Chapter 17: Buffers, Titrations, and Solubility Equilibria

Buffers, Titrations, and Solubility Equilibria

17.1 The Common-Ion Effect

The common-ion effect describes the shift in equilibrium that occurs when a solution already contains one of the ions involved in the equilibrium. This effect is crucial in understanding buffer solutions and solubility equilibria.

• Definition: The suppression of the ionization of a weak acid or base by the presence of a common ion from a strong electrolyte.

• Example: Adding sodium acetate (NaCH3COO) to acetic acid (CH3COOH) introduces the common ion CH3COO-, shifting the equilibrium and lowering [H+].

• Le Châtelier’s Principle: Adding more product ion (e.g., CH3COO-) shifts the equilibrium toward the reactants, reducing the ionization of the weak acid.

• Weak Bases: The same principle applies. Adding NH4+ to an ammonia solution shifts the equilibrium, lowering [OH-].

17.2 Buffers

Buffers are solutions that resist changes in pH when small amounts of acid or base are added. They are typically made from a weak acid and its conjugate base or a weak base and its conjugate acid.

• Composition: A buffer must contain significant amounts (≥ 10-3 M) of both the weak acid (HA) and its conjugate base (A-).

• How Buffers Work: The weak acid neutralizes added base, and the conjugate base neutralizes added acid, minimizing pH changes.

• Preparation Methods:

  1. Mix a weak acid and its conjugate base (e.g., acetic acid and sodium acetate).

  2. Mix a weak base and its conjugate acid (e.g., ammonia and ammonium chloride).

  3. Add a strong base to a weak acid (to generate the conjugate base).

  4. Add a strong acid to a weak base (to generate the conjugate acid).

The Henderson–Hasselbalch Equation

The Henderson–Hasselbalch equation provides a convenient way to calculate the pH of a buffer solution:

• For a weak acid buffer:

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

• This equation relates the pH, the acid dissociation constant (Ka), and the concentrations of the acid and its conjugate base.

• It is valid for any weak acid/base and their respective salts.

Buffer Capacity and pH Range

Buffer capacity is the amount of acid or base a buffer can neutralize before the pH changes significantly. The effectiveness of a buffer depends on the ratio of [A-] to [HA], not their absolute concentrations.

• Buffers are most effective when [A-] ≈ [HA], i.e., pH ≈ pKa.

• Buffer action is poor if [HA] > 10 × [A-] or [HA] < [A-]/10.

Calculating pH Changes in Buffers

When a strong acid or base is added to a buffer, the calculation involves two steps:

1. Stoichiometry: Calculate the new amounts of HA and A- after neutralization.

2. Equilibrium: Use the Henderson–Hasselbalch equation to find the new pH.

Buffer vs. Water: Resistance to pH Change

Buffers resist pH changes much more effectively than pure water when acids or bases are added.

17.3 Acid–Base Titrations

Principles of Titration

Titration is a technique where a solution of known concentration (titrant) is added to a solution of unknown concentration until the reaction reaches the equivalence point (moles acid = moles base).

• The equivalence point is detected by monitoring pH changes or using indicators.

Titration Curves

• Strong Acid with Strong Base: The pH rises slowly, then rapidly near the equivalence point (pH = 7), then levels off.

• Strong Base with Strong Acid: The pH starts high, drops rapidly at the equivalence point (pH = 7), then levels off.

• Weak Acid with Strong Base: Four regions: initial pH, buffer region, equivalence point (pH > 7), and excess base region.

Calculating pH During Titration

• Before equivalence: Use limiting reactant and Henderson–Hasselbalch equation.

• At equivalence: Only the conjugate base remains; calculate its concentration and use Kb to find pH.

• After equivalence: Excess strong base determines pH.

Indicators

Indicators are weak acids or bases that change color at specific pH ranges. They are used to visually determine the equivalence point in titrations.

Titrations of Polyprotic Acids

Polyprotic acids have more than one ionizable proton, resulting in multiple equivalence points. Each step is treated separately, and the pH at the halfway point to each equivalence equals the pKa for that step.

17.4 Solubility Equilibria

Solubility Product Constant (Ksp)

The solubility-product constant (Ksp) describes the equilibrium between a solid and its ions in solution.

• Example: For CaF2(s):

$\mathrm{CaF}_2(s) \rightleftharpoons \mathrm{Ca}^{2+}(aq) + 2\mathrm{F}^-(aq)$ $K_{sp} = [\mathrm{Ca}^{2+}][\mathrm{F}^-]^2$

• Solubility is the maximum amount of solute that can dissolve, usually expressed in mol/L or g/L.

Calculating Solubility from Ksp

• Set up an ICE table for the dissolution reaction.

• Substitute equilibrium concentrations into the Ksp expression and solve for solubility.

Common-Ion Effect on Solubility

The presence of a common ion decreases the solubility of a salt. For example, adding NaF to a CaF2 solution decreases CaF2 solubility due to increased [F-].

Effect of pH on Solubility

If the anion of a salt is a weak base, adding acid increases solubility by reacting with the anion and removing it from solution (e.g., F- + H+ → HF).

Complex Ion Formation

Metal ions can form complex ions with Lewis bases, increasing the solubility of otherwise insoluble salts (e.g., Ag+ + 2NH3 → Ag(NH3)2+).

Amphoterism

Amphoteric oxides and hydroxides can act as either acids or bases, making them soluble in both strong acids and bases (e.g., Al(OH)3).

17.6 Precipitation and Ion Separation

Predicting Precipitation

To determine if a precipitate will form, calculate the reaction quotient (Q) and compare it to Ksp:

• If Q = Ksp: The solution is saturated (at equilibrium).

• If Q < Ksp: No precipitate forms; more solid can dissolve.

• If Q > Ksp: Precipitation occurs.

Selective Precipitation and Qualitative Analysis

Differences in solubility can be used to separate ions from a mixture by selective precipitation. This is a key technique in qualitative analysis and in recovering valuable metals from mixtures.

Ion	Ksp
CuS	6 × 10-37
ZnS	1 × 10-25
PbSO4	6.3 × 10-7
AgCl	1.8 × 10-10
BaF2	1.0 × 10-6
CaCO3	3.3 × 10-9
Ni(OH)2	2.0 × 10-15

Summary

• The common-ion effect, buffer solutions, titrations, and solubility equilibria are interconnected concepts essential for understanding acid-base and precipitation reactions in aqueous solutions.

• Mastery of these topics is fundamental for predicting solution behavior, designing experiments, and analyzing chemical mixtures.