AP Chemistry 8.7: Acid-Base Titrations and Indicators

A titration is used to determine an unknown concentration or study an acid-base system by gradually adding a solution of known concentration.

The solution of known concentration is the titrant.

The solution being analyzed is the analyte.

A titration curve plots:

• pH vs. volume of titrant added
• The shape of the curve reveals whether the acid or base is strong or weak, where the equivalence point occurs, and sometimes the pKa or Ka of a weak acid.

The equivalence point occurs when the titrant has been added in the exact stoichiometric amount required to react with the analyte.

• For a 1:1 reaction:
• moles acid = moles base
• at equivalence.

But for a non-1:1 reaction, you must use the balanced equation.

Equivalence does not mean equal volumes.

• It means the correct stoichiometric mole ratio has been reached.

Suppose HCl is titrated with NaOH.

• Reaction:
• H⁺ + OH⁻ → H₂O

There is excess strong acid.

• Calculate remaining H⁺ using stoichiometry, divide by total volume, then calculate pH.

The strong acid and strong base have neutralized each other.

• At 25°C, the solution is approximately:
• pH = 7
• assuming the resulting ions do not significantly react with water.

There is excess strong base.

• Calculate excess OH⁻, divide by total volume, find pOH, then find pH.
• The titration curve begins acidic, rises gradually, then has a steep rise around equivalence before becoming basic.

This titration is more complicated and more important conceptually.

• Consider:
• HA + OH⁻ → A⁻ + H₂O
• The curve has several distinct regions.

Before any strong base is added, the solution contains mostly weak acid.

• Calculate initial pH using:
• Ka
• and an ICE table.

After some strong base has been added but before equivalence, part of HA has been converted into A⁻.

• The solution contains:
• HA + A⁻
• Therefore it is a buffer.
• You can often use:
• pH = pKa + log(A⁻/HA)
• after doing the neutralization stoichiometry.

At the half-equivalence point, exactly half of the original weak acid has been neutralized.

• Therefore:
• [HA] = [A⁻]
• So:
• log([A⁻]/[HA]) = log(1) = 0
• Therefore:
• pH = pKa
• This is one of the most important relationships in the entire unit.

At half-equivalence:

• pH = pKa
• Therefore:
• Ka = 10⁻ᵖᴴ
• This means a titration curve can be used to determine Ka experimentally.

At equivalence, essentially all HA has been converted into:

• A⁻
• But A⁻ is the conjugate base of a weak acid.
• It reacts:
• A⁻ + H₂O ⇌ HA + OH⁻
• Therefore:
• pH > 7
• at the equivalence point of a typical weak-acid/strong-base titration at 25°C.
• To calculate the pH, determine the concentration of A⁻ after accounting for total volume, calculate:
• Kb = Kw/Ka
• and solve its base equilibrium.

Once excess strong base has been added, the excess OH⁻ dominates the pH.

• Use stoichiometry to calculate excess OH⁻ and then calculate pH.

This is the mirror image.

• Suppose:
• B + H⁺ → BH⁺

Initially, calculate pH from the weak-base equilibrium.

Before equivalence, B and BH⁺ form a buffer.

At half-equivalence:

• [B] = [BH⁺]
• For the conjugate-acid form:
• pH = pKa of BH⁺
• or the equivalent pOH/pKb relationship can be used carefully.

At equivalence, the solution contains mostly BH⁺.

• Because BH⁺ is acidic:
• pH < 7
• at 25°C.

After equivalence, excess strong acid controls the pH.

Initial pH: very low

Buffer region: none

Equivalence pH: approximately 7 at 25°C

Initial pH: higher than comparable strong acid

Buffer region: yes

Half-equivalence: pH = pKa

Equivalence pH: greater than 7

Initial pH: basic

Buffer region: yes

Equivalence pH: less than 7

A polyprotic acid can donate multiple protons.

• For example:
• H₂A
• can lose one proton:
• H₂A → HA⁻
• and then another:
• HA⁻ → A²⁻
• If the two proton-transfer steps are sufficiently separated in strength, a titration curve may show multiple equivalence points.
• A diprotic acid can potentially show:
• two equivalence points
• while a triprotic acid can potentially show:
• three
• Each stage corresponds to removal of another proton.

An acid-base indicator is a weak acid or weak base whose protonated and deprotonated forms have different colors.

• A simplified indicator equilibrium can be written:
• HIn ⇌ H⁺ + In⁻
• where HIn and In⁻ have different colors.
• The visible color changes as the equilibrium shifts with pH.

An indicator should be selected so its color-change range overlaps the steep region around the titration's equivalence point.

These are related but not identical.

Equivalence point: exact stoichiometric amount of titrant has been added.

Endpoint: observable signal, such as an indicator color change, used experimentally to estimate the equivalence point.

• A good indicator has an endpoint very close to the equivalence point.

Whenever you are asked for pH during a titration, first determine where you are on the titration curve.

• Ask:

Before titrant?

• Use initial acid/base equilibrium.

Before equivalence?

• Perform stoichiometry. If a weak species and conjugate partner remain, use buffer chemistry.

At half-equivalence?

• Use:
• pH = pKa
• for weak-acid/strong-base titration.

At equivalence?

• Determine whether the resulting conjugate species reacts with water.

After equivalence?

• Excess strong titrant usually determines pH.

Do not assume every equivalence point has pH 7.

Only a typical strong-acid/strong-base titration has an approximately neutral equivalence point at 25°C.

Do not confuse half-equivalence with equivalence.

At half-equivalence for a weak acid:

pH = pKa

Do not forget that total volume changes as titrant is added.

Do not use Henderson-Hasselbalch at the equivalence point when essentially no original weak acid remains.

For titrations, always ask:

• Where am I on the curve?
• That tells you which chemistry and equation to use.

Before equivalence: excess strong acid/base calculation

Equivalence: approximately pH 7 at 25°C

After equivalence: excess titrant controls pH

Initial: Ka equilibrium

Before equivalence: buffer

Half-equivalence: pH = pKa

Equivalence: conjugate base hydrolysis → pH > 7

After equivalence: excess OH⁻

Initial: Kb equilibrium

Before equivalence: buffer

Equivalence: conjugate acid hydrolysis → pH < 7

After equivalence: excess H₃O⁺