Exhaustive Guide to Acid-Base Titration Curves

Fundamentals of Titration Curves

• Titration is an analytical technique where a solution of known concentration (titrant) is added from a buret to a solution of unknown concentration (analyte) until the reaction reaches completion.

• Acid-base titrations are categorized into eight distinct combinations depending on the strengths of the acid and base involved, as well as which solution is placed in the buret versus the flask:

  • Strong base added to a strong acid (e.g., adding $\text{NaOH}$ from a buret into $\text{H}_2\text{SO}_4$ in a flask).

  • Strong acid added to a strong base (e.g., adding $\text{HCl}$ from a buret into $\text{KOH}$ in a flask).

  • Strong base added to a weak acid.

  • Strong acid added to a weak base.

  • Weak acid added to a strong base.

  • Weak base added to a strong acid.

  • Weak base added to a weak acid.

  • Weak acid added to a weak base.

Strong Acid and Strong Base Titrations

Adding Strong Base to Strong Acid

• A prototypical example of this titration type is adding $0.100\text{ M NaOH}$ to $50.00\text{ mL}$ of $0.100\text{ M HCl}$.

• Equivalence Point pH:

  • The pH at the equivalence point is very, very close to pH 7 (neutral pH), because the salt produced (e.g., $\text{NaCl}$) does not undergo hydrolysis in water.

• Initial pH Calculations:

  • Because strong acids dissociate completely in aqueous solutions, the initial pH depends directly on the strong acid concentration:     $\text{pH} = -\log[\text{acid}]$

  • Concentration and initial pH relationships:

  • If the strong acid concentration is $1\text{ mol\,dm}^{-3}$, the initial pH is $0$.

  • If the strong acid concentration is $2\text{ mol\,dm}^{-3}$, the initial pH is $-0.3$.

  • If the strong acid concentration is $0.01\text{ mol\,dm}^{-3}$, the initial pH is $2$.

  • If the strong acid concentration is $0.0123\text{ mol\,dm}^{-3}$, the initial pH is $1.91$       $\text{pH} = -\log(0.0123) = 1.91$

• Curve Shape Characteristics:

  • Starts low at an acidic pH depending on the initial strong acid concentration.

  • Exhibits a very flat, gentle upward slope as base is added initially.

  • Features a dramatic, almost vertical steep rise spanning several pH units (roughly pH 3 to pH 11) centered directly at pH 7.

  • Levels off smoothly at a high basic pH as excess strong base is added.

Adding Strong Acid to Strong Base

• A typical example of this titration is adding $\text{HCl}$ from a buret to a solution of $\text{KOH}$ or $\text{NaOH}$.

• Equivalence Point pH:

  • The pH at the equivalence point is very, very close to pH 7.

• Initial pH Calculations:

  • Because strong bases dissociate completely, the concentration directly provides $\text{pOH}$, which is converted to pH at $25^\circ\text{C}$:     $\text{pOH} = -\log[\text{base}]$     $\text{pH} = 14 - \text{pOH}$

  • Concentration and initial pH relationships (at $25^\circ\text{C}$):

  • If the strong base concentration is $1\text{ mol\,dm}^{-3}$, the initial pH is $14$.

  • If the strong base concentration is $0.1\text{ mol\,dm}^{-3}$, the initial pH is $13$.

  • If the strong base concentration is $0.23\text{ mol\,dm}^{-3}$, the initial pH is $13.36$       $\text{pOH} = -\log(0.23) = 0.638 \implies \text{pH} = 14 - 0.638 = 13.36$

  • If the strong base concentration is $0.0003\text{ mol\,dm}^{-3}$, the initial pH is $10.48$       $\text{pOH} = -\log(0.0003) = 3.522 \implies \text{pH} = 14 - 3.522 = 10.48$

• Curve Shape Characteristics:

  • Starts very high at a strongly basic pH.

  • Shows a slight downward slope as strong acid is initially added.

  • Drops extremely steeply through a vertical region centered at pH 7 (spanning roughly pH 11 down to pH 3).

  • Levels off horizontally at a low acidic pH due to excess strong acid titrant.

Weak Acid and Weak Base Titration Curves

Adding Strong Base to Weak Acid

• Equivalence Point pH: Between pH 8 and pH 12 (strictly above 7), because the conjugate base of the weak acid hydrolyzes in water to produce hydroxide ions ($\text{OH}^-$).

• Initial pH: Between pH 2 and pH 7. The initial pH is NOT equal to $-\log[\text{acid}]$ because weak acids undergo incomplete dissociation in water.

• Curve Shape:

  • Starts at a higher acidic pH than a strong acid (around pH 3–4).

  • Rises relatively quickly initially before flattening into a prominent buffer region.

