Question

How to draw distribution graph if pKa of acid is 4.4 and pKa of base is 6.7?

it should look like this

Answer 1

Well, these distribution graphs should correlate with the titration curve.

If we know the first `"pKa"` is `4.4` and the second `"pKa"` is `6.7`, then we have an idea of where the half-equivalence points are (i.e. where the concentrations of acid and conjugate base are equal), because the `"pH"` `=` `"pKa"` at those points:

`"pH"_("1st half equiv. pt.") = "pKa"_1 + cancel(log\frac(["HA"^(-)])(["H"_2"A"]))^("Equal conc.'s, "log(1) = 0)`

`"pH"_("2nd half equiv. pt.") = "pKa"_2 + cancel(log\frac(["A"^(2-)])(["HA"^(-)]))^("Equal conc.'s, "log(1) = 0)`

We represent each stage of a diprotic acid as:

`"H"_2"A"(aq) rightleftharpoons overbrace("HA"^(-)(aq))^"singly deprotonated" + "H"^(+)(aq)`

`rightleftharpoons overbrace("A"^(2-)(aq))^"doubly deprotonated" + "H"^(+)(aq)`

The two midpoints shown are the first and second half-equivalence points, respectively.

• At midpoint 1, we have that `["H"_2"A"] = ["HA"^(-)]`, and that `"pH" ~~ 4.4`.

• At midpoint 2, we have that `["HA"^(-)] = ["A"^(2-)]`, and that `"pH" ~~ 6.7`.

A distribution graph shows the change in concentration of each species in solution as the `"pH"` increases. It correlates well with a base-into-diprotic-acid titration curve.

See below for an overlay of both:

Each species in solution is tracked in the bottom graph.

• The cross-over points on the distribution graph are the half-equivalence points on the titration curve.

• The maximum concentration for each species after the starting `"pH"` correlate with the first few equivalence points, and the last species to show up dominates at high `"pH"`.