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    why is it essential to have the inverse logarithm of the dissociation constant of the acid or base used close to the pH of the buffer prepared?
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    It isn't essential, just desirable.

    If pH = pKa, then [H+] = Ka, then Ka/[H+] = [A-]/[HA] = 1, i.e. [A-] = [HA], in which case it is just as good a buffer in the acid direction as the alkali direction.
 
 
 
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