Exact and Approximate Calculations of Acid-Base Equilibria

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In this Demonstration, we show exact and approximate calculations for acid-base equilibria.


The equation for acid dissociation (and similarly for base) is given by , where is the acid (base) concentration and is the acid (base) dissociation constant. This equation can be approximated in the case by . The first graphic shows the results for concentration and the dissociation calculated both exactly and approximately. The appropriate number of significant digits is used.

In the case of a strong acid/base concentration, the water dissociation is determined by , where is the acid (base) concentration and is the autoionization constant of water (at , ). When , this can be approximated by . Use the checkbox to switch from acid to base.


Contributed by: A. Ratti, D. Meliga, L. Lavagnino and S. Z. Lavagnino (June 2021)
Open content licensed under CC BY-NC-SA



Snapshot 1: Exact and approximate equations give the same result since the initial concentration is high and the extent of dissociation is very low (weak acid).

Snapshot 2: Exact and approximate equations are very different since we have a very high acid dissociation constant. In this case, the acid is completely dissociated (strong acid).

Snapshot 3: Incorrect use of the approximate equation gives the pH of a base although the solution is a slightly acidic.


[1] D. C. Harris, Quantitative Chemical Analysis, 8th ed., New York: W. H. Freeman and Company, 2010.

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