  • Has a shorter vertical region at the equivalence point located entirely in the basic region ($\text{pH} > 7$).

  • Levels off at high pH due to excess strong base.

Adding Strong Acid to Weak Base

• Equivalence Point pH: Below 7 (typically between pH 3 and pH 6), because the conjugate acid of the weak base hydrolyzes to yield hydronium ions ($\text{H}_3\text{O}^+$).

• Initial pH: Between pH 8 and pH 12 due to incomplete dissociation of the weak base.

• Curve Shape:

  • Starts at a moderately high basic pH (e.g., pH 10–11).

  • Drops slightly initially and flattens out into a buffer region.

  • Undergoes a steep drop centered below pH 7.

  • Levels off at a low acidic pH driven by excess strong acid.

Adding Weak Base to Strong Acid

• Equivalence Point pH: Below 7.

• Initial pH: Equal to $-\log[\text{acid}]$ (starts low at a strongly acidic pH because the analyte is a strong acid).

• Curve Shape:

  • Resembles a strong acid / strong base curve in its initial region, starting very low and staying flat.

  • Jumps steeply near the equivalence point below pH 7.

  • Levels off at a lower basic pH (around pH 9–10) than a strong base titration because the weak base titrant cannot raise the pH as high.

Adding Weak Acid to Strong Base

• Equivalence Point pH: Above 7.

• Initial pH: Derived from the strong base concentration: $\text{pOH} = -\log[\text{base}]$, so $\text{pH} = 14 - \text{pOH}$ (starts high at a strongly basic pH).

• Curve Shape:

  • Resembles a strong base / strong acid curve initially, remaining flat at high pH.

  • Drops sharply through the equivalence point above pH 7.

  • Levels off at a moderately acidic pH (around pH 4–5) due to the presence of excess weak acid.

Weak Acid and Weak Base Combinations

• Characteristics of Weak-Weak Titrations:

  • There is NO SHARP CHANGE IN pH at any point along the curve.

  • The curve demonstrates a steady, continuous change in pH throughout the entire titration.

  • The equivalence point occurs around pH 7 (the exact value depends on the relative $K_a$ and $K_b$ values of the species involved).

• Example Analysis ($0.1\text{ M NH}_3$ added to $0.1\text{ M CH}_3\text{COOH}$):

  • Initial pH is approximately pH 4 due to $0.1\text{ M CH}_3\text{COOH}$ (a weak monoprotic acid).

  • Exhibits a steady pH change without a steep vertical inflexion point.

  • The curve levels off at approximately pH 10 due to excess $0.1\text{ M NH}_3$ (a weak alkali).

The Buffer Region in Titrations

• Rule of Occurrence: Whenever a titration involves a weak acid or a weak base, a buffer region is present on the titration curve.

• Absence: Titrations between a strong acid and a strong base contain NO buffer region.

• Location and Appearance:

  • The buffer region is located before the equivalence point, where significant quantities of both the weak species and its conjugate partner coexist in solution.

  • Visually, the buffer region appears as a flattened, gently sloped section of the curve that resists rapid changes in pH upon addition of small amounts of titrant.

  • For example, in the titration of a weak acid with a strong base, after an initial slight rise, the buffer region spans between approximately $5\text{ mL}$ and $20\text{ mL}$ of added titrant (prior to the steep jump near the equivalence point at $25\text{ mL}$).

Practice Questions and Calculations

• Example 1: Adding $0.01\text{ mol\,dm}^{-3}\text{ KOH}$ to $0.1\text{ mol\,dm}^{-3}\text{ HCl}$:

  • Analyte is $0.1\text{ mol\,dm}^{-3}\text{ HCl}$ (a strong acid), so initial $\text{pH} = -\log(0.1) = 1.0$.

  • Titrant is $\text{KOH}$ (a strong base).

  • Equivalence point pH is exactly pH 7.

  • Shape starts at pH 1.0, stays low, jumps steeply through pH 7, and flattens out at high pH.

• Example 2: Adding $0.001\text{ mol\,dm}^{-3}\text{ CH}_3\text{COOH}$ to $0.1\text{ mol\,dm}^{-3}\text{ NaOH}$:

  • Analyte is $0.1\text{ mol\,dm}^{-3}\text{ NaOH}$ (a strong base), so initial $\text{pOH} = -\log(0.1) = 1 \implies \text{pH} = 13.0$

  • Titrant is $\text{CH}_3\text{COOH}$ (a weak acid).

  • Equivalence point pH is above 7.

  • Shape starts at pH 13.0, remains high initially, drops through an equivalence point above pH 7, and levels off in the weak acid pH range.

Comprehensive Titration Curve Comparison