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How does water act as a buffer and why is it not a good one

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Water doesn't have a large Ka (acid dissociation constant), hence the equilibrium of

H2O ⇌ H+ + OH-

lies on the far left.

therefore a container of water wouldn't have many H+ and OH- ions floating about.

There WOULD be a very very very small concentration and H+ and OH- in it, since a value of Ka means that it does ionise in itself, but on the whole there would be MORE water molecules floating about. This is why water acts as a very poor buffer.

You need the acid AND the conjugate base (salt) for a buffer to work.