Titration of a Weak Acid with a Strong Base
Consider the titration of 25.00 mL of 0.100
M CH
3CO
2H with 0.100
M NaOH. The reaction can be represented as:
Calculate the pH of the titration solution after the addition of the following volumes of NaOH titrant:
(a) 0.00 mL
(b) 25.00 mL
(c) 12.50 mL
(d) 37.50 mL
Solution
(a) The initial pH is computed for the acetic acid solution in the usual ICE approach:
and
(b) The acid and titrant are both monoprotic and the sample and titrant solutions are equally concentrated; thus, this volume of titrant represents the equivalence point. Unlike the strong-acid example above, however, the reaction mixture in this case contains a weak conjugate base (acetate ion). The solution pH is computed considering the base ionization of acetate, which is present at a concentration of
Base ionization of acetate is represented by the equation
Assuming x << 0.0500, the pH may be calculated via the usual ICE approach:
Note that the pH at the equivalence point of this titration is significantly greater than 7, as expected when titrating a weak acid with a strong base.
(c) Titrant volume = 12.50 mL. This volume represents one-half of the stoichiometric amount of titrant, and so one-half of the acetic acid has been neutralized to yield an equivalent amount of acetate ion. The concentrations of these conjugate acid-base partners, therefore, are equal. A convenient approach to computing the pH is use of the Henderson-Hasselbalch equation:
(pH = pKa at the half-equivalence point in a titration of a weak acid)
(d) Titrant volume = 37.50 mL. This volume represents a stoichiometric excess of titrant, and a reaction solution containing both the titration product, acetate ion, and the excess strong titrant. In such solutions, the solution pH is determined primarily by the amount of excess strong base:
Check Your Learning
Calculate the pH for the weak acid/strong base titration between 50.0 mL of 0.100
M HCOOH(
aq) (formic acid) and 0.200
M NaOH (titrant) at the listed volumes of added base: 0.00 mL, 15.0 mL, 25.0 mL, and 30.0 mL.
0.00 mL: 2.37; 15.0 mL: 3.92; 25.00 mL: 8.29; 30.0 mL: 12.097
Performing calculations similar to those in the preceding example permits a more full assessment of titration curves. A summary of pH/volume data pairs for the strong and weak acid titrations is provided in Table 29.1 and plotted as titration curves in Figure 29.1. A comparison of these two curves illustrates several important concepts that are best addressed by identifying the four stages of a titration:
initial state (added titrant volume = 0 mL): pH is determined by the acid being titrated; because the two acid samples are equally concentrated, the weak acid will exhibit a greater initial pH