pKa versus pKb

[MedGrl@2022]

79. The pKa of the amphoteric hydrogen carbonate ion is 10.25. What is the pKb of this ion?
A. 3.25
B. 3.75
c. 10.25
D. Cannot be determined from the information given

I thought it was B. 3.75 but EK says "779. D is correct. The equation pK. + pKb = 14 applies to conjugates only. The pKb of the carbonate ion, which is conjugate to the
hydrogen carbonate ion, is indeed 3. 75, but that is not what this question asks for!"

I am confused. Why can't you use pKa + pKb= pKw here. When can you use the equation and when can't you? What is the rule?

Thank you for all your help!!!! 🙂

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you can only get the pka from the pkb and vice versa knowing nothing else only when you're talking about conjugates. since this is an amphoteric compound, there are 2 possible dissociations here: H2CO3 ---> HCO3- ----> CO3(2-). So, like in the question, if you knew the pka of the acid HCO3- for the second reaction, you could simply figure out the pkb for the reverse of the base of the reverse reaction (CO3(2-)). The pka and pkb for that first dissociation (H2CO3 as the acid and HCO3- as the base) are a totally separate thing here. If, on the other hand you knew the pkb for HCO3-, the pka you could calculate would be for H2CO3, not HCO3-