A titration is a procedure in which one standardized substance (titrant) is carefully added to another (analyte) until complete reaction has occurred. By accurately measuring the volume of each solution required to reach the equivalence point (equal molar amounts of acid and base) of the reaction the concentration of the unknown solution can be determined. In this strong acid-strong base titration, which is a neutralization reaction, the titrant will be sodium hydroxide and the analyte will be hydrochloric acid. Strong acids and strong bases are strong electrolytes, which means that they dissociate well in water. Equation 1 is an example of a strong acid dissociating in water and Equation 2 is a neutralization reaction for a hydrochloric acid-sodium hydroxide system. The complete net ionic equation and the net ionic equation for Equation 2 can be seen in Equation 3 and 4 respectively. The only difference between the complete net ionic equation and the net ionic equation is that the spectator ions, Na+ and Cl-, have been omitted. Notice that in Equation 3 the H+ ion from the HCl(aq) is actually written as H3O+, this is because hydrogen ions are so reactive that they will bond to the nearest water molecule to form the hydronium ion.
We can monitor any acid-base titration by following changes in the H3O+ concentration in the solution. The equation that we will be using to find the pH can be seen in Equation 5.
5) pH = -log[H3O+]
Note that the square brackets represent the molarity (M, mol/L) of H3O+. We will be using a pH meter to monitor the pH of the acid solution as we add base to it. Initially the pH will be very low because the acid will be the only substance present. As we add base to the acid solution the pH will increase until we reach the equivalence point where the pH should be approximately 7. This neutralization reaction is complete at the equivalence point, when the number of moles of OH- added as titrant equals the number of moles of H3O+ originally present in solution. The pH at the equivalence point is established by the components of the titration mixture. For the titration of HCl with NaOH, a strong acid with a strong base, Equation 3 shows that the only species present at the equivalence point are Na+, Cl-,H3O+, OH- and H2O. Because neither Na+ nor Cl- react with water (neutral ions), the pH of the titration mixture at the equivalence point is established by the dissociation of water, shown in Equation 6.
6) 2 H2O(l) ( H3O+(aq) + OH-(aq)
The equilibrium constant expression representing this reaction is shown in Equation 7. At 25(C, the dissociation constant for water is 1.0 x 10-14.
7) Kw = [H3O+][OH-] = 1.0 x 10-14
At the equivalence point of our NaOH and HCl titration, H3O+ and OH- concentrations are equal (Equation 6). Therefore, [H3O+] = 1 x 10-7 M, and the pH of the solution is 7 (Equation 5). After the equivalence point we will continue to add base and the solution will become alkaline, pH>7. If we plot the pH of a titration mixture versus volume of titrant added we obtain a graph called a titration curve. Figure 1 shows a typical curve for the titration of a strong acid with a sodium hydroxide solution. We can locate the equivalenc point of the titration by drawing a vertical line through the midpoint of the steep portion of the curve. The titrant volume and pH of the solution at the equivalence point correspond to the x and y coordinates.
Figure 1:
Calculating H3O+ and OH- for Points on a Titration Curve
We can calculate the molarity of H3O+ and OH- from the pH at any point on a titration curve. Suppose we
