Derivation of molecular pK values from pH-dependences

Area of Science:

• Analytical Chemistry
• Physical Chemistry

Background:

• Understanding the ionization behavior of polyprotic acids is crucial in various chemical and biological applications.
• Titration and pH measurements are standard methods for characterizing acid-base properties.

Purpose of the Study:

• To derive and present formulas for calculating the molecular pK values of dibasic acids.
• To relate experimentally determined titration pK values and half-maximal concentration pH values to molecular pK values.

Main Methods:

• Theoretical derivation based on acid-base equilibrium principles.
• Mathematical formulation relating different pK definitions.

Main Results:

• Established that molecular pK values for a dibasic acid can be expressed as pK +/- log(p+1/p) from titration pK values (pK +/- logp).
• Derived that molecular pK values can also be expressed as pK +/- log(q-4+1/q) from pH values at half-maximal monoprotonated form (pK +/- logq).

Conclusions:

• The study provides a clear mathematical framework for determining molecular pK values from common experimental data.
• These derived formulas enhance the accurate characterization of dibasic acid ionization.