Calculation of Equivalence Points


What are the equivalence points (pH values) of the following three solutions:

These solutions refer to a total carbonate amount (DIC) of 1 mM. What happens when the DIC value is varied between 10-12 and 101 M?


In titration, the equivalence point is defined as that solution in which the acid-base reaction is completed stoichiometrically.1 In other words, we have to perform equilibrium calculations for the three reactants given above.

aqion: reaction H2O + H2CO3

In all three cases we start with pure water (button H2O) and use the reaction tool (button Reac). For the first reaction select the reactant “H2CO3” and enter “1 mmol/L” as shown in the right screenshot. With click on Start the resulting pH will be displayed.

Repeating this procedure for the other two cases yields the three equivalence points (for 25):

1 mM H2CO3 solution: pH =   4.68
1 mM NaHCO3 solution: pH =   8.27
1 mM Na2CO3 solution: pH = 10.52

Note: You will obtain exactly the same pH values (equivalence points) when NaHCO3 is replaced by KHCO3, and Na2CO3 by K2CO3. That is because NaOH and KOH are both strong bases (which dissociate completely) and thus have the same impact on the carbonate system.

DIC Variations. The results above are valid for a specific amount of total dissolved carbonate, namely DIC = 1 mM. The equivalence points will change for other DIC values. To demonstrate this effect we perform the same calculations for 13 different values of DIC between 10-12 and 101 M (in 13 logarithmic steps). The results are plotted here.


  1. The equivalence point (stoichiometric point) should be distinguished from the titration endpoint (where the indicator changes its color). Both are not exactly the same. 

[last modified: 2023-11-15]