Study Notes on Titration Curves

Module 24: Titration Curves

Introduction to Titration Curves

• Definition: A titration curve is a graphical representation of the pH of a solution as a function of the volume of titrant added.

• Focus: Examining strong acid-strong base titrations, colored indicators, and calculations related to titration.

Types of Acid-Base Reactions in Titrations

1. Strong Acid-Strong Base Titration

• Net Ionic Equation:

  • H3O++OH−ightarrow2H2O

• Completion:

  • The reaction goes to completion.

• Equilibrium Constant:

  • The equilibrium constant for the reaction is expressed as:

  • $K = rac{1}{K_w} = 10^{+14}$

2. Weak Acid-Strong Base Titration

• Net Ionic Equation:

  • extWeakAcid+OH−ightarrowH2​O+extConjugateWeakBase

• Equilibrium Constant:

  • $K = rac{1}{K_b} ext{ (for weak base)}$

  • Kb=racKaKw​
    

• Completion:

  • Reactions go to completion (high K value).

3. Weak Base-Strong Acid Titration

• Net Ionic Equation:

  • H3O++extWeakBaseightarrowH2O+extConjugateWeakAcid

• Equilibrium Constant:

  • $K = rac{1}{K_a}$

  • Ka=racKbKw​
    

• Completion:

  • Reactions go to completion (high K value).

Conclusion on Reaction Completeness

• Important Note: Weak acids cannot be titrated with weak bases as these reactions do not go to completion.

Equivalence Point in Titration

• Definition: The equivalence point is reached when the number of moles of acid equals the number of moles of base.

• Observations:

  • Sudden change in pH at this point.

  • Strong Acid with Strong Base:

  • pH at equivalence point is neutral, $pH = 7$.

  • Weak Acid with Strong Base:

  • Resulting solution has a weak base, pH > 7 .

  • Weak Base with Strong Acid:

  • Resulting solution has a weak acid, pH < 7 .

Titration Curve Characteristics

• Shape: A titration curve usually has a characteristic S-shape.

• Key Features:

  • Initial acidic region, sharp rise near the equivalence point, and plateau in the basic region.

  • At the equivalence point of strong acid-strong base titrations, $pH = 7$.

Role of Indicators in Titrations

• Definition: A colored indicator is utilized to visually signal the equivalence point in a titration.

• Key Requirement: Should change color close to the pH at the equivalence point.

• Indicators Examples:

  • Methyl Orange:

  • Acid color: Red

  • Conjugate base color: Yellow

  • Bromothymol Blue:

  • Acid color: Yellow

  • Conjugate base color: Blue

  • Phenolphthalein:

  • Acid form: Colorless

  • Conjugate base form: Bright Pink

Working Mechanism of Indicators

• Equilibrium Established: Between the conjugate acid and conjugate base of the dye.

• Color Variation Based on Ratio:

  • If $[ ext{Conjugate Base}]:[ ext{Conjugate Acid}] = 1:10$, the color of the acid is visible.

  • If $[ ext{Conjugate Base}]:[ ext{Conjugate Acid}] = 10:1$, the color of the base is visible.

Equilibrium Constant for Indicators

• Expression:

  • Ka=rac[H3O+][extConjugateBase][extConjugate Acid]

• Rearranged Ratio Expression:

  • The ratio of conjugate base to conjugate acid can determine the visible color change based on pH.

Specific Example of Indicator Usage

• For $K_a = 10^{-7}$ (pKa = 7):

  • At pH < 6 , indicator displays the color of conjugate acid.

  • At pH > 8 , indicator displays the color of conjugate base.

• Effective color change occurs within $pKa ext{ } ext{ } ext{ } ext{ } ext{ pH} = ext{pKa} ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } +1$ and $-1$.

Choosing Indicators for Different Titrations

• Selecting Appropriate Indicator:

  • Depends on the anticipated pH at the equivalence point.

  • For weak acid titrated by strong base (pH > 7), use an indicator such as Methyl Red (pKa = 5).

Example Calculation of Strong Acid-Strong Base Titration

• Reactants:

  • Titrating 25 mL of 0.1 M HCl with 0.1 M NaOH.

• Initial pH (No NaOH added):

  • Concentration of H3O+:

  • $[H_3O^+] = 0.1 M$

  • $pH = - ext{log}(0.1) = 1$.

• Calculation Steps:

  • After adding NaOH at various points:

  1. After 5 mL of NaOH:

     • Moles of HCl: $0.1 ext{ M} ext{ } imes 25 ext{ mL} = 2.5 ext{ mmol}$

     • Moles of NaOH: $0.1 ext{ M} ext{ } imes 5 ext{ mL} = 0.5 ext{ mmol}$

     • Remaining H3O+: $2.5 ext{ mmol} - 0.5 ext{ mmol} = 2 ext{ mmol}$

     • Total volume = 30 mL.

     • $[H_3O^+] = rac{2 ext{ mmol}}{30 ext{ mL}} = 0.0667 ext{ M}$

     • $pH = - ext{log}(0.0667) <br>ightarrow 1.176$.

  2. At Equivalence Point (25 mL NaOH added):

     • Total volume = 50 mL.

     • [H3O+]=extfromKw:extH3​O+=racextKw[extOH−]ext(bothneutral) ph= 7

  3. Adding more NaOH (25.1 mL):

     • Moles of NaOH > Moles of HCl.

     • $[OH^-] = rac{0.01 ext{ mmol}}{50.1 ext{ mL}} = 0.0002 ext{ M}$

     • Calculate pH:

     • pOH=−extlog(0.0002)ightarrowpOH=3.7.

     • $pH = 14 - 3.7 = 10.3$.

Summary of Titration Curve

• Key Observations:

  • Initial asymmetric rise, steep increase at equivalence point (pH 7 for strong acid-strong base).

  • Final flat section indicates excess base post equivalence point.

Case Study: Identifying Acid Type and Strength

• Titration Curve Analysis:

  • If pH at equivalence point is 7, the acid titrated is strong.

• Calculations:

  • Equilibrium data translates to the concentration of H3O+ initially and confirms molar ratios at equivalence, ensuring proper stoichiometry is maintained

• The original volume of acid can be deduced from the determined concentrations and stoichiometric ratios.

Conclusion

• The module concludes the fundamentals of titration curves, the significance of equivalence points, dynamic equilibrium indicators, and strong (versus weak) acid-base reactions. Students are encouraged to practice calculations and review the intricacies of titration systems to master the content.