Buffers, Titrations, and Solubility Equilibria: Study Notes for General Chemistry

Buffers and Buffer Solutions

Formation and Composition of Buffers

A buffer solution is a solution that resists changes in pH when small amounts of acid or base are added. Buffers are typically composed of a weak acid and its conjugate base, or a weak base and its conjugate acid.

• Example: Acetic acid (CH3COOH) and sodium acetate (NaCH3COO) form a buffer.

• Buffers work by neutralizing added H+ or OH- ions.

Calculating the pH of a Buffer Solution

The pH of a buffer can be calculated using either an equilibrium (ICE table) approach or the Henderson-Hasselbalch equation.

• ICE Table Method: Set up an equilibrium table for the weak acid dissociation and solve for [H3O+].

• Henderson-Hasselbalch Equation: Provides a shortcut for calculating buffer pH:

Henderson-Hasselbalch Equation:

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

• Where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid.

• For buffers made from weak bases and their conjugate acids:

$\text{pOH} = \text{p}K_b + \log \left( \frac{[\text{BH}^+]}{[\text{B}]} \right)$

• Assumes the 'x is small' approximation is valid (i.e., the change in concentration due to dissociation is negligible).

Buffer Range and Buffer Capacity

• Buffer Range: The pH range over which a buffer is effective, typically $\text{p}K_a \pm 1$.

• Buffer Capacity: The amount of acid or base a buffer can neutralize before the pH changes significantly. Maximum capacity occurs when [HA] = [A-].

• A buffer is most effective when $0.1 < \frac{[\text{base}]}{[\text{acid}]} < 10$.

Preparing a Buffer Solution

• Mix a weak acid with its conjugate base (or a weak base with its conjugate acid) in appropriate proportions.

• Alternatively, prepare a buffer by partially neutralizing a weak acid with a strong base (or vice versa).

• To prepare a buffer of a specific pH, use the Henderson-Hasselbalch equation to determine the required ratio of acid to base.

Titrations and Titration Curves

Acid-Base Titrations

An acid-base titration involves the gradual addition of an acid or base of known concentration (the titrant) to a solution of unknown concentration until the reaction reaches the equivalence point.

• Equivalence Point: The point at which moles of acid equal moles of base.

• Indicator: A chemical that changes color at (or near) the equivalence point, signaling the end of the titration.

Titration Curves

• A plot of pH versus volume of titrant added.

• Strong Acid–Strong Base: Sharp jump in pH at equivalence point (pH = 7 for neutral salt).

• Weak Acid–Strong Base: Buffer region before equivalence point; equivalence point pH > 7.

• Weak Base–Strong Acid: Buffer region before equivalence point; equivalence point pH < 7.

• Half-Equivalence Point: The point where half the acid (or base) has been neutralized; $\text{pH} = \text{p}K_a$ for weak acids.

Calculating pH During Titration

• Before equivalence: Use buffer calculations (Henderson-Hasselbalch equation).

• At equivalence: Calculate pH based on the salt formed (hydrolysis may occur).

• After equivalence: Excess titrant determines pH.

Solubility Equilibria

Solubility Product Constant (Ksp)

The solubility product constant ($K_{sp}$) is the equilibrium constant for the dissolution of a sparingly soluble ionic compound.

• For a salt AB: $\text{AB}(s) \rightleftharpoons \text{A}^+(aq) + \text{B}^-(aq)$

• $K_{sp} = [\text{A}^+][\text{B}^-]$

• For more complex salts, the $K_{sp}$ expression includes stoichiometric coefficients:

Salt	Ksp Expression
AB	$K_{sp} = x^2$
AB2	$K_{sp} = 4x^3$
AB3	$K_{sp} = 27x^4$
A2B3	$K_{sp} = 108x^5$

Molar Solubility

• Molar solubility is the number of moles of solute that will dissolve in one liter of solution to form a saturated solution.

• Can be calculated from $K_{sp}$ using an ICE table.

Effect of Common Ion and pH on Solubility

• The presence of a common ion decreases solubility (common ion effect).

• Solubility of salts containing basic anions increases in acidic solution due to reaction with H+.

Predicting Precipitation and Selective Precipitation

• Compare the ion product (Q) to $K_{sp}$:

  • If Q > $K_{sp}$, precipitation occurs.

  • If Q < $K_{sp}$, no precipitation.

• Selective precipitation is used to separate ions by adding a reagent that precipitates one ion before another.

Complex Ion Equilibria

• Some metal ions form complex ions with ligands, increasing their solubility.

• Equilibrium expressions for complex ions involve formation constants ($K_f$).

Tables

pKa and Conjugate Base Table

The following table summarizes pKa values and conjugate bases for common weak acids:

Acid Name	Acid Formula	pKa	Conjugate Base Name	Conjugate Base Formula
Acetic acid	CH3COOH	4.76	Acetate	CH3COO-
Benzoic acid	C6H5COOH	4.20	Benzoate	C6H5COO-
Formic acid	HCOOH	3.75	Formate	HCOO-
Lactic acid	CH3CH(OH)COOH	3.86	Lactate	CH3CH(OH)COO-
Hydrocyanic acid	HCN	9.21	Cyanide	CN-

Key Equations

• Henderson-Hasselbalch Equation for acids: $\text{pH} = \text{p}K_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right)$

• Henderson-Hasselbalch Equation for bases: $\text{pOH} = \text{p}K_b + \log \left( \frac{[\text{BH}^+]}{[\text{B}]} \right)$

• Solubility product: $K_{sp} = [\text{A}^+]^m [\text{B}^-]^n$ for a salt AmBn

Examples and Applications

• Calculating buffer pH after addition of strong acid or base: Perform a stoichiometric calculation to determine new concentrations, then use the Henderson-Hasselbalch equation.

• Determining the pH at various points during a titration: Use buffer equations before equivalence, salt hydrolysis at equivalence, and excess titrant after equivalence.

• Calculating molar solubility from $K_{sp}$ and vice versa using ICE tables and equilibrium expressions.

Additional info: These notes synthesize and expand upon the provided slides and textbook images, ensuring all key concepts from buffer chemistry, titrations, and solubility equilibria are covered for General Chemistry students.