Chemical Kinetics – Reaction Mechanisms, Molecularity & Rate Laws

Reaction Mechanisms

  • A reaction mechanism = the step-by-step pathway that converts reactants to products.

  • Some reactions are 1-step (elementary) but, as the number/complexity of particles rises, multi-step pathways become overwhelmingly more probable.

  • Each elementary step has its own collision event that obeys its own rate law.

Net (Overall) Equation vs. Elementary Steps

  • Net equation = balanced chemical equation that shows only initial reactants and final products.

  • Elementary steps reveal hidden, short-lived species that never appear in the net equation.

  • Example given (color-coded R = red, Y = yellow, B = blue):

    • Net (overall) reaction: 2R + 2Y + B \longrightarrow R2Y2B

    • Possible 4-step mechanism:

    1. R + R \rightarrow R_2

    2. R2 + B \rightarrow R2B

    3. Y + Y \rightarrow Y_2

    4. R2B + Y2 \rightarrow R2Y2B

Reaction Intermediates

  • Defined as species produced in one step and consumed in a later step.

  • Highly energetic/unstable, exist only micro-seconds.

  • Because they cancel when steps are summed, they never appear in the net equation.

  • In the example above: R2, R2B and Y_2 are intermediates.

Collision-Probability Argument

  • A successful collision requires: right particles + right time + right place + correct orientation + E \ge E_a (activation energy).

  • Three-, four-, or five-particle simultaneous collisions are statistically rare.

    • Classroom demo: 16 R, 16 Y, 16 B particles at T = 300\,\text K ⇒ mostly 2-body collisions.

    • Even at 700\,\text K the vast majority remain 2-body; very few triple hits.

  • Multi-step mechanisms therefore decompose seemingly 5-body events into sequential 2- or 1-body events.

Rate-Determining (Slow) Step

  • Overall rate is governed by the slowest elementary step (longest time).

  • Example timing:

    • Step 1 = 1\,\text s

    • Step 2 = 0.01\,\text s

    • Step 3 = 42.6\,\text h (slow step)

    • Step 4 = 1\,\mu\text s

    • Total ≈ 42\,\text h\,36\,\text{min}; Step 3 controls the rate.

  • Rate law is written from reactants of the slow step only.

    • If Step 3 is Y + Y \rightarrow Y_2 then
      \text{rate}=k[Y]^2

    • Interpretation: bimolecular w.r.t. Y, second order overall for this mechanism.

  • Important AP disclaimer: final rate law must use only species present in the net reaction. If the slow step contains an intermediate, extra algebra (steady-state or pre-equilibrium) must remove it.

Molecularity & Reaction Order

  • Molecularity = number of molecules involved in an elementary step’s collision; determines the possible kinetic order for that step.

  • Common cases:

    • Unimolecular (1 particle) → first-order kinetics

    • Speed limited by internal bond rearrangement or shape change of a single molecule.

    • Bimolecular (2 particles) → second-order kinetics

    • Bond breaking & new bond forming occur in concert between attacker & victim.

    • Termolecular (3 particles) → third-order kinetics

    • Very rare unless one particle is a catalyst that “holds” the other two (induced-fit model).

    • >3 (quad-, quint-molecular) ≈ negligible in ordinary chemistry.

  • Zero-order kinetics

    • Rate independent of reactant concentration.

    • Analogies: people exiting a room (door size = rate limiter); reactions limited by catalyst surface area.

Diagram Interpretation Tips

  • If transition diagram shows bond breaking & forming simultaneously between two species → bimolecular.

  • If only one species deforms then fragments → unimolecular.

  • If catalyst plus two reactants converge → termolecular.

  • SN2 illustration: CH$3$I initially tetrahedral; as nucleophile approaches, CH$3$ group becomes pseudo-planar, iodide repelled → bond forming & breaking together (bimolecular).

Worked Mechanism Problem from Lecture

Given:

  1. 2A + B \rightarrow X (slow)

  2. C + C \rightarrow Y

  3. Y + X \rightarrow Z

  4. X \rightarrow D + E

  5. Net equation – cancel intermediates X, Y:
    3A + B + 2C \rightarrow D + E + Z

  6. Rate law – use slow step (#1): three reactant particles \Rightarrow third order overall
    \text{rate}=k[A]^2[B]

Five Classical Factors Affecting Rate

  1. Nature of reactants (bond type, state, complexity).

  2. Temperature (via E_a & collision frequency).

  3. Concentration or pressure (gas) – treated identically because both alter collision frequency.

  4. Surface area (heterogeneous reactions/catalysts).

  5. Presence of catalyst or inhibitor (homogeneous, heterogeneous or biochemical).

Thermodynamic vs. Kinetic Stability (Exam Reminder)

  • Thermodynamic: sign/magnitude of \Delta H, \Delta G, \Delta S.

    • Endothermic often more thermodynamically stable; exothermic less so.

  • Kinetic: magnitude of E_a, complexity of activated complex → governs rate not energy favorability.

  • Spontaneity depends on \Delta G = \Delta H - T\Delta S; exothermic generally spontaneous at Earth-like T.

Key Equations

  • Elementary-step rate law (general):
    \text{rate}=k\prodi[\text{Reactant}i]^{mi} where mi = stoichiometric coefficient within that step.

  • Arrhenius: k = A e^{-E_a/RT}

  • Overall reaction time illustration: t{total}=\sum t{step}; slowest t{step}\approx t{total}.

Study / Test Checklist

  • Write & cancel to obtain net equations from multi-step mechanisms.

  • Identify slow step → derive rate law with correct molecularity & only net-equation species.

  • Recognize zero-, first-, second-, third-order behaviour in graphs or data.

  • Interpret potential-energy vs. reaction-coordinate diagrams: E_a, \Delta H, catalyzed vs. uncatalyzed paths.

  • Distinguish thermodynamic vs. kinetic control; apply five rate factors; relate pressure ↔ concentration for gases.

  • Be comfortable with example numeric forms:

    • E_a displayed in \text{kJ mol}^{-1}

    • Rate-constant units:
      • 0-order \text{M s}^{-1},
      • 1-order \text s^{-1},
      • 2-order \text{M}^{-1}\text s^{-1},
      • 3-order \text{M}^{-2}\text s^{-1}.

(Le Chatelier & K_{eq} topics deferred to next unit.)