Premed · Premed · General Chemistry 2
Lecture 8: Acid-Base Titrations
General Chemistry II
Learning Objectives
By the end of this lecture, students will be able to:
- Describe the titration process and identify the equivalence point and endpoint
- Sketch and interpret titration curves for strong acid/strong base, weak acid/strong base, and strong acid/weak base titrations
- Calculate the pH at key points during a titration
- Identify the half-equivalence point and its significance
- Select appropriate indicators for different titrations
- Analyze polyprotic acid titration curves
Lecture Content
I. Titration Fundamentals
A titration is an analytical technique in which a solution of known concentration, called the titrant, is gradually added to a solution of unknown concentration, called the analyte, until the reaction between them is complete. The equivalence point is reached when stoichiometrically equivalent amounts of acid and base have reacted, satisfying the relationship n_a M_a V_a = n_b M_b V_b, where n represents the number of acidic or basic protons per molecule. The endpoint is the point at which the indicator changes color; ideally, it coincides with the equivalence point. The titration curve, a plot of pH on the y-axis versus volume of titrant added on the x-axis, provides a visual record of the entire process.
II. Strong Acid - Strong Base Titration
Consider the titration of HCl with NaOH. The initial pH is low, determined by the concentration of the strong acid. As base is added, the pH rises gradually, but there is no buffer region because no weak acid-conjugate base pair is formed. Near the equivalence point, the pH rises very steeply over just a fraction of a milliliter. The equivalence point pH is exactly 7.00 because the resulting salt, NaCl, does not hydrolyze. Beyond the equivalence point, the pH continues to rise as excess base accumulates.
Calculating the pH at various stages is straightforward. Before the equivalence point, calculate the excess moles of H+ remaining and divide by the total volume. At the equivalence point, the pH is 7.00. After the equivalence point, calculate the excess moles of OH- and divide by the total volume.
<image>A strong acid-strong base titration curve showing pH vs. volume of NaOH added to 25.0 mL of 0.100 M HCl. The curve starts at pH approximately 1.0, rises gradually, then shows a near-vertical jump from about pH 3 to pH 11 around 25.0 mL (the equivalence point, marked with a dot and labeled "Equivalence point, pH = 7.00"). After the jump, the pH levels off approaching 13. Key points are labeled: initial pH, the steep region, and the post-equivalence region. The volume axis shows 0, 12.5, 25.0, 37.5, and 50.0 mL markings.</image>
III. Weak Acid - Strong Base Titration
The titration of a weak acid such as CH3COOH with NaOH differs from the strong acid case in several important ways. The initial pH is higher, determined by the Ka and concentration of the weak acid rather than by complete dissociation. As base is added, a buffer region develops where the pH changes gradually because a mixture of HA and A- is present. At the half-equivalence point, exactly half the acid has been neutralized, so [HA] = [A-] and the Henderson-Hasselbalch equation gives pH = pKa. This provides a convenient experimental method for determining pKa.
The equivalence point pH is greater than 7 because all the original acid has been converted to its conjugate base A-, which hydrolyzes to produce OH-. The steep region near the equivalence point is less dramatic than in the strong acid/strong base case.
Calculating pH at the various stages uses different methods for each region. At the initial point, solve a weak acid ICE table problem. In the buffer region before the equivalence point, first do the stoichiometry to find the moles of HA and A-, then apply the Henderson-Hasselbalch equation. At the half-equivalence point, pH simply equals pKa. At the equivalence point, all HA has been converted to A-, so you solve a Kb problem for the conjugate base. After the equivalence point, excess OH- dominates and you calculate [OH-] from the excess base.
IV. Strong Acid - Weak Base Titration
Titrating a weak base such as NH3 with HCl produces essentially the mirror image of the weak acid/strong base curve. The initial pH is basic, determined by the Kb and concentration of the weak base. A buffer region forms as the NH3/NH4+ pair accumulates. At the half-equivalence point, pH equals the pKa of the conjugate acid NH4+ (equivalently, pOH = pKb of the weak base). The equivalence point pH is less than 7 because the conjugate acid BH+ hydrolyzes to produce H3O+. Below the equivalence point, the pH decreases sharply and continues to decrease as excess strong acid is added.
V. Weak Acid - Weak Base Titration
Titrations of a weak acid with a weak base are not commonly performed in practice because the equivalence point is extremely difficult to detect. The pH change near the equivalence point is very gradual with no steep region, making it impossible to identify the equivalence point precisely. No suitable indicator can mark this transition reliably.
<image>An overlay of three titration curves on the same axes (pH vs. volume of base added). Curve 1 (red): Strong acid (HCl) + strong base (NaOH), equivalence point at pH 7.00, steepest vertical region. Curve 2 (blue): Weak acid (CH3COOH) + strong base (NaOH), equivalence point at pH approximately 8.7, the half-equivalence point is marked and labeled "pH = pKa = 4.76," buffer region is shaded. Curve 3 (green): Very weak acid + strong base, equivalence point at even higher pH, smaller steep region. All three curves start at different initial pH values but receive the same volume of base at the equivalence point. A legend identifies each curve.</image>
VI. Acid-Base Indicators
An acid-base indicator is itself a weak acid (HIn) whose conjugate base (In-) has a different color. The indicator equilibrium HIn <=> H+ + In- shifts between the two colored forms as the pH changes. The indicator changes color over a range of approximately pKa(indicator) +/- 1 pH unit.
The key to selecting an appropriate indicator is to match its color-change range to the pH at the equivalence point. For a strong acid/strong base titration, where the equivalence point is at pH 7, indicators such as bromothymol blue or phenol red work well. For a weak acid/strong base titration, the equivalence point pH is above 7, so an indicator that changes in the basic range, such as phenolphthalein (pKa approximately 9.1), is appropriate. For a strong acid/weak base titration, the equivalence point pH is below 7, so an indicator changing in the acidic range, such as methyl orange (pKa approximately 3.7), should be used. Common indicators and their transition ranges include methyl orange (pH 3.1-4.4, red to yellow), bromothymol blue (pH 6.0-7.6, yellow to blue), and phenolphthalein (pH 8.2-10.0, colorless to pink).
VII. Polyprotic Acid Titrations
Polyprotic acids exhibit multiple equivalence points, one for each ionizable proton. Titrating H3PO4 with NaOH, for example, produces three equivalence points corresponding to the successive deprotonations: H3PO4 -> H2PO4-, then H2PO4- -> HPO4^2-, and finally HPO4^2- -> PO4^3-. Half-equivalence points occur at pH = pKa1, pKa2, and pKa3, respectively.
When the Ka values are sufficiently different (Ka1/Ka2 > 100), the equivalence points are distinct and appear as separate steep regions on the titration curve. For a diprotic acid like H2CO3, two buffer regions and two equivalence points are observed, with the amphiprotic species HCO3- dominating between the two equivalence points.
<image>A titration curve for a diprotic acid (H2A) titrated with NaOH. The x-axis shows volume of NaOH added, the y-axis shows pH. Two distinct steep regions are visible, corresponding to the first and second equivalence points. The first equivalence point is labeled at the first steep inflection (pH between the two pKa values). The second equivalence point is labeled at the second steep inflection. Half-equivalence points are marked: "pH = pKa1" at half the first equivalence volume, and "pH = pKa2" at the midpoint between the first and second equivalence volumes. The dominant species in each region is labeled: H2A (before first eq. pt.), HA- (between eq. pts.), and A^2- (after second eq. pt.).</image>
