Question

Calculate the concentration of all species in a 0.160 M solution of H2CO3

Answer 1

H2CO3 ionizes in two steps:
H₂CO₃ ⇌ HCO₃⁻ + H⁺ Ka1 = 4.3X10^-7

HCO₃⁻ ⇌ CO₃²⁻ + H⁺ Ka2 = 5.6X10^-11

Using the first Ka:
Ka1 = [H+][HCO3-]/[H2CO3] = 4.3X10^-7
[H+] = [HCO3-] = x Then,
x²/0.160 = 4.3X10^-7
x = [H+] = [HCO3-] = 2.6X10^-4 M

A small amount of the HCO3- will ionize by the second equation, but this will be very small relative to the first ionization. So,
5.6X10^-11 = [H⁺][CO3^2-]/[HCO3^-]
Since from the first ionization, [H+] = [HCO3^-], and because these will not change significantly because of the second ionization,

[CO3^2-] = 5.6X10^-11

Since [H+] = 2.6X10^-4, [OH-] = 1X10^-14 / 2.6X10^-4 = 3.8X10^-11

[H+] = [HCO3-] = 2.6X10^-4 M ; [OH-] = 3.8X10^-11 M