What are the concentrations of the main two citric acid ions in a 50 mm citric acid solution at ph 4.2?

Citric acid , (COOH)CH2-C(OH)(COOH)-CH2(COOH) is a triprotic acid with three acidic protons. It can be represented as H3A

The equilibrium reaction are:

1) H3A H2A- + H+            pKa1 = 3.14

2) H2A- HA2- + H+        pKa2 = 4.76

3) HA2- A3- + H+            pKa3 = 6.40

The given pH = 4.2 which is closest to pKa2. hence the two ions that will be present are: H2A- and HA2-

As per Henderson Hasselbach equation:

pH = pka + log [HA2-]/[H2A-](1)

[HA2-]/[H2A-] = 10^(pH-pKa) = 10^(4.2-4.76) = 0.275

i.e. [HA2-] = 0.275 [H2A-](2)

It is given that: [HA2-] + [H2A-] = 50 mM (3)

substituting for HA2- IN eq(3) we get:

1.275 [H2A-] = 50 mM

[H2A-] = 50/1.275 = 39.22 mM

[HA2-] = 0.275(39.22) = 10.79 mM