What is the concentration?

Question

Calculate the concentration of bicarbonate ion, HCO₃^-, in a 0.050 M H₂CO₃ solution that has the stepwise dissociation constants K_a1 = 4.3 × 10^-7 and K_a2 = 5.6 × 10^-11.

Answer 1

Looking at the dissociation of H₂CO₃:

H₂CO₃ <==> H⁺ + HCO₃^- ... Ka1 = 4.3x10^-7

HCO₃^- <==> H⁺ + CO₃^2- ... Ka2 = 5.6x10^-11 (negligible compared to Ka1)

Because Ka2 is more than 1000 times less than Ka1, it can, in general, be ignored as contributing significantly to the [HCO₃^-]. Thus, we conduct the calculations as follows:

Ka1 = 4.3x10^-7 = [H⁺][HCO₃^-] / [H₂CO₃]

4.3x10^-7 = (x)(x) / 0.05 - x and assuming x is small relative to 0.05, we an ignore it (*see below)

x² = 2.15x10^-8

x = 1.5x10^-4 M (*this is only about 0.3% of 0.05 so our assumption above was valid)

This would be the [HCO₃^-] as well as the [H⁺].