Getting Started
An acid-base titration is a quantitative laboratory technique used to determine the unknown concentration of an acid or base solution. On a macroscopic scale, we carefully add a solution of known concentration (the titrant) to a solution of unknown concentration (the analyte) until the reaction is complete. On an atomic scale, this process involves the systematic transfer of protons (H⁺) from an acid to a base, allowing us to track the change in pH and uncover key properties of the substances involved.
What You Should Be Able to Do
After completing this section, you should be able to:
Calculate the concentration of an unknown acid or base using data from a titration experiment.
Interpret a titration curve to determine the pKa of a weak acid or the pKb of a weak base.
Explain why the pH at the equivalence point of a titration is not always 7.0.
Analyze the titration curve of a polyprotic acid to identify its distinct pKa values and the number of acidic protons.
Identify the major chemical species present at any point during a titration.
Key Concepts & Analysis
We can understand a titration as a dynamic process where the chemical composition and pH of a solution change over time as a reactant is added.
Baseline Condition: The Initial Solution
Before any titrant is added (at 0 mL of added titrant), the flask contains only the analyte dissolved in water. The initial pH of the solution is determined entirely by the properties of this analyte.
For a strong acid analyte (e.g., HCl): The acid completely dissociates. The initial pH is calculated directly from its initial concentration: pH = -log[H₃O⁺].
For a weak acid analyte (e.g., CH₃COOH): The acid only partially dissociates, establishing an equilibrium: HA(aq) + H₂O(l) ⇌ H₃O⁺(aq) + A⁻(aq). The initial pH is higher than that of a strong acid of the same concentration and must be calculated using the acid dissociation constant, Ka.
The Process: Adding the Titrant
As a titrant (e.g., NaOH) is added, it reacts with the analyte in a neutralization reaction. The chemical environment changes continuously, leading to distinct regions on the titration curve.
The Pre-Equivalence Region (Buffer Region for Weak Species): In the titration of a weak acid with a strong base, the added base converts some of the weak acid (HA) into its conjugate base (A⁻). The solution now contains significant amounts of both HA and A⁻, forming a buffer. In this region, the pH changes slowly because the buffer resists large pH shifts. A special point in this region is the half-equivalence point, where exactly half of the original acid has been neutralized. At this point, [HA] = [A⁻], and according to the Henderson-Hasselbalch equation (pH = pKa + log([A⁻]/[HA])), the pH is equal to the pKa of the weak acid. This provides a direct experimental method for determining Ka.
The Equivalence Point: This is the stoichiometric point of the reaction, where the moles of added titrant are exactly equal to the initial moles of analyte. At this moment, the original analyte has been completely consumed. The pH at the equivalence point is determined by the species remaining in the solution.
Strong Acid-Strong Base: The products are water and a neutral salt (e.g., NaCl). The pH is 7.0 at 25°C.
Weak Acid-Strong Base: The product is the conjugate base of the weak acid (e.g., CH₃COO⁻). This conjugate base reacts with water in a process called hydrolysis: A⁻(aq) + H₂O(l) ⇌ HA(aq) + OH⁻(aq). The production of hydroxide ions makes the solution basic, so the pH at the equivalence point is greater than 7.
Weak Base-Strong Acid: The product is the conjugate acid of the weak base (e.g., NH₄⁺). This conjugate acid hydrolyzes water to produce hydronium ions: BH⁺(aq) + H₂O(l) ⇌ B(aq) + H₃O⁺(aq). The solution is acidic, and the pH is less than 7.
The Post-Equivalence Region: After the equivalence point, all the analyte has been consumed. Any further addition of titrant results in an excess of that substance. The pH of the solution is now determined primarily by the concentration of the excess strong acid or strong base titrant.
The Resulting Change: The Titration Curve
A titration curve, a graph of pH versus the volume of titrant added, visually represents this entire process. The curve's shape is a direct result of the changing chemical composition. Key features include:
The initial pH (the y-intercept).
A region of gradual pH change (the buffer region).
A sharp, vertical increase in pH around the equivalence point.
A final leveling-off of pH in the post-equivalence region.
For a polyprotic acid (e.g., H₂CO₃), which has more than one acidic proton, the titration curve will show multiple equivalence points and multiple half-equivalence points, one for each proton. This allows for the determination of each successive pKa value (pKa₁, pKa₂, etc.).
