Titration Curve of a Weak Acid and its pKa (Biochemistry Notes)

What is Titration?

Titration is a method to determine the concentration of a dissolved substance (analyte or titrand) in a known volume by reacting it with another substance of known concentration and volume (titrant). The volume of the reactants plays a crucial role in the titration and thus the titration is better called as ‘volumetric analysis’.

There are different types of titrations in which the Acid-Base Titration is the most common one. The acid-base titration is used to determine the amount (concentration) of an acid in a given solution. In an acid-base titration, a known volume of acid (of unknown concentration) is titrated against a solution of strong base (usually NaOH) of known concentration in the presence of an indicator. After the titration, the concentration of the acid in the sample is calculated using the concept N1V1 = N2V2.

Where,

N1 – Normality of the unknown acid
N2 – Normality of the known base
V1 – Volume of unknown acid
V2 – Volume of the known base

What is Titration Curve?

The titration curve is a graphical representation of a titration in which the volume of titrant is plotted on X-axis (as the independent variable) and the pH of the solution is plotted on the Y-axis (as the dependent variable). In simple terms, the titration curve is the plot of pH of the analyte (titrand) versus the volume of the titrant added as the titration progresses.

For the preparation of a titration curve of an acid-base titration, the base is added in small increments and the pH of the acid in each step is determined with a pH meter. A titration curve can be prepared for a titration of strong acid vs strong base, weak acid vs strong base, strong acid vs weak base and weak acid vs weak base. In the present post will discuss the titration curve of a weak acid with strong base. Such a titration reveals the pKa of the weak acid explains the buffer action of the weak base pair.

The titration curve reveals the pKa of a weak acid

Here, as an example, we have selected acetic acid (CH₃COOH) as the weak acid and it is titrated against a strong base NaOH. The NaOH is added as small increments of equal volume and at each step, the pH of the solution is measured and a titration curve is prepared as mentioned above.

As in the picture below, the titration curve of a weak acid has a characteristic shape. It also reveals the pKa (the negative logarithm of Ka) of the acid. The pKa is the pH at which the system consists of an equimolar concentration of the proton donor (CH₃COOH) and proton acceptor (CH₃COO¯). This relationship between pKa and pH and Buffer-action can be determined from the Henderson-Hasselbalch Equation that we have already discussed in the previous post.

Learn more: Derive Henderson Hasselbalch Equation

Learn more: How to Calculate pH from pKa? (Solved Problems)

Let’s study the titration curve of Acetic Acid (CH₃COOH) and its characteristic shape in details:

Ø  Since CH₃COOH is a weak acid, well before the addition of NaOH, a few molecules of the acids will be ionized. (CH₃COOH  ⇋ CH₃COO¯   +   H⁺)

Ø  The degree of the ionization can be calculated from the dissociation constant – Ka of the acetic acid. (The Ka of acetic acid it is 1.74 X 10⁵M.)

Ø  As the NaOH is gradually added, the OH¯ ions present in it will combine with the free H⁺ ions in the medium to form H₂O.

Ø  As the titration proceeds, the free H⁺ ions are removed by the addition of OH¯, more and more acetic acid molecules will dissociate to satisfy its own equilibrium constant.

Ø  At the mid-point of titration, one half of the original acetic acid has undergone dissociation and the rest will be intact.

Ø  At this point, the concentration of proton donor (HA) and proton acceptor (A¯) will be equal.

Ø  Here the proton donors are intact acetic acid molecules (CH₃COOH) and proton acceptors are acetate ions (CH₃COO¯).

Ø  At this mid-point of titration, the pH of the equimolar solution of acetic acid and acetate ions will be exactly equal to the pKa of acetic acid.

Ø  The pKa of acetic acid is 4.76 as given in the picture.

Ø  As the titration is continued by adding more NaOH increments, the remaining non-dissociated acetic acid molecules are gradually converted into acetate ions.

Ø  At the end of titration, all the acetic acid molecules in the solution will be converted into acetate ions.

Ø  The titration curve of other weak acids such as phosphoric acid and ammonium also shows similar shape.

Significance of Titration Curve of a Weak Acid

Ø  The titration curve of a weak acid reveals its pKa.

Ø  pKa is a pH at which the concentration of weak acid and its conjugate base will be in equimolar concentrations. This equimolar concentration of a weak acid and its conjugate base can act as a buffer. (Buffer is a solution which can resist the change in pH).

Ø  Thus, titration curve also reveals the buffer action of weak acid and its conjugate base.

References Lehninger A.B., (2018), Textbook of Biochemistry, Ed. 5, Pearson International, New York

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