Aqueous Equilibrium and Thermodynamics: Study Guide for CHEM 104 Exam 3

Chapter 18: Aqueous Equilibrium

Acid-Base Definitions

Acids and bases are fundamental concepts in chemistry, defined by different models:

• Arrhenius Acid: Produces H+ ions in water.

• Arrhenius Base: Produces OH- ions in water.

• Bronsted-Lowry Acid: Proton (H+) donor.

• Bronsted-Lowry Base: Proton acceptor.

Example: HCl in water acts as an Arrhenius and Bronsted-Lowry acid, donating H+ to water.

Conjugate Acid-Base Pairs

When an acid donates a proton, it forms its conjugate base; when a base accepts a proton, it forms its conjugate acid.

• Conjugate Acid: Formed when a base gains a proton.

• Conjugate Base: Formed when an acid loses a proton.

Example: In the reaction NH3 + H2O ⇌ NH4+ + OH-, NH3 is the base, NH4+ is its conjugate acid.

Autoionization of Water and Ion-Product Constant

Water can ionize itself, producing H+ and OH- ions.

• Autoionization: 2 H2O ⇌ H3O+ + OH-

• Ion-Product Constant: $Kw = [H^+][OH^-] = 1.0 \times 10^{-14}$ at 25°C

Note: [H+] and [H3O+] are equivalent.

pH and pOH Calculations

pH is a measure of acidity; pOH measures basicity. Both are calculated using logarithms.

• $pH = -\log[H^+]$

• $pOH = -\log[OH^-]$

• $pH + pOH = 14.00$

Example: If [H+] = 1.0 × 10-3 M, pH = 3.00.

Strong and Weak Acids/Bases

Strong acids and bases dissociate completely; weak acids and bases only partially dissociate.

• Common Strong Acids: HCl, HNO3, H2SO4

• Common Strong Bases: NaOH, KOH

• Weak Acids/Bases: Have equilibrium constants (Ka, Kb)

Example: Calculate pH for 0.01 M HCl: pH = 2.00.

Equilibrium Constants (Ka and Kb)

Ka and Kb quantify the strength of weak acids and bases.

• $Ka = \frac{[H^+][A^-]}{[HA]}$

• $Kb = \frac{[OH^-][BH^+]}{[B]}$

• Calculate Ka or Kb from concentration and pH.

Percent Ionization

Percent ionization shows the fraction of acid/base molecules that ionize in solution.

• $\text{Percent Ionization} = \frac{[\text{Ionized Acid/Base}]}{[\text{Initial Acid/Base}]} \times 100\%$

Relationship Between Acid and Conjugate Base Strength

The stronger the acid, the weaker its conjugate base, and vice versa.

• $Kw = Ka \times Kb$

• $pKw = pKa + pKb = 14.00$

Acidic, Basic, or Neutral Salt Solutions

Salt solutions can be acidic, basic, or neutral depending on the ions produced.

• Salts from strong acid and strong base: neutral

• Salts from weak acid and strong base: basic

• Salts from strong acid and weak base: acidic

Common Ion Effect

The addition of a common ion suppresses the ionization of a weak acid or base.

• Shifts equilibrium according to Le Chatelier's Principle.

Buffers

Buffers are solutions that resist changes in pH upon addition of small amounts of acid or base.

• Composed of a weak acid and its conjugate base, or a weak base and its conjugate acid.

• Buffer pH calculated using Henderson-Hasselbalch equation:

$pH = pKa + \log\frac{[\text{base}]}{[\text{acid}]}$

Buffer Capacity and pH Changes

Buffers can absorb added acid or base until their capacity is exceeded.

• Calculate pH changes using Henderson-Hasselbalch equation.

Acid-Base Titration and Titration Curves

Titration involves adding a solution of known concentration to another to determine its concentration.

• Equivalence Point: Point at which stoichiometric amounts of acid and base have reacted.

• Interpret titration curves to identify equivalence point.

• Calculate pH before, at, and after equivalence point for strong acid/strong base and strong base/weak acid titrations.

Relationship between pH and pKa: At halfway to equivalence point, pH = pKa.

