Titration Curves


Acid/base titrations are acid/base reactions with interesting characteristics. The goal of this article is to present the procedure for determining the pH of a solution at any point in an acid/base titration.


Strong acid/strong base titration curve


A titration will usually generate a characteristic titration curve from a plot of pH vs. volume of titrant added. The pH of the solution is recorded upon the addition of a small amount of titrant. Below is a titration curve for the titration of a strong acid with a strong base. A strong base is added dropwise to a strong acid.

\[\mathrm{H^+}(aq) + \mathrm{OH^-}(aq) \longrightarrow \mathrm{H_2O}(l)\]

Important Note!

You may look at the reaction above and wonder what H+ is. It is the strong acid! We normally represent an acid as HA (think HCl). We know that when a strong acid is placed in water, it will dissociate completely.

\[\mathrm{HA}(aq) \longrightarrow \mathrm{H^+}(aq) +\mathrm{A^-}(aq) \]

The A anion is too weak to react with water (to affect the pH), and therefore is now completely ignored. The proton, H+, is captured by water to form the hydronium ion.

\[\mathrm{H^+}(aq) + \mathrm{H_2O}(l) \longrightarrow \mathrm{H_3O^+}(aq)\] The added base in this titration really reacts with hydronium to give water.

\[\mathrm{H_3O^+}(aq) + \mathrm{OH^-}(aq) \longrightarrow 2\mathrm{H_2O}(l)\] The reaction above is synonymous with the following reaction

\[\mathrm{H^+}(aq) + \mathrm{OH^-}(aq) \longrightarrow \mathrm{H_2O}(l)\]

Titration Details

  • 50.00 mL of a 0.1 M strong, monoprotic acid
  • 0.1 M strong base
  • 25 °C

Since the titration starts with a strong acid, the pH of the solution is very low (about 1) when no base has been added. As base is slowly added, the pH slowly creeps up. The equivalence point is the point at which all acid and base has been neutralized (shown by the red line; here the pH = 7 at that point). This is marked by a sharp increase or jump in pH on the plot. As we continue to add more base, the pH of the solution skyrockets.

Using our knowledge of acids and bases, equilibrium expressions, and buffers, we should be able to calculate the pH of the solution anywhere on our titration curve!


Weak acid/strong base titration curve


The following titration curve is characteristic of a weak acid (pKa = 5.0) and strong base titration.

\[\mathrm{HA}(aq) + \mathrm{OH^-}(aq) \rightleftharpoons \mathrm{H_2O}(l) + \mathrm{A^-}(aq)\]

Titration Details

  • 50.00 mL of a 0.1 M weak, monoprotic acid (pKa = 5)
  • 0.1 M strong base
  • 25 °C

The initial pH of the solution indicates a weakly acidic solution. A strong base is the titrant as the large, final pH indicates. The equivalence point is at a pH > 7.

We can see the comparison of multiple tiration curves when using different weak acids with different pKa values. Recall that the smaller the pKa value, the stronger the acid In the plot below, the pKa values are 9, 7, and 5 for the top, middle, and bottom curves, respectively.


Diprotic weak acid/strong base titration curve


A diprotic acid (such as carbonic acid, H2CO3), will yield two equivalence points due to the two ionization steps it can undergo.

\[\mathrm{H_2CO_3}(aq) + \mathrm{OH^-}(aq) \rightleftharpoons \mathrm{H_2O}(l) + \mathrm{HCO_3^-}(aq)\] \[\mathrm{HCO_3^-}(aq) + \mathrm{OH^-}(aq) \rightleftharpoons \mathrm{H_2O}(l) + \mathrm{CO_3^{2-}}(aq)\]

Titration Details

  • 50.00 mL of a 0.1 M weak, diprotic acid (carbonic acid; pKa1 = 6.3; pKa2 = 10.3)
  • 0.1 M strong base
  • 25 °C


Strong acid/weak base titration curve


The following titration curve is characteristic of a strong acid and weak base (pKb = 9) titration (a strong acid is added to a weak base).

\[\mathrm{H^+}(aq) + \mathrm{B}(aq) \rightleftharpoons \mathrm{HB^+}(aq)\]

Titration Details

  • 50.00 mL of a 0.1 M weak base (pKb = 5)
  • 0.1 M strong acid
  • 25 °C

The initial pH of the solution indicates a weakly basic solution. A strong acid is the titrant as the small, final pH indicates. The equivalence point is at a pH < 7.

We can see the comparison of multiple tiration curves when using different weak bases with different pKb values. Recall that the smaller the pKb value, the stronger the base. In the plot below, the pKb values are 5, 7, and 9 for the top, middle, and bottom curves, respectively.


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