Chemical Kinetics & Equilibria – Comprehensive Study Notes

Scope and Importance of Chapter 22

• Covers Chemical Kinetics (rate/speed) and Chemical Equilibria / Thermodynamics (extent/energy)

• College-level treatment normally: one full semester chapter on kinetics + eight on equilibria; AP text compresses into 1–2 chapters ➜ concept-dense

• Two industrial questions answered:

  • “How fast can we harvest product?” (time = money)

  • “How much energy (cost) is required?” (profit margin)

Symbols & Fundamental Constants Introduced

• Lower-case $k$

  • “Rate constant” in kinetics; quantifies reaction speed en route to equilibrium

• Upper-case $K$ (or $K_{eq}$)

  • “Equilibrium constant” in thermodynamics; quantifies product vs reactant amounts at equilibrium

  • Mathematical definition for a general reaction $aA+bB \rightleftharpoons cC+dD$ :
    $K=\dfrac{[C]^c[D]^d}{[A]^a[B]^b}$ (concentrations at equilibrium)

Chemical Kinetics ("How Fast?")

• Rate Constant $k$ depends on five factor clusters

  • 1. Activated Complex / Collision Requirements

  • Reactant particles must meet right time, right place, correct angle on the appropriate functional group (link to Ch. 13)

  • Sufficient energy to break old bonds & form new (activation energy barrier)

  • 2. Surface Area (heterogeneous reactions)

  • 3. Reactant Concentration (or amount / pressure for gases)

  • 4. Thermal Environment (temperature)

  • 5. Presence of a Catalyst (alters mechanism, lowers activation energy, increases rate without being consumed)

• Only one calculation method for $k$ learned in this course (others exist in college level)

Thermodynamics / Chemical Equilibria ("How Much?")

• Equilibrium constant $K$

  • $K=\dfrac{\text{[products]}}{\text{[reactants]}}$ (at equilibrium)

  • For stoichiometric (near-100 % yield) reactions: $[\text{products}]\to100\%$, $[\text{reactants}]\to0$ ⇒ $K\to\infty$; reverse reaction negligible

  • Most real reactions give finite $K$; product yield <100 %

• Determined by enthalpy ($\Delta H$), entropy ($\Delta S$), and temperature ($T$)

  • Gibbs–Helmholtz (Gibbs free-energy) equation:
    $\Delta G = \Delta H - T\Delta S$

  • \Delta G<0 ➜ spontaneous (thermodynamically favorable)

  • \Delta G>0 ➜ non-spontaneous at that $T$ (needs energy input)

• General Trends (with caveats)

  • Exothermic (negative $\Delta H$) reactions tend to be spontaneous/favorable

  • Positive $\Delta S$ (increased randomness) tends to favor spontaneity

  • Temperature can reverse or reinforce spontaneity (e.g.
    $\Delta G$ sign may flip with $T$)

  • Crystals: highly ordered (low $\Delta S$) yet stable ⇢ exception

Spontaneity, Instantaneity & Stability Vocabulary

• Spontaneous ≠ Instantaneous

  • Ice melting at $80^{\circ}\text{F}$: spontaneous but slow for large block

• Non-spontaneous ≠ Impossible

  • Ice melting at $20^{\circ}\text{F}$ requires heater (energy input)

• Thermodynamic Stability vs. Favorability

  • Textbook term “thermodynamically stable”: basically non-spontaneous (large positive $\Delta G$); author prefers “thermodynamically favorable” (negative $\Delta G$)

• Kinetic Stability

  • Reaction is spontaneous (negative $\Delta G$) yet so slow that change is unobservable ➜ e.g.
    diamond → graphite; rare but important

Reaction Rate Trends & Practical Notes

• Organic synthesis analogous to “baking a cake”: timescale varies; few reactions truly instantaneous

• Stoichiometric (one-way) reactions often faster than equilibrium ones, but no universal rules across ~$1.4\times10^{7}$ known chemicals

• Lab constraints: high-school labs 88 min; hence chosen reactions are near-instantaneous for convenience

Reversible vs. Stoichiometric Reactions

• Stoichiometric notation: single arrow $\rightarrow$, forward step dominates, $K\approx\infty$

• Equilibrium notation: double arrow $\rightleftharpoons$, forward & reverse considered

  • Maxwell–Boltzmann distribution ensures some high-speed product collisions re-form reactants

  • Always some reactant left; cannot reach 100 % yield

Dynamic Equilibrium – Rate Perspective

• Starting conditions: 100 % reactant, 0 % product

  • Forward rate high, reverse rate zero

• As products form, forward rate drops (reactant concentration falls), reverse rate rises (product concentration rises)

• Equilibrium reached when:
  $\text{rate}<em>{\text{forward}} = \text{rate}</em>{\text{reverse}}$ (slopes of concentration–time curves are equal/parallel)

• Product : Reactant ratio at equilibrium is NOT necessarily 50 : 50

  • Could be 92 % products / 8 % reactants if products highly favorable

  • Could be 0.000001 % products / 99.999999 % reactants if products unfavorable, yet still worth studying (e.g.
    lead ion contamination: harmful at parts-per-billion)

Graphical Illustrations (Described)

1. Moderate product favorability

   • Equilibrium at ~$35\%$ products, $65\%$ reactants

   • Forward rate curve (red) decays; reverse (green) rises; slopes equal at equilibrium point

2. High product favorability

   • Equilibrium at $80{-}85\%$ products

   • Same slope-matching concept; emphasizes variable yields

Analogies & Teaching Aids

• TED-Ed “arm-transfer” people demo

  • Collisions = people bumping

  • Right orientation + sufficient energy required to “swap limbs” (bond breaking/forming)

  • Both forward and reverse limb transfers occur until rates equal ➜ equilibrium

  • Video caution: graphic shows 50/50 distribution; instructor notes this is not universal

• Ice cube outside vs. heater – demonstrates spontaneity vs.
  required energy input

• Lead poisoning example – tiny equilibrium yield can have major biological impact

Factors Controlling Reaction Design in Industry & Labs

• Time constraints → aim for faster kinetics (increase $k$)

• Energy/heat constraints → seek exothermic or lower-$\Delta H$ processes

• Safety/control → non-spontaneous or kinetically slow reactions may be preferred despite added cost

• Catalysts widely used to balance speed and energy demands

Key Equations & Symbols Recap

• Rate constant: $k$ (units depend on reaction order)

• Equilibrium constant: $K$
  $K=\dfrac{[\text{products}]}{[\text{reactants}]}$

• Gibbs Free Energy: $\Delta G = \Delta H - T\Delta S$

• Relationship spontaneity:
  \Delta G<0 \;\Rightarrow\;\text{spontaneous} \Delta G>0 \;\Rightarrow\;\text{non-spontaneous}

• Stoichiometric yield: $K\to\infty$

Common Misconceptions Clarified

• Non-spontaneous does not mean impossible; it means “energy input required”

• Spontaneous does not ensure fast or explosive; speed governed by $k$

• Equilibrium ≠ 50/50 mixture; ratio depends on $K$

• Exothermic reactions are usually spontaneous but can be non-spontaneous under certain $T$ or $\Delta S$ conditions

Links & Further Study

• TED-Ed equilibrium video (link provided on Edmodo)

• Next lesson preview: quantitative determination of reaction rates & detailed factor analysis