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It is not to do with buffers.

If you take pure water at 25°C, it dissociates:

H2O ↔ H+ + OH- ( I use H- instead of H3O+ for simplicity)

You ask about bases:

If you add a base, such as NaOH to the water, you introduce a high concentration of OH- ions to the water.

This causes the dissociation equilibrium of the H2O to move to the left. ( In accordance with Le Chettellier) But the re-association of the H+ and OH - from the water is not complete - there are always some H+ ions dissociated

This is determined by the equation:

[H+] [OH-] = 10^-14

You can see this from the pure water where [H+] and [OH-] are both 1*10^-7M - the equation is satisfied

Now on adding the base, the [OH-] increases to 5*10^-3M , What is [H+] in this solution:

[H+] = 10^-14 / (5*10^-3) = 2*10^-12M

There will be a reducing concentration of H+ as [OH-] increases, but always some H+ present

The converse happens with an acid solution

You add acid, say HCl to the water so that [H+] = 5.10^-3

[OH-] = (10^-14)/ (5*10^-3) = 2*10^-2M

Even in the acid solution there will be some OH- ions present.

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