Titration Curves and Acid-Base Reactions: Study Notes

Titration Curves and Reactions Between Acids and Bases

Introduction

Titration is a fundamental laboratory technique in general chemistry used to determine the concentration of an unknown acid or base by reacting it with a standard solution. The analysis of titration curves provides insight into the nature of acid-base reactions, the selection of appropriate indicators, and the calculation of equivalence points.

Types of Acid-Base Titrations

1. Strong Acid + Strong Base

• Reaction: $\mathrm{HCl(aq) + NaOH(aq) \rightarrow NaCl(aq) + H_2O(l)}$

• Equivalence Point: The point at which moles of acid equal moles of base. For strong acid-strong base titrations, the pH at equivalence is 7.00.

• Example: Titration of 0.100 M HCl with 0.100 M NaOH.

2. Weak Acid + Strong Base

• Reaction: $\mathrm{HA(aq) + OH^-(aq) \rightarrow A^-(aq) + H_2O(l)}$

• Equivalence Point: The pH at equivalence is greater than 7 due to the formation of a weak conjugate base.

• Example: Titration of 1.0 M cyanic acid (HCNO) with 1.0 M NaOH.

3. Weak Base + Strong Acid

• Reaction: $\mathrm{B(aq) + H^+(aq) \rightarrow BH^+(aq)}$

• Equivalence Point: The pH at equivalence is less than 7 due to the formation of a weak conjugate acid.

• Example: Titration of 1.0 M NH3 with 1.0 M HCl.

Key Concepts in Titration Curves

Equivalence Point

• The equivalence point is when stoichiometrically equivalent amounts of acid and base have reacted.

• At this point, the number of moles of H+ equals the number of moles of OH-.

• The pH at equivalence depends on the strengths of the acid and base involved.

Indicators and Their Selection

• Indicators are weak acids or bases that change color at a specific pH range.

• The indicator must be chosen so that its color change (end point) occurs as close as possible to the equivalence point of the titration.

• The effective color change occurs when $\mathrm{pH = pK_a(Ind) \pm 1}$.

Common Indicators Table

Indicator	pH Range	Acid Color	Base Color
Methyl Orange	3.1 – 4.4	Red	Yellow
Bromothymol Blue	6.0 – 7.6	Yellow	Blue
Phenolphthalein	8.2 – 10.0	Colorless	Pink

How Indicators Work

• Indicators exist in equilibrium between their acid (HIn) and base (In-) forms:

$\mathrm{HIn(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + In^-(aq)}$

• The color observed depends on the ratio $\mathrm{[In^-]/[HIn]}$.

• Color change is noticeable when $\mathrm{[In^-]/[HIn]} \approx 1$ (i.e., $\mathrm{pH = pK_a(Ind)}$).

Calculation of pH During Titration

Strong Acid – Strong Base Example

• Calculate moles of acid and base at each addition point.

• Determine the limiting reagent and calculate the concentration of excess H+ or OH-.

• Calculate pH using $\mathrm{pH = -\log[H^+]}$ or $\mathrm{pOH = -\log[OH^-]}$ and $\mathrm{pH + pOH = 14}$.

Sample Titration Data Table

Base Added (mL)	[OH-] (M)	pH
0	0	1.00
1	0.0167	1.22
12	0.00208	1.68
24	0.000	7.00
25	0.00417	11.62

Weak Acid – Strong Base Example

• Before equivalence, use the Henderson-Hasselbalch equation:

$\mathrm{pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right)}$

• At equivalence, calculate pH based on the hydrolysis of the conjugate base.

• After equivalence, excess OH- determines pH.

Weak Base – Strong Acid Example

• Analogous to weak acid-strong base, but calculations are performed for base and its conjugate acid.

• Use the Henderson-Hasselbalch equation for bases:

$\mathrm{pOH = pK_b + \log\left(\frac{[BH^+]}{[B]}\right)}$

Then, $\mathrm{pH = 14 - pOH}$

Summary of Titration Curve Features

• Strong acid + strong base: Sharp, symmetrical curve; equivalence at pH 7.

• Weak acid + strong base: Buffer region before equivalence; equivalence at pH > 7.

• Weak base + strong acid: Buffer region before equivalence; equivalence at pH < 7.

• Indicator selection depends on the expected pH at equivalence.

Key Equations

• Henderson-Hasselbalch Equation (Acid):

$\mathrm{pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right)}$

• Henderson-Hasselbalch Equation (Base):

$\mathrm{pOH = pK_b + \log\left(\frac{[BH^+]}{[B]}\right)}$

• Relationship between pH and pOH:

$\mathrm{pH + pOH = 14}$

Summary Table: Titration Types and Equivalence Point pH

Titration Type	Equivalence Point pH	Indicator Choice
Strong Acid + Strong Base	7	Bromothymol Blue
Weak Acid + Strong Base	>7	Phenolphthalein
Weak Base + Strong Acid	<7	Methyl Orange

Conclusion

Understanding titration curves and the reactions between acids and bases is essential for accurate laboratory analysis and for predicting the outcomes of acid-base reactions. Mastery of these concepts enables the selection of appropriate indicators and the correct calculation of solution pH at various stages of titration.