Chapter 18: Ionic Equilibrium – Buffers, Titrations, and Solubility

Chapter 18: Ionic Equilibrium

Introduction to Ionic Equilibrium

Ionic equilibrium is a fundamental concept in general chemistry, describing the balance between ions in solution, particularly in weak acid/base systems, buffer solutions, and solubility equilibria. Mastery of this topic is essential for understanding acid-base chemistry, titrations, and precipitation reactions.

Buffers: Solutions that Resist pH Changes

Definition and Importance of Buffers

Buffers are solutions that resist significant changes in pH when small amounts of acid or base are added. They are crucial in biological and chemical systems where maintaining a stable pH is necessary, such as in blood plasma.

• Composition: Buffers typically consist of a weak acid and its conjugate base, or a weak base and its conjugate acid.

• Example: The blood buffer system contains H2CO3 (carbonic acid) and HCO3- (bicarbonate).

How Buffers Work

Buffers function by neutralizing added acids (H3O+) or bases (OH-) through equilibrium reactions:

• When acid is added, the conjugate base component of the buffer reacts with the added H3O+ to form the weak acid, minimizing pH change.

• When base is added, the weak acid component reacts with OH- to form water and the conjugate base, again minimizing pH change.

Common Buffer Systems

• Acetic acid/acetate buffer: HC2H3O2 and NaC2H3O2

• Ammonia/ammonium buffer: NH3 and NH4Cl

Buffer pH Calculation: The Henderson-Hasselbalch Equation

The pH of a buffer solution can be calculated using the Henderson-Hasselbalch equation:

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

• [A-]: Concentration of the conjugate base

• [HA]: Concentration of the weak acid

• pKa: $pK_a = -\log K_a$

Buffer Effectiveness: Range and Capacity

The effectiveness of a buffer depends on both the relative and absolute concentrations of the acid and base components.

• Buffer Range: The pH range over which a buffer is effective is typically $pK_a \pm 1$.

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

Examples and Practice Problems

• Calculate the pH of a buffer containing 0.14 M HF (pKa = 3.15) and 0.071 M KF.

• Calculate the pH after adding a strong acid or base to a buffer solution using stoichiometry followed by equilibrium calculations.

Titration and Titration Curves

Acid-Base Titration

Titration is a laboratory technique used to determine the concentration of an unknown acid or base by reacting it with a standard solution of known concentration. The progress of the titration is monitored by measuring pH as titrant is added.

• Equivalence Point: The point at which stoichiometrically equivalent amounts of acid and base have reacted.

• End Point: The point at which the indicator changes color, ideally close to the equivalence point.

Titration Curves

Titration curves plot pH versus the volume of titrant added. The shape of the curve depends on the strengths of the acid and base involved.

• Strong acid–strong base: Sharp rise in pH at equivalence point (pH = 7).

• Weak acid–strong base: Initial pH is higher, buffer region before equivalence, equivalence point pH > 7.

• Weak base–strong acid: Initial pH is high, equivalence point pH < 7.

Indicators

Acid-base indicators are weak acids or bases that change color at specific pH ranges, used to signal the end point of a titration.

Indicator	pH Range
Phenolphthalein	8.3–10.0
Methyl orange	3.1–4.4
Bromothymol blue	6.0–7.6
Additional info:	See image_20 for a full table of indicator ranges.

Solubility Equilibria

Solubility Product Constant (Ksp)

The solubility product constant ($K_{sp}$) describes the equilibrium between a solid ionic compound and its dissolved ions in solution. For a generic salt $AB_2$:

$AB_2(s) \rightleftharpoons A^{2+}(aq) + 2B^-(aq)$

$K_{sp} = [A^{2+}][B^-]^2$

• Molar solubility: The number of moles of solute that dissolve per liter of solution.

Calculating Solubility and Ksp

• Set up an ICE table to relate the solubility of the solid to the concentrations of ions at equilibrium.

• Substitute equilibrium concentrations into the $K_{sp}$ expression and solve for solubility.

Compound	Ksp	Solubility (M)
Mg(OH)2	2.06 × 10–13	3.72 × 10–5
CaF2	1.46 × 10–10	3.32 × 10–4

Common Ion Effect on Solubility

The presence of a common ion decreases the solubility of a salt due to Le Châtelier's principle. For example, adding NaCl to a solution of PbCl2 decreases the solubility of PbCl2 by increasing [Cl-].

Effect of pH on Solubility

The solubility of salts containing basic anions increases as pH decreases (solution becomes more acidic), because the anion reacts with H+ to form a weak acid or water, shifting the equilibrium to dissolve more solid.

Precipitation and Selective Precipitation

Precipitation Conditions

Precipitation occurs when the ion product (Q) exceeds the solubility product constant ($K_{sp}$):

$Q = [A^{2+}][B^-]^2$

• If Q > Ksp: Precipitate forms

• If Q < Ksp: No precipitate forms

Complex Ion Equilibria

Complex Ion Formation

Complex ions are formed when a metal cation binds to one or more ligands (Lewis bases) via coordinate covalent bonds. This process can increase the solubility of certain salts in the presence of ligands.

• Example: $Ag^+ + 2NH_3 \rightleftharpoons [Ag(NH_3)_2]^+$

• Formation constant (Kf): The equilibrium constant for the formation of a complex ion.

$K_f = \frac{[Ag(NH_3)_2^+]}{[Ag^+][NH_3]^2}$

Complex Ion	Kf
Ag(NH3)2+	1.7 × 107
Cu(NH3)42+	1.0 × 1013
Zn(OH)42–	2 × 1015
Additional info:	See image_27 for a full table of formation constants.

Effect of Complex Ion Formation on Solubility

The formation of complex ions can greatly increase the solubility of sparingly soluble salts b y removing metal ions from solution and shifting the dissolution equilibrium to the right.