14.7 Acid-Base Titrations

Acid-Base Titrations

Acid-base titrations let you figure out the concentration of an unknown acid or base by carefully reacting it with a solution of known concentration. They're one of the most practical tools in chemistry for quantitative analysis.

The shape of the titration curve you get tells you a lot: whether the acid or base is strong or weak, where the equivalence point falls, and what indicator you should use. This section covers how to read those curves, calculate pH at key points, and choose the right indicator.

Analysis of Titration Curves

A titration curve plots pH (y-axis) against the volume of titrant added (x-axis). The curve's shape depends on whether you're working with strong or weak acids and bases.

Strong acid + strong base:

• The pH starts low (acidic) and stays relatively flat until you get close to the equivalence point
• Near the equivalence point, the pH shoots up steeply because even a tiny addition of base dramatically shifts the ratio of $H^+$ to $OH^-$
• The equivalence point is at pH = 7 because the products are just water and a neutral salt (like $NaCl$)

Weak acid + strong base:

• The pH rises more gradually before the equivalence point because the weak acid only partially dissociates
• A buffer region appears around the half-equivalence point, where roughly equal amounts of the weak acid and its conjugate base resist pH changes
• The equivalence point is at pH > 7 because the conjugate base of the weak acid (e.g., acetate ion from acetic acid) is slightly basic in solution

Weak base + strong acid:

• The pH decreases gradually as the strong acid neutralizes the weak base
• A buffer region forms near the half-equivalence point, where the weak base and its conjugate acid are both present in significant amounts
• The equivalence point is at pH < 7 because the conjugate acid of the weak base (e.g., $NH_4^+$ from ammonia) is slightly acidic in solution

Calculation of pH in Titrations

You need to be able to calculate the pH at four key stages of a titration: before any titrant is added, at the half-equivalence point, at the equivalence point, and after the equivalence point.

1. Initial pH (before adding any titrant)

• For a strong acid like $HCl$: the acid fully dissociates, so $pH = -\log[HA]$, where $[HA]$ is the initial acid concentration.
• For a weak acid like acetic acid: you need to use the equilibrium expression. A useful shortcut formula is $pH = \frac{1}{2}(pK_a - \log C)$, where $C$ is the initial concentration of the weak acid.

2. Half-equivalence point (weak acid–strong base only)

At this point, exactly half the weak acid has been neutralized. That means $[HA] = [A^-]$, so the Henderson-Hasselbalch equation simplifies to:

$pH = pK_a$

This is a quick way to experimentally determine the $pK_a$ of an unknown weak acid.

3. Equivalence point

• Strong acid + strong base: $pH = 7$ (neutral salt in solution)
• Weak acid + strong base: $pH > 7$. You can estimate it with $pH = \frac{1}{2}(pK_w + pK_a + \log C_b)$, where $C_b$ is the concentration of the conjugate base at the equivalence point. A simpler approximation sometimes used is $pH = \frac{1}{2}(pK_w + pK_a)$, but keep in mind this ignores the effect of dilution on concentration.
• Weak base + strong acid: $pH < 7$. Similarly, $pH = \frac{1}{2}(pK_w - pK_b - \log C_a)$, where $C_a$ is the concentration of the conjugate acid at the equivalence point.

4. After the equivalence point

Once you've passed the equivalence point, excess titrant determines the pH:

• Excess strong base: Calculate $[OH^-]$ from the excess moles of base divided by total volume, find $pOH = -\log[OH^-]$, then $pH = 14 - pOH$
• Excess strong acid: Calculate $[H^+]$ from the excess moles of acid divided by total volume, then $pH = -\log[H^+]$

Function of Acid-Base Indicators

Acid-base indicators are themselves weak acids (or bases) that change color at different pH values. They give you a visual signal that the titration has reached its endpoint.

The indicator exists in equilibrium between its acid form and base form:

$HIn \rightleftharpoons H^+ + In^-$

$HIn$ and $In^-$ are different colors. When the pH of the solution crosses the indicator's $pK_a$, the dominant form switches and you see a color change. The transition typically spans about 2 pH units centered around the indicator's $pK_a$.

Choosing the right indicator: Pick one whose color change range overlaps with the pH at the equivalence point of your titration.

For example, phenolphthalein changes color around pH 8–10, which matches the equivalence point of a weak acid–strong base titration (pH > 7). Using methyl orange for that same titration would cause the color to change well before the equivalence point, giving you an inaccurate result.

Key Terms

• Neutralization: The reaction between an acid and a base that produces water and a salt.
• Conjugate acid-base pairs: Species that differ by one proton ($H^+$). For example, acetic acid ($CH_3COOH$) and acetate ion ($CH_3COO^-$) are a conjugate pair. These are central to how buffers work.
• Acid dissociation constant ($K_a$): Quantifies how strongly an acid dissociates in water. A larger $K_a$ means a stronger acid.
• Ion product of water ($K_w$): Equal to $[H^+][OH^-] = 1.0 \times 10^{-14}$ at 25°C. This relationship connects pH and pOH.
• Stoichiometry: The mole ratios from the balanced equation that let you calculate how much titrant is needed to reach the equivalence point.
• Volumetric analysis: A quantitative method based on measuring the volume of a solution of known concentration (the titrant) needed to completely react with an unknown sample.