Key Models & Representations
The characteristics of a titration are determined by the strength of the acid and base involved.
| Titration Type | Key Species at Equivalence Point | pH at Equivalence Point | Titration Curve Feature |
|---|---|---|---|
| Strong Acid - Strong Base | Water (H₂O) and a neutral salt (e.g., Na⁺, Cl⁻) | = 7.0 | Steep, symmetric inflection centered at pH 7. |
| Weak Acid - Strong Base | Conjugate base (A⁻) and a neutral cation (e.g., Na⁺) | > 7.0 (Basic) | Inflection point is in the basic range. A buffer region precedes it. |
| Weak Base - Strong Acid | Conjugate acid (BH⁺) and a neutral anion (e.g., Cl⁻) | < 7.0 (Acidic) | Inflection point is in the acidic range. A buffer region precedes it. |
Key Terms, Quantities, & Concepts
Titration: A controlled neutralization reaction performed to determine the concentration of an unknown solution.
Analyte: The substance of unknown concentration that is being analyzed in a titration.
Titrant: The substance of known concentration that is added during a titration.
Equivalence Point: The point in a titration where the moles of added titrant are stoichiometrically equal to the initial moles of the analyte.
Half-Equivalence Point: The point in the titration of a weak acid or base where half of the analyte has been converted to its conjugate. At this point, pH = pKa (or pOH = pKb).
Buffer Region: The section of a weak acid/base titration curve where a buffer system is present, characterized by a gradual change in pH.
pKa: The negative base-10 logarithm of the acid dissociation constant (Ka). A lower pKa indicates a stronger acid.
Polyprotic Acid: An acid capable of donating more than one proton per molecule (e.g., H₂SO₄, H₃PO₄).
Hydrolysis: A reaction in which an ion reacts with water to produce H₃O⁺ or OH⁻, causing the solution's pH to deviate from neutral.
Skill Snapshots
Causation
Cause: Adding a strong base to a weak acid solution.
Effect: The weak acid is converted to its conjugate base, creating a buffer system that resists large changes in pH.
Cause: Reaching the equivalence point in a weak acid-strong base titration.
Effect: The predominant species is the conjugate base (A⁻), which hydrolyzes water to produce OH⁻, resulting in a basic solution (pH > 7).
Cause: The concentration of the analyte is very low.
Effect: The vertical jump in pH at the equivalence point is less pronounced, making it more difficult to determine the equivalence point accurately with an indicator.
Comparison
The initial pH of a 0.10 M strong acid (e.g., HCl) is 1.0, whereas the initial pH of a 0.10 M weak acid (e.g., CH₃COOH) is significantly higher (around 2.87).
A titration curve for a monoprotic acid displays one steep equivalence point region, whereas the curve for a diprotic acid displays two distinct equivalence point regions.
The equivalence point is a theoretical, stoichiometric point, whereas the endpoint is the experimental point where a visual indicator changes color.
Change and Continuity Over Time (CCOT)
Baseline: The initial pH of the analyte solution is determined solely by its concentration and its acid/base dissociation constant.
Change 1: As titrant is added before the equivalence point, the analyte is consumed and its conjugate is formed, causing a gradual change in pH.
Change 2: Near the equivalence point, the concentration of the analyte becomes very small, so a tiny addition of titrant causes a large, rapid change in pH.
Continuity: The total number of moles of the analyte species (e.g., the sum of moles of HA and A⁻) remains constant throughout the titration process.
Common Misconceptions & Clarifications
Misconception: The pH at the equivalence point is always 7.
- Clarification: This is only true for a strong acid-strong base titration. When a weak acid or weak base is involved, the conjugate species formed at the equivalence point will hydrolyze water, making the solution basic or acidic, respectively.
Misconception: The equivalence point and the endpoint are the same thing.
- Clarification: The equivalence point is the theoretical point where moles are equal. The endpoint is the observable, experimental point where a chemical indicator changes color. A well-chosen indicator will have an endpoint pH that is very close to the equivalence point pH.
Misconception: At the half-equivalence point, the reaction is halfway finished.
- Clarification: This is correct, but the chemical significance is that the concentrations of the weak acid and its conjugate base are equal ([HA] = [A⁻]). This unique condition makes the pH of the solution equal to the pKa of the acid, providing a powerful experimental shortcut.
One-Paragraph Summary
Acid-base titrations are a fundamental analytical technique for determining an unknown concentration by reacting a solution with a standard of known concentration. The process is visualized using a titration curve, which plots pH against the volume of added titrant. This curve reveals crucial information: the initial pH reflects the analyte's strength, a buffer region shows gradual pH change, and a steep inflection marks the equivalence point where moles of titrant equal initial moles of analyte. For weak species, the pH at the half-equivalence point directly yields the pKa, and the pH at the equivalence point is non-neutral due to salt hydrolysis. By analyzing these key features, we can quantify concentrations and determine the fundamental properties of acids and bases.