Question

Explain how the titration of a weak acid by addition of a strong base could be used to determine the pKa value of the weak acid.

Answer 1

The plot of pH vs the volume of the strong base added is usually a S-shaped curve with a positive intercept on the pH axis. The pH at the equivalence point can be easily determined as the equivalence point is the middle point of the steeply rising portion of the curve. Alternatively, the equivalence point can be easily determined by plotting Δ(pH)/(ΔV) vs V where V denotes the volume of the strong base added. The above plot shows a sharp peak or inflexion at the equivalence point and the remaining portions of the curve are almost parallel to the volume axis. Therefore, the volume required to reach the equivalence point can be easily determined from the plot of the titration curve.

Once the pH at the equivalence point is determined, the value of the pH at half the equivalence point is determined. The value of the pH at the half equivalence point is the pK_a of the weak acid.

Let the weak acid be denoted as HA and B is a strong base. The acid-base neutralization reaction is given as

HA (aq) + B (aq) <=======> A^- (aq) + BH⁺ (aq)

A^- is the conjugate base of the weak acid HA and shows buffer action.

As per the stoichiometry of the reaction,

Mols HA = mols B = mols A^-

At the half equivalence point, exactly half the number of mols of HA is neutralized to form A^-. Since the volume of the solution stays constant, hence, the numbers of mols of HA and A^- at the half equivalence point are equal to half the initial number of mols of HA present and therefore, the concentrations of HA and A^- are equal.

Using the Henderson-Hasslebach equation,

[HA] = [A^-]

and thus,

pH = pK_a + log [A^-]/[HA]

= pK_a + log (1)

= pK_a (the square braces denote molar concentrations).