HPO42- and pKa

[leathersofa]

TBR says how if a solution contained pure HPO4^2-, the pH would be an average of pKa2 and pKa3. I do not understand how the pH would be an average of both pKa's mathematically. Could someone explain this? Thank you!

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[eudovcic]

At pKa=2 the concentration of conjugate base and acid is equal. So [H2PO4^1-]=[HPO4^2-]. pH=2.
At pKa=3 the same occurs. [HPO4^2-]=[PO4^3-]. pH=3.

So at the average of both your solution should be all HPO4^2- and pH is an average of both.

As for the mathematics, I'm not sure. It's either 2.5 or 1.26.

 

[leathersofa]

So at the average of both your solution should be all HPO4^2- and pH is an average of both.

can you please expound this part a little more? i'm confused how the pH is an average since the concentrations equal each other?

 

[FeinMS]

can you please expound this part a little more? i'm confused how the pH is an average since the concentrations equal each other?

You know H3PO4->H2PO4->HPO4->PO4 (omitted formal charge due to laziness) At pKa2, [H2PO4]=[HPO4] and at pKa3, [HPO4]=[PO4]. In other words, they're 50:50. So you can guess that at half point between pKa2 and pKa3, there will be only HPO4.

It's the very same thing as finding the isoelectric point of a peptide. You average 2 pKa values, so you get 100% of neutral species.

 

[leathersofa]

alright, i get what you mean now. thank you!