[Rutherford]

In a buffer solution (pH=8), some amount of NaHCO₃ is added and the pH remained the same. In what ratio are the concentrations of H₂CO₃, HCO₃^- and CO₃^2- (K_a1=4.45*10^-7, Ka2=4.69*10^-11) in the obtained solution?

Mine answer wasn't in agreement with the book's (I just got 1 number different), so I will write mine attempt:
I will mark the concentration of the hydrogen carbonate with c where a+b=c.
HCO₃^-+H₂O H₃O⁺+CO₃^2- K_a2=4.69*10^-11
a-x≈a              10^-8      x
HCO₃^-+H₂O OH^-+H₂CO₃ Kb=2.25*10^-8
b-y≈b              10^-6      y
To solve this I have to assume that a≈b=a, and I get that x=a/213.22, y=a/44.
Now c:x:y= 2a : a/213.22 : a/44.44=426:1:4.8, while in the book it is 213:1:4.8. Where have I mistaken, or is it a mistake in the book?

[Borek]

So a is the concentration of HCO₃^-, and b is the concentration of HCO₃^-, and their sum is the concentration of HCO₃^-?

[Rutherford]

Nice catch ! It should be a≈b≈c. Thanks very much!