Calculation of Equivalence Points
Problem
What are the equivalence points (pH values) of the following three solutions:
 1 mM H_{2}CO_{3} (or pure CO_{2}) solution
 1 mM NaHCO_{3} solution
 1 mM Na_{2}CO_{3} solution
These solutions refer to a total carbonate amount (DIC) of 1 mM. What happens when the DIC value is varied between 10^{12} and 10^{1} M?
Answer
In titration, the equivalence point is defined as that solution in which the acidbase reaction is completed stoichiometrically.^{1} In other words, we have to perform equilibrium calculations for the three reactants given above.
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  H_{2}CO_{3} solution:  pH = 4.68 
1 mM  NaHCO_{3} solution:  pH = 8.27 
1 mM  Na_{2}CO_{3} solution:  pH = 10.52 
Note: You will obtain exactly the same pH values (equivalence points) when NaHCO_{3} is replaced by KHCO_{3}, and Na_{2}CO_{3} by K_{2}CO_{3}. 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 10^{1} M (in 13 logarithmic steps). The results are plotted here.
Footnotes

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