Question

Consider the determination of the concentration of CO32- in a solution of H2CO3. (Ka1=4.3x10-7, Ka2=5.6x10-11) What appropriate approximation(s) can be made in the second step of determining this concentration?

Answer 1

Let us consider the acid as H2A

H2A +H2O <------> H3O⁺ +HA^- For this Ka1 = [H3O+][HA-] /[H2A]

HA^-  +H2O -<------> H3O⁺ + A^-2   Ka2 = [H3O+][A^-2] /[HA^-]

The approximations used are

   i) for a fairly concentrated solution of dibasic acid, ionization of water can be neglected.

ii)In general diprotic acids have Ka2 << Ka1, that is only first ionization is important

   thus H2A + H2O <------> H3O⁺ + HA^-

c 0 0 initial concentrations

c(1-x) cx cx equilibrium concentrations

The approximation gives [H3O+] = [HA-] = cx

iii) Since

Ka2 = [H3O+][A^-2] /[HA^-]

and [H3O+] = [HA-] = cx then substituting these in Ka2

we get [A^-2] = Ka2

Thus in case of carbonic acid [CO₃^-2] = Ka2 = 5.6x 10^-11

i