Bivalent
Interactive Ligand Binding (lig)
Symmetrical dicarboxylic acid:
When fully protonated ("saturated"), a dicarboxylic acid undergoes a two-step dissociation reaction with
decreasing hydronium ion concentration. When completely deprotonated ("desaturated"), a dicarboxylate
undergoes a two-step association reaction with increasing hydronium ion concentration.
For correct statistical analysis is it necessary to keep
track of binding to the right and left sides of the molecule.
Two-step dissociation |
| | kd1 |  |  | | HOOC-CH2-COOH |
- H+ | +H+ |
| -OOC-CH2-COOH |  | kd1' | | | ka2 |  | | kd2 |
- H+
 |  + H+ |
|  ka2' | |  ka1 |
 + H+ | - H+
 |
| |  | ka1' | | |  | HOOC-CH2-COO- |
+H+ | - H+  |
| -OOC-CH2-COO- |  |  |  | kd2' | | |
|
Two-step association |
kd1-cooh = [H+] * [-OOC-CH2-COOH] / [HOOC-CH2-COOH] (step d1) | kd1'-cooh = [H+] * [HOOC-CH2-COO-] / [HOOC-CH2-COOH] (step d1') | kd2-cooh = [H+] * [-OOC-CH2-COO-] / [-OOC-CH2-COOH] (step d2) | kd2'-cooh = [H+] * [-OOC-CH2-COO-] / [HOOC-CH2-COO-] (step d2') | kd1 = kd1' = 1/ka2 = 1/ka2' | kd2 = kd2' =1/ka1 = 1/ka1' |
| ka1-cooh = [-OOC-CH2-COOH] / [ H+] * [-OOC-CH2-COO-] (step a1) | ka1'-cooh =[HOOC-CH2-COO-] / [H+] * [-OOC-CH2-COO-] (step a1') | ka2-cooh = [HOOC-CH2-COOH] / [H+] * [-OOC-CH2-COOH] (step a2) | ka2'-cooh = [HOOC-CH2-COOH] / [H+] * [HOOC-CH2-COO-] (step a2') | ka1 = ka1' = 1/kd2 = 1/kd2' | ka2 = ka2' = 1/kd1 = 1/kd1' |
|
Continue the acid-base titration analysis of dicarboxylic acid by
opening the Excel spreadsheet below.
- Up and down arrow dials adjust the pH1/2, i.e., the midpoint of the titration, pkaave, where kaave = (ka1 * ka2)1/2
- Up and down arrow dials also adjust the ratio ka1/ka2 = S, the "saturation ratio" of microscopic equilibrium association constants.
Dicarboxylic Acid-Base Titration:

Interactive Bivalent Ligand Binding
© Duane W. Sears
Revised: August 10, 1998