TBR Buffers

[nwu]

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TBR says that to make a buffer between a weak acid and SB titrant, we need only 1/2 equivalent of the SB titrant. Makes sense.

But then I ran into some questions involving equivalents in the Titration passages. Here is an explanation to a question I missed (Decided to leave out question, explanation is enough to understand my confusion):

"When one and one-half equivalents of base NaOH are added to one equivalent of phosphoric acid H3PO4, the first proton is completely removed. The remaining 1/2 equivalent continues to remove the second proton from half the dihydrophosphate so this results in H2PO4=HPO4, this conjugate pair means that pH=pka2 which is a pH a little over 7."

When I did this question I saw that it was a WA and a SB so we only need 1/2 equivalent of the SB to get to our buffer region. So we start out with 1.5 equivalents of NaOH, so I thought okay I only need 1/2 NaOH to get to the first pka1 conjugate pair. So 1.5-1=1. Now I have 1 equivalent of NaOH left, we need another 1/2 to get to pka2. So 1-.5= .5
Finally, we need another 1/2 NaOH to get to pka3 so .5-.5=0. So when I did it I thought we had stripped phosphoric acid all the way down to pH=pka3 conjugate pair buffer region. Well, clearly I'm wrong b/c TBR says we only get to pka2.

What am I doing wrong here?

Thanks for the help.

 

[justadream]

@nwu

I could be wrong but I think you need 1 equivalent of the base to get it down to H2Po4-.

The last half equivalent is used to make half of the H2Po4 become: HPO4(2-).

Thus, you are left with equal amounts of H2Po4- and HPO4(2-). That combo becomes the buffer.