# Acid-Base Titrations

> AP Chemistry · AP Chemistry 2024-2029 Curriculum
> Source: https://www.owlsprep.com/study/ap-chemistry-u8-acid-base-titrations/

We cover core titration stoichiometry, key titration curve features, correct indicator selection, and type-specific profile analysis fully aligned to AP Chemistry exam scoring standards.

**Prerequisites:** [Bronsted-Lowry Acid-Base Definitions](https://www.owlsprep.com/study/ap-chemistry-u8-bronsted-lowry-acid-base/); [Weak Acid Dissociation and $K_a$ Calculations](https://www.owlsprep.com/study/ap-chemistry-u8-weak-acid-base-equilibria/)

## Learning objectives

- Calculate unknown concentration of acid or base using titration stoichiometry data
- Interpret titration curve features including equivalence point, half-equivalence point, and buffer region
- Select appropriate acid-base indicator for a given titration profile
- Distinguish between strong-strong, strong-weak, and diprotic titration characteristics

## Core Titration Stoichiometry

All titration calculations start with a balanced neutralization reaction to identify the mole ratio between analyte and titrant. The simplified $M_1V_1 = M_2V_2$ formula only works for 1:1 mole ratios, so you must always confirm stoichiometry first before solving for unknown concentration.

**Standardization** — The process of determining the exact concentration of a titrant by titrating it against a primary standard of known mass and purity, required for all accurate lab titrations.

**Worked example:** 22.5 mL of 0.150 M NaOH titrant neutralizes 30.0 mL of unknown HCl analyte. Calculate the molarity of the HCl solution.

1. Write the balanced 1:1 neutralization equation: $HCl + NaOH \rightarrow NaCl + H_2O$
2. Calculate total moles of NaOH added: $n_{NaOH} = 0.150 \text{ mol/L} \times 0.0225 \text{ L} = 0.003375 \text{ mol}$
3. Moles of HCl = moles of NaOH for 1:1 ratio = 0.003375 mol
4. Solve for HCl molarity: $M_{HCl} = 0.003375 \text{ mol} / 0.0300 \text{ L} = 0.1125 \text{ M}$

**Check your understanding**

Confirm your understanding of stoichiometry before moving on:

1. What volume of 0.200 M NaOH is required to neutralize 25.0 mL of 0.100 M $H_2SO_4$?

   - 12.5 mL
   - 25.0 mL
   - 50.0 mL
   - 100 mL

   *Why:* The 2:1 mole ratio of NaOH to $H_2SO_4$ gives 0.0025 mol $H_2SO_4$ requiring 0.005 mol NaOH, equal to 25.0 mL of 0.200 M NaOH.

## Titration Curve Key Features

A titration curve plots pH of the flask solution on the y-axis against volume of added titrant on the x-axis. All curves have 4 distinct regions: initial analyte pH, buffer region (for weak analytes), steep vertical equivalence point jump, and post-equivalence excess titrant region.

$$pH_{half-equivalence} = pK_a \text{ (for weak acid analyte titrated with strong base)}$$

**Worked example:** A titration of 0.1 M acetic acid ($pK_a = 4.76$) with 0.1 M NaOH reaches half-equivalence after adding 15 mL of titrant. What is the pH at this point?

1. At half-equivalence, half of the weak acid has been converted to its conjugate acetate base
2. The ratio of [weak acid] / [conjugate base] = 1, so log(1) = 0 in the Henderson-Hasselbalch equation
3. pH = pKa = 4.76, no additional calculation required

> **tip**
>
> AP exam graders award full points for stating that half-equivalence point pH equals pKa without showing extra work, as long as you identify the point correctly on the curve.

## Indicator Selection

Acid-base indicators are weak organic dyes that change color over a narrow pH range of ~1 unit. For accurate results, the indicator's pKa must fall entirely within the steep vertical jump of the titration curve to minimize the gap between end point and equivalence point.

| Indicator | pKa | Color Change | Best For |
| --- | --- | --- | --- |
| Methyl Orange | 3.4 | Red to Yellow | Strong acid + weak base titrations |
| Bromothymol Blue | 7.1 | Yellow to Blue | Strong acid + strong base titrations |
| Phenolphthalein | 9.3 | Colorless to Pink | Weak acid + strong base titrations |

**Exam command terms**

AP exam questions use specific phrasing for indicator selection prompts:

- **Justify your indicator choice** — You must explicitly state that the indicator pKa falls inside the equivalence point vertical region to earn the point

