pH of Monoprotic Acid and Base Solutions

Use this Demonstration to calculate the concentration of hydronium/hydroxide ions, pH/pOH and the fraction of dissociation for a mixture of a monoprotic acid and a monoprotic base. You can input the relevant molar concentrations, volumes and acid/base dissociation constants.
Exact quartic and cubic equations are solved rather than the quadratic approximations to the Henderson–Hasselbalch equation commonly encountered in general chemistry textbooks. By taking the self-ionization of water and temperature into account, more accurate results are achieved, particularly for solutions of low concentration.


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This Demonstration is based on [1] by Limpanuparb and Ho.
Snapshot 1: calculation for an acid solution diluted to a very low concentration, using a quartic equation
Snapshot 2: calculation for a buffer solution using a cubic equation, with input parameters that the Henderson–Hasselbalch equation neglects
Snapshot 3: calculation for a solution of pure water (no acid or base) at a high temperature, showing the effect of self-ionization of water
The quartic equation used for calculation [2, 3] is
The cubic equation used for calculation [4] is
Definitions of input variables:
is the acid dissociation constant; (assume 0 for strong acid).
is the molar concentration of acid.
is the volume of acid in mL.
is the molar concentration of conjugate base.
is the base dissociation constant; , (assume 0 for strong base).
is the molar concentration of base.
is the volume of base in mL.
is the molar concentration of conjugate acid.
Definitions of output variables:
is the molar concentration of hydronium ion.
is the molar concentration of hydroxide ion.
pH and pOH are the negative of the common logarithm of and , respectively.
Fraction of dissociation is the ratio of equilibrium concentration of dissociated acid/base to initial concentration of the acid/base.
[1] T. Limpanuparb and J. Ho, "Visualization of Validity Ranges for Acid Approximations: Error Contour Plots as a Function of Concentration and ," Journal of Chemical Education, 2023. doi:10.1021/acs.jchemed.3c00751.
[2] P. Glaister, "A Unified Titration Formula," Journal of Chemical Education, 76(1), 1999 132. doi:10.1021/ed076p132.
[3] R. de Levie, "Explicit Expressions of the General Form of the Titration Curve in Terms of Concentration: Writing a Single Closed-Form Expression for the Titration Curve for a Variety of Titrations without Using Approximations or Segmentation," Journal of Chemical Education, 70(3), 1993 209. doi:10.1021/ed070p209.
[4] H. L. Pardue, I. N. Odeh and T. M. Tesfai, "Unified Approximations: A New Approach for Monoprotic Weak Acid-Base Equilibria," Journal of Chemical Education, 81(9), 2004 1367. doi:10.1021/ed081p1367.
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