General Chemistry II: Acid-Base Equilibria, Buffers, and Solubility Study Guide

Acid-Base Equilibria

Weak Acid Dissociation and pH Calculation

Weak acids partially dissociate in water, establishing an equilibrium between the acid, its conjugate base, and hydronium ions. The extent of dissociation is quantified by the acid dissociation constant, $K_a$.

• Key Equation: $HA_{(aq)} + H_2O_{(l)} \rightleftharpoons A^-_{(aq)} + H_3O^+_{(aq)}$

• Initial, Change, Equilibrium (ICE) Table: Used to track concentrations during dissociation.

• pH Calculation: $pH = -\log[H_3O^+]$

• Acid Dissociation Constant: $K_a = \dfrac{[A^-][H_3O^+]}{[HA]}$

• Example: For $0.085$ M HA, $[H_3O^+] = 5.02 \times 10^{-4}$ M, $pH = 3.30$, $K_a = 3.0 \times 10^{-6}$

Polyprotic Acids and Stepwise Dissociation

Polyprotic acids, such as carbonic acid ($H_2CO_3$), dissociate in multiple steps, each with its own $K_a$ value. The first dissociation typically contributes most to the $[H_3O^+]$.

• First Dissociation: $H_2CO_3 + H_2O \rightleftharpoons HCO_3^- + H_3O^+$, $K_{a1}$

• Second Dissociation: $HCO_3^- + H_2O \rightleftharpoons CO_3^{2-} + H_3O^+$, $K_{a2}$

• ICE Table: Used for each step to determine equilibrium concentrations.

• Example: For $0.155$ M $H_2CO_3$, $K_{a1} = 4.3 \times 10^{-7}$, $[HCO_3^-] = 2.58 \times 10^{-4}$ M, $pH = 3.88$

Buffer Solutions

Buffer Composition and pH Calculation

Buffers are solutions that resist changes in pH upon addition of small amounts of acid or base. They typically consist of a weak acid and its conjugate base.

• Henderson-Hasselbalch Equation: $pH = pK_a + \log\left(\dfrac{[\text{base}]}{[\text{acid}]}\right)$

• Example: For a buffer with $0.125$ M $HNO_2$ and $0.145$ M $NaNO_2$, $K_a = 4.6 \times 10^{-4}$, $pH = 2.96$

• Effect of Added Acid/Base: Adjust concentrations in the Henderson-Hasselbalch equation after reaction with added $HCl$ or $NaOH$.

Buffer Capacity and Titration

Buffer capacity refers to the amount of acid or base a buffer can neutralize before a significant pH change occurs. During titration, the pH changes gradually until the equivalence point is reached.

• Stoichiometric Point: The point at which the amount of acid equals the amount of base in the buffer.

• Example: Addition of $1.5$ g $HCl$ to the buffer changes the pH to $3.13$.

Solubility and Precipitation Equilibria

Solubility Product Constant ($K_{sp}$)

The solubility product constant describes the equilibrium between a solid and its ions in solution. It is used to predict whether a precipitate will form.

• Key Equation: For $FeCO_3$, $K_{sp} = [Fe^{2+}][CO_3^{2-}]$

• Minimum Concentration for Precipitation: Calculate $[CO_3^{2-}]$ needed to begin precipitation using $K_{sp}$ and known ion concentrations.

• Example Table:

Salt	$K_{sp}$	Ion Concentration	$[CO_3^{2-}]$ (min)
FeCO3	$3.0 \times 10^{-11}$	$[Fe^{2+}] = 0.022$ M	$1.4 \times 10^{-9}$ M
MgCO3	$6.82 \times 10^{-6}$	$[Mg^{2+}] = 0.014$ M	$4.9 \times 10^{-4}$ M

• Maximum Concentration: The highest $[CO_3^{2-}]$ before the next cation begins to precipitate.

• Remaining Cation Concentration: After precipitation begins, calculate the remaining concentration using $K_{sp}$.

Complex Ion Equilibria

Formation and Dissolution of Complex Ions

Complex ions form when a metal ion binds to ligands, affecting solubility. The formation constant ($K_f$) and solubility product ($K_{sp}$) are used to calculate equilibrium concentrations.

• Key Equation: $Zn(OH)_2(s) + 2OH^- \rightleftharpoons [Zn(OH)_4]^{2-}$

• Overall Equilibrium Constant: $K = K_{sp} \times K_f$

• Example: For $0.20$ M $OH^-$, $K_{sp} = 3.0 \times 10^{-15}$, $K_f = 2.0 \times 10^5$, $pOH = 1.03$, $pH = 12.97$

Titration of Weak Bases

pH Changes During Titration

When a weak base is titrated with a strong acid, the pH changes as the base is neutralized. Calculations involve equilibrium expressions and stoichiometry.

• Key Equation: $C_5H_5N + H_2O \rightleftharpoons C_5H_5NH^+ + OH^-$

• Base Dissociation Constant: $K_b = \dfrac{[C_5H_5NH^+][OH^-]}{[C_5H_5N]}$

• pOH and pH Calculation: $pOH = -\log[OH^-]$, $pH = 14 - pOH$

• Example Table:

Volume HCl Added	pH
0.0 mL	9.16
20.0 mL	4.98

• Stoichiometric Point: Calculated by equating moles of acid and base.

Key Terms and Definitions

• Acid Dissociation Constant ($K_a$): Quantifies the strength of a weak acid.

• Base Dissociation Constant ($K_b$): Quantifies the strength of a weak base.

• Solubility Product ($K_{sp}$): Describes the equilibrium between a solid and its ions in solution.

• Formation Constant ($K_f$): Describes the stability of a complex ion.

• Buffer: A solution that resists changes in pH.

• ICE Table: A method for tracking concentrations in equilibrium problems.

Summary Table: Equilibrium Constants and Their Applications

Constant	Application	Example Value
$K_a$	Weak acid dissociation	$3.0 \times 10^{-6}$
$K_b$	Weak base dissociation	$1.7 \times 10^{-9}$
$K_{sp}$	Solubility equilibrium	$3.0 \times 10^{-11}$
$K_f$	Complex ion formation	$2.0 \times 10^5$

Additional info: These notes expand on the solution key by providing full academic context, definitions, and structured examples for each equilibrium and titration concept covered in the exam questions.