Key Formulas

Formula	Description
$M = \frac{\text{moles solute}}{\text{volume of solution (L)}}$	Molarity
$M_1V_1 = M_2V_2$	Dilution equation
$pH = -\log[H^+]$	pH calculation
$pOH = -\log[OH^-]$	pOH calculation
$pH + pOH = 14.00$	Relationship at 25°C
$Kw = [H^+][OH^-] = 1.0 \times 10^{-14}$	Ion-product constant
$Kw = Ka \times Kb$	Relationship between Ka and Kb
$pKa = -\log Ka$	pKa calculation
$pKb = -\log Kb$	pKb calculation
$pKw = pKa + pKb = 14.00$	Relationship at 25°C
$pH = pKa + \log\frac{[\text{base}]}{[\text{acid}]}$	Henderson-Hasselbalch equation

Chapter 19: Thermodynamics

Spontaneous vs. Nonspontaneous Processes

Spontaneous processes occur without external intervention; nonspontaneous processes require energy input.

• Example: Ice melting at room temperature is spontaneous.

Entropy (S)

Entropy is a measure of disorder or randomness in a system.

• Higher entropy means greater molecular disorder.

• Phase changes (solid → liquid → gas) increase entropy.

Second Law of Thermodynamics

The entropy of the universe increases in any spontaneous process.

• $\Delta S_{univ} = \Delta S_{sys} + \Delta S_{surr}$

Microstates and Entropy Change

Entropy is related to the number of possible microstates (arrangements) of particles.

• More microstates = higher entropy.

Predicting Entropy Changes

Entropy increases with:

• Phase changes to more disordered states (solid → liquid → gas)

• Dissolution of solids

• Increase in number of gas molecules

Calculating Entropy Change

• $\Delta S = S_{final} - S_{initial}$

• For phase changes: $\Delta S = \frac{q_{rev}}{T}$

Entropy Change for Universe

The total entropy change is the sum of system and surroundings.

• Spontaneous if $\Delta S_{univ} > 0$

Exothermic and Endothermic Processes

• Exothermic: increases entropy of surroundings

• Endothermic: decreases entropy of surroundings

• $\Delta S_{surr} = -\frac{\Delta H_{sys}}{T}$

Gibbs Free Energy (G)

Gibbs free energy determines spontaneity of a process.

• $\Delta G = \Delta H - T\Delta S$

• If $\Delta G < 0$, process is spontaneous.

• If $\Delta G > 0$, process is nonspontaneous.

Standard Entropy and Free Energy Changes

• Use standard molar entropies to calculate $\Delta S^\circ$ for reactions.

• $\Delta G^\circ_{rxn} = \Delta H^\circ - T\Delta S^\circ$

• Alternatively, $\Delta G^\circ_{rxn} = \sum \Delta G^\circ_{f,products} - \sum \Delta G^\circ_{f,reactants}$

Third Law of Thermodynamics

The entropy of a perfect crystal at absolute zero is zero.

Reversible and Irreversible Processes

• Reversible: Can be reversed by infinitesimal changes.

• Irreversible: Cannot be reversed without significant changes.

Free Energy and Equilibrium

At equilibrium, the free energy change is zero.

• $\Delta G = 0$ at equilibrium

Free Energy and Equilibrium Constant

• $\Delta G^\circ = -RT \ln K$

• Interconvert between $\Delta G^\circ$ and K

Key Thermodynamics Formulas

Formula	Description
$\Delta S = S_{final} - S_{initial}$	Entropy change
$\Delta S_{surr} = -\frac{\Delta H_{sys}}{T}$	Entropy change of surroundings
$\Delta G = \Delta H - T\Delta S$	Gibbs free energy
$\Delta G^\circ_{rxn} = \sum \Delta G^\circ_{f,products} - \sum \Delta G^\circ_{f,reactants}$	Standard free energy change
$\Delta G^\circ = -RT \ln K$	Free energy and equilibrium constant

Additional info: Standard molar entropies and free energies of formation are typically found in tables in textbooks. R is the gas constant (8.314 J/mol·K).