8.5 Acid-Base Titrations

An acid-base titration tracks how pH changes as you add a titrant of known concentration to an analyte of unknown concentration. The titration curve, usually graphed as pH versus volume of titrant added, helps you locate the equivalence point, half-equivalence point, buffer region, and key acid-base relationships.

AP Chem Titration Basics

An AP Chem titration uses a titrant with known concentration to find information about an analyte with unknown concentration. In an acid-base titration, you track pH as titrant is added and use the titration curve to identify the equivalence point, half-equivalence point, buffer region, and sometimes pKa.

The biggest exam skill is reading the curve correctly. The equivalence point is where moles of titrant equal moles of analyte. The half-equivalence point in a weak acid or weak base titration is where the conjugate acid-base pair concentrations are equal, so pH = pKa or pOH = pKb.

Why This Matters for the AP Chemistry Exam

Titrations pull together almost everything in Unit 8: pH, weak acid and base equilibria, buffers, and stoichiometry. On the AP Chemistry exam, you will be expected to use experimental data to make calculations and support claims, and titration questions are a common way that shows up.

Expect to read information off a titration curve, identify equivalence and half-equivalence points, calculate or estimate concentration or pH at a specific point, and justify which indicator fits a given titration. You may also reason about why curves have characteristic shapes for different acid-base systems and explain how experimental errors could affect your results. For weak systems, recognizing the buffer region and using the pH at the half-equivalence point to find pKa shows up often.

Key Takeaways

• A titration curve plots pH against volume of titrant added and summarizes the whole titration.
• At the equivalence point, moles of titrant equal moles of analyte; use this to find an unknown concentration.
• Strong acid-strong base titrations give a neutral pH (7 at 25 degrees C) at equivalence; weak acid titrations give a basic equivalence point and weak base titrations give an acidic one.
• For weak acid or weak base titrations, the half-equivalence point is where pH = pKa (or pOH = pKb), because the conjugate pair concentrations are equal there.
• The region before the equivalence point in a weak titration is a buffer region with both the weak species and its conjugate present.
• For polyprotic acids, the number of distinct equivalence points tells you the number of acidic protons, and each half-equivalence point gives a pKa.

What Is a Titration?

A titration is a lab procedure used to find the concentration of an unknown solution called the analyte (also called the titrand). Using a burette, you add small amounts of the titrant, a solution of known concentration, into the analyte until you reach the equivalence point.

The equivalence point is where the moles of analyte equal the moles of titrant added. For monoprotic acids and bases, you can write this as:

nM_aV_a = mM_bV_b

where n and m are stoichiometric coefficients, and M and V are the molarities and volumes of the analyte and titrant. This relationship is the key to finding an unknown concentration.

Titration Curves

As you drip an acid or base into the unknown solution, you track the pH after each addition. Plotting pH against the volume of titrant gives the titration curve.

Strong Acid-Strong Base Example

Consider dripping 1 M NaOH into 25 mL of 1 M HCl.

Before adding titrant: With 1 M HCl, pH = -log(1) = 0.

Before the equivalence point: The net ionic reaction is

H+ + OH- <=> H2O

Adding OH- removes some H+, so the pH rises slowly while H+ is still in excess.

At the equivalence point: Moles of HCl (25 mmol) equal moles of NaOH added. Solving M_aV_a = M_bV_b shows this happens at 25 mL. With no excess reactant, only water and spectator ions remain, so the pH is 7. This neutral equivalence point is true for any strong acid-strong base titration.

After the equivalence point: Now base is in excess, so the pH rises slowly again as more base is added.

The full curve starts low, rises slowly, jumps sharply through the equivalence point, then levels off high.

Titrations with Weak Acids and Bases

Most acids and bases are not strong. The process is almost the same when you titrate a weak acid with a strong base (more common on the exam) or a weak base with a strong acid, but there are two important differences.

A buffer region forms. Before the equivalence point, you have both the weak acid and its conjugate base (or the weak base and its conjugate acid) in solution at the same time. That is a buffer. Take the titration of NaOH into acetic acid:

CH3COOH + NaOH <=> CH3COONa + H2O

CH3COOH + OH- <=> CH3COO- + H2O

When acetic acid is in excess, both CH3COOH and CH3COO- are present, so the solution resists pH change. The half-equivalence point sits at exactly half the volume of the equivalence point. At that point the conjugate pair concentrations are equal, so pH = pKa (or pOH = pKb if you are titrating a weak base with a strong acid). This is a clean way to read pKa straight off a curve.

The equivalence point is not at pH 7. Because a conjugate species is produced, the equivalence point pH shifts. Titrating a weak acid with a strong base gives a basic equivalence point, because the conjugate base reacts with water. Titrating a weak base with a strong acid gives an acidic equivalence point, because the conjugate acid reacts with water.

Polyprotic Acid Titrations

Polyprotic acids like H2SO4 and H3PO4 have more than one acidic proton, and each proton ionizes in a separate step. Each step has its own dissociation constant (Ka1, Ka2, Ka3...), and these values get smaller in order, meaning each successive proton is harder to remove.

When you titrate a polyprotic acid with a strong base, you get multiple equivalence points, one for each acidic proton. The curve looks like a staircase: buffer regions (flatter plateaus) separated by sharp rises at each equivalence point.

