TBR G. Chem - Buffers and Titrations - Equivalence

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cbfc

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"At 2 pH units beyond the pKa of the acid, the ratio of conjugate base to acid is 100:1, which means that the reaction is almost at equivalence."

Why is it 2 pH units? Why not 3 or 4? It says that if the pKa of the acid is 7.20, the best indicator to use is one that is active around ph = 9.20. Why?
 
Since the pH of the buffer region is essentially equal to the pKa of the conjugate acid plus or minus one, and because you're 2 pH units above that value, you're now outside of the buffer region. So for example if you make a buffer with a conjugate acid/base pair where the pKa of the conjugate acid is 4.5, then the buffer region pH is roughly between 3.5 and 5.5. 2 pH units above this would be 6.5. At this point, you are out of the buffer region, and close to the equivalence point - remember there's typically a sharp increase in pH (or decrease if titrating base with acid) once the buffer has been overcome with titrant.

Another note is that buffers have a conjugate acid/base pair in a ratio of between 10:1 or 1:10. If that ratio is bigger than that, you're out of the buffer. So since the pH is one pH unit outside of the buffer range (remembering that pH = pKa +/- 1, and we're 2 units above that pKa), that extra pH unit accounts for the extra order of magnitude we see in the ratio of conjugate base to acid, 100:1. We're out of the buffer range because we've overcome that 10:1 threshold. Just another way to look at it.
 
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