Chemistry Notes

7.2.9 Titration Curves

7 min read

Anatomy of a pH Curve

A titration curve plots pH (y-axis) against Volume of Titrant Added (x-axis). The Shape tells us three things:

  1. Initial pH: Indicates the strength of the acid or alkali in the flask.
  2. Equivalence Point: The precise volume where moles of acid = moles of base.
  3. Vertical Section: The steep jump in pH. This determines which indicator can be used.
  4. Final pH: Indicates the strength of excess alkali or acid.

Context

The examples below assume you are starting with of Acid in the flask and adding Alkali from a burette. If you reverse the setup (Alkali in flask), the curve is the mirror image (flipped horizontally).

Strong Acid + Strong Alkali

Example:

The diagram shows the pH titration curve of hydrochloric acid with sodium hydroxide
The diagram shows the pH titration curve of hydrochloric acid with sodium hydroxide

The Process:

  1. The Start (Acid Only):

    • The flask contains only strong acid ().
    • Since is fully dissociated, is high.
    • Initial pH: Starts very low ( pH 1 for ).

  2. The Approach (Adding Alkali):

    • As is added, reacts with : .
    • The pH rises very slowly at first.
    • Why? The concentration of is decreasing, but because pH is logarithmic (), a large change in concentration is needed to shift the pH number significantly.

  3. The Vertical Section (The Surge):

    • As the moles of alkali approach the moles of acid, the remaining becomes tiny.
    • Adding just one more drop of causes a massive proportional change in .
    • The pH shoots vertically from pH 3 to pH 10.

  4. The Equivalence Point:

    • This is the midpoint of the vertical section.
    • At this exact volume, moles of acid = moles of alkali.
    • The solution contains only Water and Salt ().
    • Since is neutral, the Equivalence pH is exactly 7.0.

  5. The Excess (Alkali Only):

    • Beyond the equivalence point, there is no left to react.
    • The beaker now accumulates excess ions from the strong base.
    • The pH levels off (asymptotes) at the pH of the strong alkali.
    • Final pH: High ( pH 13-14).

Strong Acid + Weak Alkali

The diagram shows the pH titration curve of hydrochloric acid with ammonia
The diagram shows the pH titration curve of hydrochloric acid with ammonia

The Process:

  1. The Start (Acid Only):

    • The flask contains only strong acid ().
    • Initial pH: Very low (approx pH 1), identical to the Strong/Strong curve.

  2. The Approach:

    • As Weak Alkali () is added, it reacts with :
    • The pH rises slowly.

  3. The Vertical Section:

    • The sharp rise in pH is shorter than in a Strong/Strong titration.
    • Typical Jump: pH 3 to pH 7.

  4. The Equivalence Point (The Key Difference):

    • The midpoint occurs below pH 7 (approx pH 5).
    • Why? At equivalence, the solution contains only the salt Ammonium Chloride ().
    • The Ammonium ion () is the conjugate acid of a weak base. It reacts with water (hydrolysis) to release protons:
    • This release of makes the final salt solution acidic.

  5. The Excess (Weak Alkali):

    • Beyond equivalence, excess accumulates.
    • Since is a weak base (partially dissociated), it produces fewer ions than NaOH.
    • Final pH: Levels off at a lower value (approx pH 11).

Weak Acid + Strong Alkali

The diagram shows the pH titration curve of ethanoic acid with sodium hydroxide
The diagram shows the pH titration curve of ethanoic acid with sodium hydroxide

The Process:

  1. The Start (Acid Only):

    • The flask contains only weak acid ().
    • Since it only partially dissociates, the is low.
    • Initial pH: Higher than a strong acid (approx pH 3).

  2. The “Buffer Region” (The unique flat part):

    • Unlike the Strong Acid curve, the pH rises steeply at first, then flattens out into a shallow slope.
    • Why? You are creating a Buffer Solution.
    • As you add , you convert some Acid () into its Salt ().
    • The flask now contains a mixture of a Weak Acid and its Conjugate Base.
    • This mixture actively resists changes in pH, keeping the line relatively flat until the acid is nearly used up.

