Aqueous Ionic Equilibrium: Buffers, Titrations, and Solubility

Chapter 17: Aqueous Ionic Equilibrium

Buffered Solutions

Buffered solutions are solutions that resist changes in pH when small amounts of strong acids or bases are added. They are essential in many chemical and biological systems to maintain a stable pH environment.

• Definition: A buffer is a solution containing significant amounts of both a weak acid and its conjugate base (or a weak base and its conjugate acid).

• Action: When H+ is added, it reacts with the conjugate base; when OH− is added, it reacts with the weak acid.

• Example: A mixture of acetic acid (HC2H3O2) and sodium acetate (NaC2H3O2).

Key Points on Buffered Solutions

• Buffers contain a weak acid or base and a common ion (its conjugate).

• When a strong acid or base is added, first consider the stoichiometry (neutralization), then the equilibrium.

Buffering Capacity

The buffering capacity is the amount of acid or base a buffer can absorb without a significant change in pH. It depends on the absolute concentrations of the acid and base in the buffer.

Calculating the pH of a Buffer Solution

To calculate the pH of a buffer, use the equilibrium expression or the Henderson-Hasselbalch equation. The latter is especially useful when the concentrations of acid and base are known.

• Equilibrium Table Example:

• Henderson-Hasselbalch Equation:

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

• Example Calculation:

Formation of Buffers

Buffers can be made by mixing a weak acid with its conjugate base (often as a salt), or a weak base with its conjugate acid.

• Example: Mixing ammonia (NH3) with ammonium chloride (NH4Cl) forms a basic buffer.

Buffering Effectiveness: Capacity and Range

A buffer is most effective when the concentrations of acid and base are large and nearly equal. The effective pH range of a buffer is typically pKa ± 1.

• Buffering Capacity: A concentrated buffer can neutralize more acid or base than a dilute buffer.

Henderson-Hasselbalch Equation for Basic Buffers

For a buffer made from a weak base and its conjugate acid, the Henderson-Hasselbalch equation can be adapted:

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

And since pH + pOH = 14, you can convert between them as needed.

Relationship Between pKa and pKb

For a conjugate acid-base pair:

$K_a \times K_b = K_w = 1.0 \times 10^{-14}$

$pK_a + pK_b = 14$

Titrations and Titration Curves

Titration Curves

A titration curve is a plot of pH versus the volume of titrant added. The equivalence point is where stoichiometrically equivalent amounts of acid and base have reacted.

• Strong Acid–Strong Base Titration: The equivalence point is at pH 7.

• Strong Base–Strong Acid Titration: The equivalence point is also at pH 7.

• Weak Acid–Strong Base Titration: The equivalence point is above pH 7 due to the formation of a weak conjugate base.

• Effect of Acid Strength: The initial pH and the shape of the curve depend on the acid's Ka.

• Strong Acid–Weak Base Titration: The equivalence point is below pH 7 due to the formation of a weak conjugate acid.

• Comparing Titration Curves: The shape and equivalence point pH differ for strong acid/strong base, weak acid/strong base, and weak base/strong acid titrations.

• Polyprotic Acid Titration: Polyprotic acids show multiple equivalence points, one for each ionizable proton.

Acid-Base Indicators

Indicators are weak acids or bases that change color at a particular pH range, marking the end point of a titration. The best indicator has a pKa close to the equivalence point pH.

• Common Indicators: Phenolphthalein (pH 8.3–10.0), Bromothymol Blue (pH 6.0–7.6), Methyl Red (pH 4.2–6.0).

• Indicator Color Change: The color change occurs over a narrow pH range.

• Indicator pH Ranges:

• Indicator Choice on Titration Curve: The indicator should change color near the equivalence point.

Solubility Equilibria

Solubility-Product Constant (Ksp)

The solubility-product constant, Ksp, is the equilibrium constant for the dissolution of a sparingly soluble ionic compound in water.

• General Form: For MnXm(s) ↔ nMm+(aq) + mXn−(aq),

$K_{sp} = [M^{m+}]^n [X^{n-}]^m$

• Example: PbCl2(s) ↔ Pb2+(aq) + 2Cl−(aq)

• Ksp Expression: $K_{sp} = [Pb^{2+}][Cl^-]^2$

Common Ion Effect

The solubility of a salt is decreased when one of its constituent ions is already present in the solution. This is known as the common ion effect.

Predicting Precipitation

To determine if precipitation will occur, compare the reaction quotient Q to Ksp:

• If Q > Ksp, precipitation occurs.

• If Q < Ksp, no precipitation occurs.

• If Q = Ksp, the solution is saturated.

Selective Precipitation

Selective precipitation is used to separate ions in a mixture by adding a reagent that precipitates one ion but not others, based on differences in Ksp values.

Complex Ion Formation

Transition metals can form complex ions with ligands. The equilibrium constant for complex ion formation is called the formation constant (Kf).

• Example: Ag+(aq) + 2 NH3(aq) ↔ Ag(NH3)2+(aq)

Solubility of Amphoteric Metal Hydroxides

Some metal hydroxides are amphoteric, meaning they are more soluble in both acidic and basic solutions due to their ability to react as either acids or bases.

• Example: Al(OH)3 is more soluble in both acidic and basic solutions.

Additional info: These notes cover the essential concepts of aqueous ionic equilibrium, including buffer systems, titration curves, solubility equilibria, and complex ion formation, as relevant to a general chemistry course.