Reaction Rates & Factors Affecting Kinetics

Chemical kinetics asks “how fast does a reaction reach equilibrium?”
At equilibrium forward & reverse rates are equal; measuring either direction is valid.
Rate can be expressed as:
- Appearance of products per unit time.
- Disappearance of reactants per unit time.
Choose whichever species is easiest to monitor (colour loss, gas volume, precipitate mass, temperature change, etc.).

Lab example (bleach + food colouring):
- Start timer when reagents mixed.
- Stop timer once colour completely disappears; time = period to consume dye.
Organic-lab example:
1. Let synthesis run for a fixed time (e.g. 10 min of an hrs-long reaction).
2. Withdraw aliquot with syringe.
3. "Quench" with a reagent that instantly stops reaction.
4. Titrate aliquot vs. standard solution; calculate remaining concentration → % progressed.

General definition: $C = \dfrac{\text{amount of solute}}{\text{amount of solution}}$
Most common unit: molarity (M, $\text{mol L}^{-1}$ ).
Bracket notation: $[X]$ means “molar concentration of species X.”
Other uses of brackets:
- Lewis structures for polyatomic ions (e.g. $[NO_3]^{-}$ ) → NOT concentration.

Rate = change in concentration over time: $\text{Rate} = \dfrac{\Delta[X]}{\Delta t}$
SI units: $\text{mol L}^{-1}\,s^{-1}\;(\text{or }M\,s^{-1}).$

Reaction occurs only when particles:
1. Collide with proper orientation.
2. Collide with energy $\geq$ activation energy $E_a$ .
More collisions and/or a larger fraction of “effective” collisions ⇒ faster rate.

Ionic species in aqueous solution react rapidly: ions are already separated, orientation less critical.
Covalent molecules often require bond rearrangements or shape changes → slower.
- Example: Tetrahedral centre shielded by four ligands must first undergo solvolysis; solvent (e.g. H₂O) removes one ligand → trigonal planar intermediate now accessible.
“Activated complex” or transition state: highly organized, short-lived arrangement of all reactants just before products form; more complex → higher $E_a$ → slower.

Higher $[\text{reactant}]$ ⇒ more collisions per second ⇒ generally faster.
Zero-order kinetics exception: rate independent of $[\text{reactant}]$ ; analogy – full classroom emptying limited by doorway width, not student number.
Pressure for gases: $P\uparrow$ compresses volume, increases molar density $\Rightarrow$ effectively a concentration increase.
Clarification: Merely shrinking container volume of a liquid phase does NOT change its concentration unless solvent is removed (teacher’s criticism of video example).

Raising T provides two simultaneous benefits:
1. Average molecular speed ↑ ⇒ collision frequency ↑.
2. Maxwell–Boltzmann curve broadens; larger fraction of molecules possess $E \ge E_a$ .
Theoretical limit: T so high that ~100 % of collisions are effective; impractical due to side reactions, energy cost, safety.
Maxwell–Boltzmann sketch description:
- X-axis = particle speed.
- Y-axis = # particles.
- Area under curve right of $E_a$ threshold increases with T.

Heterogeneous reactions (solid–gas, solid–liquid) occur only at interface.
Grinding a solid to powder exposes interior atoms ⇒ collision sites ↑ ⇒ rate ↑.
Practical use of LOW surface area: pharmaceutical tablets encased in cellulose dissolve slowly, providing controlled drug release; powdered form would act too fast/dangerous.

Catalyst: substance that speeds reaction without being consumed.
- Lowers $E_a$ by providing alternate pathway or orienting reactants.
- Biological example: enzymes.
Matchmaker analogy (video): Catalyst arranges reactants so less initial energy required.
Types (detail promised in next lecture):
- Homogeneous (same phase as reactants).
- Heterogeneous (different phase; often solid surface).
Inhibitor: compound that slows reaction, often by blocking catalyst or reactant sites.

Double arrows:
- Resonance structures: $\leftrightarrow$ inside Lewis structure.
- Equilibrium: $\rightleftharpoons$ between reagents & products line.
Density is technically a concentration unit (mass/volume).
Reaction rate measurements don’t need to be in seconds; any consistent time unit works, but s is SI.
Ethical/practical implication: manipulating temperature or concentration in industry must balance rate, cost, selectivity, safety, environmental impact.

Concentration: $C = \dfrac{n}{V}$ ( $n = \text{mol}, V = L$ )
Rate definition: $\text{Rate} = \dfrac{\Delta [X]}{\Delta t}$
Units: $\text{M}\,s^{-1} = \dfrac{\text{mol}}{L\cdot s}$
Activation energy concept: reactions require $E \ge E_a$ (numeric values context-dependent).

Potential-energy diagram:
- Reactants → transition state (peak) → products.
- Catalyst lowers peak height ( $E_a$ ).
Maxwell–Boltzmann distribution shifts right & flattens at higher T; shaded area beyond $E_a$ enlarges.

You must be able to:
- Write units for rate correctly.
- Explain each of the five factors with collision-theory language.
- Distinguish concentration vs. pressure effects.
- Interpret Maxwell–Boltzmann curves qualitatively.
- Describe how catalysts alter $E_a$ and reaction mechanism.
- Apply analogies to real kinetic scenarios (e.g., surface area in meds, zero-order door analogy).
Common pitfalls:
- Confusing resonance arrows with equilibrium arrows.
- Thinking volume compression changes liquid concentration without solvent removal.
- Forgetting that rate laws are empirical; “nature of reactants” influences mechanism and therefore rate law order.

Detailed mechanisms of catalysis: homogeneous vs. heterogeneous.
Concept of inhibitors & poisoning of catalysts.
Deriving rate laws experimentally (zero-, first-, second-order) & integrated rate equations.
Arrhenius equation: $k = A e^{-E<em>a/RT}$ and graphical determination of $E</em>a$ .