  3. The Vertical Section:

    • As the acid is exhausted, the buffering action fails.
    • The pH rises sharply, but the vertical section is shorter than for a strong acid.
    • Typical Jump: pH 7 to pH 11.

  4. The Equivalence Point (The Key Difference):

    • The midpoint occurs above pH 7 (approx pH 9).
    • Why? At equivalence, the solution contains only the salt Sodium Ethanoate ().
    • The Ethanoate ion () is the conjugate base of a weak acid. It reacts with water (hydrolysis):
    • This production of ions makes the final salt solution alkaline.

  5. The Excess (Strong Alkali):

    • Beyond equivalence, excess from the accumulates.
    • The curve follows the same path as the Strong Acid/Strong Alkali titration.
    • Final pH: High (approx pH 13-14).

Weak Acid + Weak Alkali

The diagram shows the pH titration curve of a weak acid with a weak alkali
The diagram shows the pH titration curve of a weak acid with a weak alkali

The Process:

  • The Start (Weak Acid):

    • The flask contains only weak acid ().
    • Initial pH: Approx pH 3 (Partial dissociation).

  • The Shape (The Problem):

    • The graph shows a gradual, continuous rise in pH from start to finish.
    • There is NO Vertical Section.
    • Why? This is a “double buffer” situation.
      1. Before equivalence, the mixture () acts as an acidic buffer, resisting pH rise.
      2. After equivalence, the excess weak base () acts as a basic buffer, resisting pH rise.
    • The result is a sluggish curve that never jumps sharply.

  • The Equivalence Point:

    • There is no steep jump, only a subtle “Point of Inflexion” (a slight wiggle in the line).
    • It occurs approximately at pH 7.
    • Why pH 7? The salt formed is Ammonium Ethanoate. The acidity of the cation () roughly cancels out the alkalinity of the anion (), resulting in a roughly neutral solution.

  • The End (Weak Alkali):

    • The graph flattens out at the pH of the weak alkali.
    • Final pH: Approx pH 11.

  • Practical Consequence (Crucial for Exams):

    • A standard titration cannot be performed for this combination.
    • Since there is no vertical section, there is no sharp change in pH.
    • No chemical indicator is suitable (no indicator will give a sharp colour change).
    • A pH meter would be required to detect the point of inflexion.

Why Standard Titration Fails

For a Weak Acid + Weak Alkali reaction, a standard titration using a visual indicator is impossible.

  • The Problem: The pH curve has no vertical section. The pH changes gradually throughout the entire reaction.
  • The Consequence: There is no “sharp” change in pH. No chemical indicator can undergo a distinct color change at the endpoint; the color would change slowly and gradually over a large volume range, making precise measurement impossible.

Solution: Thermometric Titration

Since pH is unreliable for this combination, we measure Temperature instead.

  • The Principle: Neutralization is an exothermic reaction.
  • The Method:
    • As alkali is added, the temperature RISES continuously.
    • At the equivalence point, the reaction stops, so heat production stops.
    • Adding excess alkali causes the temperature to FALL (due to dilution/cooling).
  • The Result: Plotting Temperature vs Volume gives two lines intersecting at a peak. This peak volume is the precise endpoint.

Alternative: Using a pH Meter

While indicators fail, a pH Meter can still be used to determine the endpoint for a Weak Acid + Weak Base titration.

  • Method: A data logger records the pH continuously as the alkali is added.
  • Analysis: The data is plotted as a graph (pH vs Volume). Although there is no vertical jump, there is a Point of Inflexion (a specific point where the curvature changes direction).
  • Calculus: Mathematically, this corresponds to the maximum value of the first derivative (), allowing the endpoint to be identified computationally.

Graph View

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