Analytical

Theoretical acid-base titration curve calculations – I part

Theory:

This theoretical calculation can be represented by a titration of hydrochloric acid solution vs. sodium hydroxide solution (reverse titration = a mirror image). Both of the reactants are almost completely ionized in solutions. A reaction that takes place is a simple neutralization reaction in which H+ and OH combine together to form a water molecule [1]

H+ + Cl + Na+ + OH H2O + Na+ + Cl

Dependence of pH value on the volume of titrant added is called titration curve. For known concentration of the reagents titration curve can be calculated. It acquires the calculations of the species present in  the solution at various stages of titration.

Assuming we have a solution of hydrochloric acid with concentration 0,1M and a volume of 50 mL. If it acts as an ideal solution pH at the very begging of titration can be calculated as

titracia2

Concentration of oxonium ions is the same as the concentration of hydrochloric acid thus pH = -log[0,1] = 1. Before the equivalence point the oxonium ions react with hydroxide ions forming water molecules. This means that the oxonium ions are consumed and their concentration decreases whereas pH will slowly increase. Near the endpoint of titration, decrease in the concentration of the oxonium ions would proceed much more quickly and pH will rapidly raise.

titracia 1

In the equivalence point, no hydroxide or oxonium ions are present in the solution (except for those created in autoprotolysis of water) so we have pH value of 7. After the equivalence point, when more base is added, hydroxide ions concentration increases rapidly and pH reaches values of 11 very quickly. The calculations of this part are as follows

titracia4

A final graph in titration of strong acid with strong base is shown below. (Assymetry of the curve plotted is observed in a case when different concentrations of solutions used.)

Graph1

Literature:

[1] Christian, Gary D. Analytical Chemistry. 5th ed. New York: J. Wiley & Sons, 1994. Print.