. $\endgroup$ – Oscar Lanzi Jun 6 '16 at 13:20

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