Phosphoric acid (H3PO4) has three acidic protons:

• Ka1 = 7.5 x 10^-3 (pKa1 = 2.12)
• Ka2 = 6.2 x 10^-8 (pKa2 = 7.21)
• Ka3 = 4.8 x 10^-13 (pKa3 = 12.32)

Counting Acidic Protons

To find how many acidic protons a polyprotic acid has, count the distinct equivalence points on the curve. Each sharp vertical rise is one proton being neutralized. For H3PO4 you would see equivalence points spaced at even volume intervals, though a very high pKa step can be hard to see clearly.

Major Species Along the Curve

As you add base to H3PO4, the major species shift in order:

1. Before any base: H3PO4 fills

2. First buffer region: mix of H3PO4 and H2PO4-

3. First equivalence point: H2PO4- is the major species

4. Second buffer region: mix of H2PO4- and HPO4^2-

5. Second equivalence point: HPO4^2- fills

6. Third buffer region: mix of HPO4^2- and PO4^3-

7. Third equivalence point: PO4^3- is the major species

At each half-equivalence point, the pH equals the corresponding pKa, and the conjugate pair concentrations are equal.

For the AP Chemistry exam, focus on identifying the number of acidic protons, the major species at any point, and the pKa associated with each proton. Computing the exact concentration of every species across a polyprotic curve is outside what you will be asked to do; the goal is qualitative reasoning about which species are present in large versus small amounts.

How to Use This on the AP Chemistry Exam

Problem Solving

Finding concentration at the equivalence point

Find the concentration of HF when titrating HF with NaOH if the equivalence point occurs after adding 20 mL of 0.1 M NaOH to 10 mL of HF.

At the equivalence point, moles of acid equal moles of base, so M_aV_a = M_bV_b:

M_a(10 mL) = (0.1 M)(20 mL)

M_a = (0.1)(20)/10 = 0.2 M

The concentration of HF is 0.2 M. The same setup works to find an unknown volume at the equivalence point.

Weak acid / strong base titration

Find the pH after titrating 25 mL of 0.1 M CH3COOH with 10 mL of 0.1 M KOH (Ka = 1.8 x 10^-5).

Write the net ionic reaction:

CH3COOH + OH- <=> CH3COO- + H2O

Find millimoles and run the stoichiometry:

25 x 0.1 = 2.5 mmol CH3COOH

10 x 0.1 = 1.0 mmol OH-

Both the weak acid and its conjugate base are present, so use the Henderson-Hasselbalch equation:

pH = pKa + log([A-]/[HA]) = 4.74 + log(1.0/1.5) = 4.56

Weak base / strong acid titration

Find the pH after titrating 30 mL of 0.5 M NH3 with 10 mL of 0.1 M HCl (Kb = 1.8 x 10^-5).

Net ionic reaction:

NH3 + H+ <=> NH4+

Find millimoles and run the stoichiometry:

30 x 0.5 = 15 mmol NH3

10 x 0.1 = 1.0 mmol HCl

Use the base form of Henderson-Hasselbalch to find pOH:

pOH = pKb + log([HB+]/[B]) = 4.74 + log(1.0/14) = 3.59

Then pH = 14 - 3.59 = 10.41.

Reading a Titration Curve

• Find the equivalence point at the steep, near-vertical jump in pH. The volume there gives you the moles of titrant that match the moles of analyte.
• For a weak acid or weak base, locate the half-equivalence point at half the equivalence volume. Read the pH there to get the pKa (or use pOH for pKb).
• Spot the buffer region as the flatter stretch before the equivalence point, where pH changes slowly.
• Check whether the equivalence point pH is neutral, acidic, or basic to figure out whether you have a strong-strong, weak base-strong acid, or weak acid-strong base titration.

Common Trap

When picking an indicator, choose one whose color change happens near the pH at the equivalence point. The endpoint (where the indicator changes color) is not automatically the same as the equivalence point, so a poor indicator choice can throw off your result.

Common Misconceptions

• The equivalence point is not always pH 7. Only strong acid-strong base titrations are neutral at equivalence. A weak acid titrated with strong base ends basic, and a weak base titrated with strong acid ends acidic.
• Endpoint and equivalence point are not the same thing. The equivalence point is set by the chemistry (moles match); the endpoint is when your indicator changes color. They are close only when you choose a good indicator.
• Half-equivalence is not equivalence. The half-equivalence point is where pH = pKa and the buffer is strongest, at half the equivalence volume. Mixing these up is a common scoring loss.
• Reading the wrong volume. The equivalence volume is at the center of the steep jump, not where the curve first starts to bend. Use the steep, near-vertical part.
• pH = pKa only at the half-equivalence point of a weak titration. It does not hold for strong-strong titrations, which have no buffer region.
• More volume of titrant does not mean a stronger acid or base. Equivalence volume depends on moles of analyte, not on strength. Strength affects the shape of the curve and the equivalence pH, not the equivalence volume.

Related AP Chemistry Guides

• Unit 8 Overview: Acids and Bases
• 8.1 Introduction to Acids and Bases
• 8.2 pH and pOH of Strong Acids and Bases
• 8.4 Acid-Base Reactions and Buffers
• 8.3 Weak Acid and Base Equilibria
• 8.7 pH and pKa