Chapter 17: Additional Aspects of Aqueous Equilibria – Buffers, Common Ion Effect, and Titrations

Additional Aspects of Aqueous Equilibria

Introduction

This chapter explores advanced topics in aqueous equilibria, focusing on buffer solutions, the common ion effect, and titrations involving weak acids and bases. These concepts are essential for understanding how solutions resist changes in pH and how acid-base reactions are quantified in the laboratory.

Common Ion Effect

Definition and Principle

• Common Ion Effect: The shift in equilibrium that occurs when a solution contains two substances that share a common ion. The presence of the common ion suppresses the ionization of a weak electrolyte.

• When a weak electrolyte (e.g., acetic acid, CH3COOH) and a strong electrolyte (e.g., sodium acetate, CH3COONa) containing a common ion are mixed, the weak electrolyte ionizes less than it would alone.

• This effect is explained by Le Châtelier’s Principle: adding a product (the common ion) shifts the equilibrium toward the reactants.

Example 1: Acetic Acid and Sodium Acetate

• Strong electrolyte: $\mathrm{CH_3COONa~(aq) \rightarrow Na^+~(aq) + CH_3COO^-~(aq)}$

• Weak electrolyte: $\mathrm{CH_3COOH~(aq) + H_2O~(l) \rightleftharpoons H_3O^+~(aq) + CH_3COO^-~(aq)}$

• Adding sodium acetate increases $\mathrm{CH_3COO^-}$, shifting the acetic acid equilibrium left, forming more $\mathrm{CH_3COOH}$.

Example 2: Nitrous Acid and Sodium Nitrite

• Strong electrolyte: $\mathrm{NaNO_2~(aq) \rightarrow Na^+~(aq) + NO_2^-~(aq)}$

• Weak electrolyte: $\mathrm{HNO_2~(aq) + H_2O~(l) \rightleftharpoons H_3O^+~(aq) + NO_2^-~(aq)}$

• Adding sodium nitrite increases $\mathrm{NO_2^-}$, shifting the equilibrium left, forming more $\mathrm{HNO_2}$.

Example 3: Ammonia and Ammonium Chloride

• Adding $\mathrm{NH_4Cl}$ (common cation to $\mathrm{NH_3}$) increases $\mathrm{NH_4^+}$, shifting the equilibrium:

• $\mathrm{NH_3~(aq) + H_2O~(l) \rightleftharpoons NH_4^+~(aq) + OH^-~(aq)}$

• This decreases $\mathrm{OH^-}$ concentration and increases $\mathrm{NH_3}$.

Buffers

Definition and Function

• Buffer: A solution that resists significant changes in pH upon addition of small amounts of strong acid or base.

• Composed of a weak acid and its conjugate base, or a weak base and its conjugate acid.

• Buffers work by neutralizing added $\mathrm{H_3O^+}$ or $\mathrm{OH^-}$ through equilibrium reactions.

Preparation of Buffers

• Mix a weak acid with a salt of its conjugate base (e.g., acetic acid and sodium acetate).

• Mix a weak base with a salt of its conjugate acid (e.g., ammonia and ammonium chloride).

• Do not use salts of strong acids and bases (e.g., NaCl, KNO3) as they do not form buffers.

Buffer Action

• When $\mathrm{H_3O^+}$ is added, the conjugate base reacts to form the weak acid, minimizing pH change.

• When $\mathrm{OH^-}$ is added, the weak acid reacts to form the conjugate base, again minimizing pH change.

Buffer Calculations

• Use the Henderson-Hasselbalch equation to calculate the pH of a buffer:

$\mathrm{pH = p}K_a + \log \left( \frac{[\text{conjugate base}]}{[\text{acid}]} \right)$

• For buffers made from weak bases and their salts, use:

$\mathrm{pOH = p}K_b + \log \left( \frac{[\text{conjugate acid}]}{[\text{base}]} \right)$

• These equations are valid when buffer component concentrations are much greater than $K_a$ or $K_b$.

Buffer Range and Capacity

• Buffer range: The pH range over which a buffer effectively resists pH changes, typically $\pm 1$ pH unit from $\mathrm{p}K_a$.

• Buffer capacity: The amount of acid or base a buffer can neutralize before a significant pH change occurs. Higher concentrations of buffer components increase buffer capacity.

Identifying Buffer Solutions

Mixture	Buffer?	Reason
NaOH + NaOAc	No	Strong base and weak acid salt
HCl + NaCl	No	Strong acid and neutral salt
NH3 + NH4Cl	Yes	Weak base and its salt
NaOAc + HOAc	Yes	Weak acid and its salt
Citric acid + sodium citrate	Yes	Weak acid and its salt
HNO3 + NaNO3	No	Strong acid and neutral salt
Benzoic acid + cesium benzoate	Yes	Weak acid and its salt

Titrations

Definition and Purpose

• Titration: The process of gradually adding a solution of known concentration (titrant) to a solution of unknown concentration until the reaction is complete, allowing determination of the unknown concentration.

• Commonly used to analyze acids and bases.

Equivalence Point and Indicators

• Equivalence point: The point in a titration where stoichiometrically equivalent amounts of acid and base have reacted.

• Indicator: A weak acid or base that changes color at a specific pH range, used to signal the equivalence point.

Common Indicators and Their pH Ranges

Indicator	pH Range	Acid Color	Base Color
Methyl violet	0–2	Yellow	Violet
Methyl orange	2.9–4.0	Red	Yellow
Bromothymol blue	6.0–7.6	Yellow	Blue
Phenolphthalein	8.3–10.0	Colorless	Pink

Titration Curves

• A titration curve plots pH versus volume of titrant added.

• For strong acid–strong base titrations, the equivalence point is at pH 7. For weak acid–strong base titrations, the equivalence point is above pH 7.

Calculations in Titrations

• Before equivalence point: Calculate the amount of acid/base remaining and use equilibrium calculations to find pH.

• At equivalence point: For strong acid–strong base, pH = 7. For weak acid–strong base, pH is determined by the conjugate base formed.

• After equivalence point: Calculate the excess titrant and determine pH from its concentration.

General Titration Equations

• At equivalence: $\mathrm{mol_{acid} = mol_{base}}$

• For strong acid–strong base: $\mathrm{pH = 7}$ at equivalence (if monoprotic and at 25°C).

• For weak acid–strong base: Use $K_b$ of the conjugate base to find pOH, then pH.

Summary Table: Key Concepts

Concept	Key Points
Common Ion Effect	Suppression of weak electrolyte ionization by a strong electrolyte with a common ion
Buffer	Resists pH change; made from weak acid/base and its salt
Henderson-Hasselbalch Equation	$\mathrm{pH = p}K_a + \log \left( \frac{[\text{base}]}{[\text{acid}]} \right)$
Titration	Determines unknown concentration using a reaction with a known solution
Indicator	Signals endpoint of titration by color change

Additional info: The notes also cover how to use ICE tables for equilibrium calculations, the importance of buffer concentration for effective pH control, and the use of dimensional analysis in titration problems.