General Chemistry Study Notes: Thermochemistry, Acids & Bases, and Aqueous Ionic Equilibria

CHAPTER 6 — THERMOCHEMISTRY

Key Heat Formulas

Thermochemistry studies the energy changes, especially heat, that accompany chemical reactions and physical changes.

• q = C × ΔT: q is heat, C is heat capacity, ΔT is temperature change.

• q = c × m × ΔT: c is specific heat capacity, m is mass.

• q = n × ΔH (molar enthalpy): n is moles, ΔH is enthalpy change.

• q_{rxn} = -q_{solution}: In calorimetry, heat lost/gained by reaction equals heat gained/lost by solution.

• q_{rxn} = -C_{cal} × ΔT: For bomb calorimeter, C_{cal} is calorimeter heat capacity.

Calorimetry

• Coffee cup calorimeter: Measures ΔH at constant pressure.

• Bomb calorimeter: Measures ΔU at constant volume.

Heat Flow

• Endothermic: System absorbs heat (q > 0) - positive

• Exothermic: System releases heat (q < 0) - negative

Hess's Law

Hess's Law allows calculation of enthalpy changes for reactions by combining known reactions.

• Reverse reaction: sign of ΔH flips.

• Multiply reaction: ΔH multiplies accordingly (flip rxn = change sign)

• Add reactions: add ΔH values.

Standard Enthalpies of Formation

• $ΔH_{rxn} = ΣΔH_f^{ ext{products}} - ΣΔH_f^{ ext{reactants}}$

• Elements in standard state: $ΔH_f = 0$

CHAPTER 15 — ACIDS & BASES

Brønsted-Lowry Theory

The Brønsted-Lowry definition classifies acids as proton donors and bases as proton acceptors.

• Acid: H+ donor

• Base: H+ acceptor

• Conjugate acid/base pairs differ by one H+

Strong Acids and Bases

• Strong Acids: HCl, HBr, HI, HNO3, HClO4, H2SO4 (first step)

• Strong Bases: NaOH, KOH, Ca(OH)2, Ba(OH)2, Sr(OH)2

Weak Acids & Bases

• Ka: $Ka = [H^+][A^-]/[HA]$

• Kb: $Kb = [OH^-][BH^+]/[B]$

Neutralization Reactions

• Weak acid neutralization: $HA + OH^- \rightarrow A^- + H_2O$

Kw Relationships

• $Kw = 1.0 \times 10^{-14}$

• $pH + pOH = 14$

• $pH = -\log[H^+]$

• $pOH = -\log[OH^-]$

ICE Table Reminder

• HA, H+, A-

• Initial, Change, Equilibrium

• Use for weak acid/base equilibrium calculations

Approximations

• Valid if x < 5% of initial concentration

• If $K_a/c$ < 400, safe to use approximation

Percent Ionization

• % ionization = (ionized acid / initial acid) × 100%

Conjugate Relationship

• $K_a \times K_b = K_w$

• $pK_a + pK_b = 14$

Acid/Base of Salt Solutions

• Neutral cations: Li+, Na+, K+

• Acidic cations: NH4+, Al3+, Fe3+

• Neutral anions: Cl-, Br-, NO3-

• Basic anions: conjugate bases of weak acids (F-, CH3COO-, CN-)

CHAPTER 16 — AQUEOUS IONIC EQUILIBRIA (BUFFERS & TITRATIONS)

Buffers

A buffer is a solution containing a weak acid and its conjugate base in significant amounts, which resists changes in pH upon addition of small amounts of acid or base.

• Add acid: base (A-) converts H+ to HA

• Add base: HA converts OH- to A-

• Important: Buffer is destroyed when either HA or A- is consumed.

Henderson–Hasselbalch Equation

• $\text{buffer pH} = \log \left( \frac{[\text{base}]}{[\text{acid}]} \right) + pK_a$

• Use for buffer pH calculation

• After titration: pH = pK_a (at half-equivalence)

• Buffer range: pH = pK_a ± 1

Making Buffers

• Mix HA + A-

• Add strong base to HA (creates A-)

• Add strong acid to A- (creates HA)

• Choose acid with pK_a close to target pH

Buffer Capacity

• Increases with total concentration

• HA = A- (pH = pK_a) gives maximum capacity

Indicators

• Indicator is a weak acid

• Color change occurs at pK_a

• Choose indicator whose pK_a ≈ equivalence point pH

Titrations

Titrations are used to determine the concentration of an unknown acid or base by reacting it with a standard solution.

Strong Acid + Strong Base

• Reaction goes to completion

• Equivalence point: pH ≈ 7

• Before equivalence: pH from leftover H3O+

• After equivalence: pH from excess OH-

Weak Acid + Strong Base

• 5 Regions:

  1. Initial pH: solve weak acid ICE table

  2. Buffer region: use HA + A-

  3. Half-equivalence: pH = pK_a

  4. Equivalence: solution contains A- (weak base) → pH > 7

  5. After equivalence: pH from excess strong base

• Shape differences vs. SA/SB:

  • Starts higher

  • Has buffer plateau

  • Equivalence pH > 7

Weak Base + Strong Acid

• Reverse logic of WA/SB titration

• Initial pH: base

• Buffer region

• Half-equivalence: pH = pK_b

• Equivalence point: pH < 7 (weak acid formed)

Neutralizing Reactions

• Strong acid + strong base: always complete

• Weak acid + strong base: stoichiometry then equilibrium

• Weak base + strong acid: stoichiometry then equilibrium

Super-Compressed Exam Formulas

• $q = mCΔT$ (heat), $q_{rxn} = -q_{soln}$, $ΔH_{rxn} = ΣΔH_f^{ ext{products}} - ΣΔH_f^{ ext{reactants}}$

• $pH = -\log[H^+]$, $pOH = -\log[OH^-]$, $pH + pOH = 14$

• $K_a = [H^+][A^-]/[HA]$, $K_b = [OH^-][BH^+]/[B]$, $K_a \times K_b = K_w$, $pK_a + pK_b = 14$

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