- **Explain why phenolphthalein is not suitable** — You must note that its pKa lies outside the steep jump, creating large titration error

## Titration Type Profile Comparison

**Comparing methods**

The 4 most common titration types on the AP exam have distinct, easily identifiable curve profiles:

- **Strong Acid + Strong Base** — No buffer region, equivalence point pH = 7, very wide vertical jump spanning pH 3 to 11
  - Pros: Any indicator works, minimal calculation error

- **Weak Acid + Strong Base** — Clear buffer region, equivalence point pH >7 due to conjugate base hydrolysis, narrow vertical jump
  - Pros: Easy to measure pKa directly from half-equivalence point

- **Strong Acid + Weak Base** — Equivalence point pH <7 due to conjugate acid hydrolysis, narrow vertical jump at low pH
  - Cons: Cannot use phenolphthalein as indicator

- **Diprotic Weak Acid + Strong Base** — Two distinct, evenly spaced equivalence points, two half-equivalence points for pKa1 and pKa2
  - Cons: Requires two separate indicators matched to each jump

**Worked example:** Calculate the pH at equivalence point for titration of 25 mL 0.1 M acetic acid with 0.1 M NaOH

1. Total volume at equivalence point = 25 mL + 25 mL = 50 mL
2. Moles of acetate ion formed = 0.0025 mol, so [acetate] = 0.05 M
3. Use $K_b = K_w / K_a = 10^{-9.24}$ to solve for $[OH^-] = \sqrt{0.05 \times 10^{-9.24}} = 5.3 \times 10^{-6}$ M
4. pOH = 5.28, so pH = 8.72 >7, confirming basic equivalence point

## Common pitfalls

- **Wrong:** Using $M_1V_1 = M_2V_2$ for all titrations regardless of mole ratio
  - Why it fails: The formula only works for 1:1 acid-base stoichiometry, and fails for diprotic or triprotic acids reacting with monoprotic bases
  - Correct: Always write the balanced neutralization equation first to confirm mole ratio before calculating unknown concentration
- **Wrong:** Treating end point and equivalence point as identical values
  - Why it fails: End point is the observed indicator color change, not the exact stoichiometric point, and a poor indicator selection creates large calculation error
  - Correct: Select an indicator whose pKa falls fully inside the steep vertical region of the titration curve to minimize the gap between end and equivalence point
- **Wrong:** Assuming equivalence point pH is always 7 for all titrations
  - Why it fails: For strong-weak titrations, the conjugate of the weak analyte hydrolyzes in solution to make the equivalence point acidic or basic
  - Correct: Calculate equivalence point pH using the hydrolysis reaction of the conjugate ion formed at that point
- **Wrong:** Applying the Henderson-Hasselbalch equation past the equivalence point
  - Why it fails: No excess weak acid or weak base remains after equivalence point, so no buffer system exists to apply the formula
  - Correct: Calculate pH using the concentration of excess strong titrant added past the equivalence point
- **Wrong:** Ignoring total dilution volume when calculating pH at any titration point
  - Why it fails: Adding titrant to the analyte flask increases total solution volume, lowering the molarity of all dissolved species
  - Correct: Always use the combined total volume of analyte and added titrant for all molarity calculations

## Cheatsheet

| Titration Type | Equivalence Point pH | Half-Equivalence Point Property | Suitable Indicator |
| --- | --- | --- | --- |
| Strong Acid + Strong Base | = 7 | No buffer region | Phenolphthalein, Methyl Orange |
| Weak Acid + Strong Base | > 7 | pH = pKa of weak acid | Phenolphthalein |
| Strong Acid + Weak Base | < 7 | pOH = pKb of weak base | Methyl Orange |
| Diprotic Acid + Strong Base | Two distinct points | pKa1 and pKa2 measurable | Two matched indicators |

## What's next

Mastering acid-base titrations is critical for scoring full points on the AP Chemistry FRQ lab question, which appears on nearly every exam administration. This concept directly builds on prior weak acid equilibrium knowledge, and will be extended in upcoming units to include redox titrations, precipitation titrations, and complexometric titrations that follow nearly identical data analysis workflows. You will also apply titration curve interpretation skills to solve buffer capacity problems, which are a common distractor on AP MCQ sections. Before moving on, confirm you can independently calculate the unknown concentration of a 0.1 M NaOH titrant used to neutralize 25 mL of 0.05 M $H_2SO_4$, and identify the approximate pH at its equivalence point.

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