Stoichiometry, equilibrium, and kinetics: conservation of mass, balanced equations, Le Chatelier's principle, Arrhenius rate law, catalysis. The macroscopic dynamical side of chemistry.
chemical-reactions
Lavoisier conservation of mass
In a closed chemical system, total mass is conserved across any reaction. Holds to chemical precision; relativistic mass-energy equivalence…
Stoichiometry
Quantitative accounting of reactants and products in a balanced chemical equation via mole ratios. Direct consequence of conservation of…
Chemical equilibrium
At dynamic equilibrium for a reaction aA + bB ⇌ cC + dD, forward and reverse rates are equal and concentrations obey K =…
Le Chatelier's principle
If an external perturbation (concentration, pressure, temperature) is applied to a system at chemical equilibrium, the system shifts in the…
Arrhenius rate law
Temperature dependence of a reaction rate constant k(T) = A exp(-E_a/(k_B T)), where A is the pre-exponential (frequency) factor and E_a…
Catalysis
Acceleration of a reaction by a species (the catalyst) that provides a lower-activation-energy pathway without being consumed overall.…
Combustion mass balance
Lavoisier's sealed-vessel experiments (1770s) showing that the total mass of reactants equals total mass of products when gaseous species…
Reaction mechanism
Step-by-step account of a chemical reaction listing elementary steps, intermediates, transition states, and the rate-determining step.…
Transition-state theory
Eyring's 1935 framework: reaction rates controlled by the population of an activated complex at the saddle point of the potential-energy…
Rate-determining step
Slowest elementary step in a multi-step mechanism that sets the overall reaction rate. Experimentally identifiable via kinetic-isotope…
Reaction intermediate
Short-lived species formed in one elementary step and consumed in another, with a local potential-energy minimum (unlike a transition…
Reaction order
For a rate law rate = k [A]^m [B]^n …, the exponents m, n are the orders of reaction with respect to A and B; the sum m + n + … is the…
Activation energy (Eₐ)
The minimum energy barrier between reactants and products that colliding molecules must surmount in order for an elementary reaction step…
Arrhenius equation
Temperature dependence of a reaction's rate constant: k = A exp(−Eₐ / RT), where A is the pre-exponential (frequency) factor, Eₐ is the…
Reaction order & rate law
v = k[A]ᵃ[B]ᵇ; orders from initial-rates or integrated rate laws. Zero/first/second order integrated forms. Elementary vs overall rate.
Arrhenius equation
k = A e^(-Ea/RT). Pre-exponential + activation energy from Arrhenius plot ln k vs 1/T. Tolman interpretation: Ea = ⟨E⟩reacting - ⟨E⟩bulk.
Le Chatelier's principle
Stressed equilibrium shifts to partially counteract change in T, P, or concentration. Industrial consequences: Haber pressure/temperature…
Arrhenius equation (reformulated)
k = A exp(-Ea/RT); A = pZ with steric/collision factors; modified Arrhenius k = A T^n exp(-Ea/RT) for wide T ranges.
BEMA HAPOTHLE of ΔG‡
ΔG‡(AB) = f(ΔG°, ΔG‡_ideal) with cross-relations; predicts mixed reaction barriers from homonuclear data; acid/base catalysis.
Hammett σ/ρ linear free-energy relation
log(k/k₀) = ρσ for meta/para substituents; ρ > 0: electron-poor TS; Taft separation of polar/steric.
Brønsted catalysis law
log k_HA = α log K_HA + C; α is degree of proton transfer at TS; Brønsted plots probe mechanism.
Kinetic isotope effects (KIE)
Primary ¹H/²H KIE up to ~7 for C-H cleavage; tunneling can give 15-50; secondary KIE probe rehybridization.
Curtin–Hammett principle
Product ratio from rapidly interconverting conformers depends on ΔG‡ not conformer populations; conformer trapping exceptions.
Principle of least motion
Preferred mechanism involves minimal atomic rearrangement; suprafacial/antarafacial choices in pericyclic reactions.
Principle of microscopic reversibility
Forward and reverse reactions follow same minimum-energy path at equilibrium; basis of detailed balance.
RRKM unimolecular theory
Statistical redistribution of energy among internal modes; k(E) depends on density of states; master-equation extensions.
Lindemann–Hinshelwood mechanism
Unimolecular collisional activation A+M ⇌ A* + M → P; falloff between low/high P regimes; precursor to RRKM.
Intrinsic reaction coordinate (IRC)
Minimum-energy path from TS down to reactants/products in mass-weighted coords; basis of direct dynamics.
Catalytic cycles & TOF analysis
Kozuch energetic-span TOF = k_BT/h exp(-δE/RT); identifies rate-determining state vs step; guides catalyst design.
Solvent cage effect & diffusion control
Smoluchowski k_d ≈ 4πR D N_A; radical recombination within solvent cage; viscosity dependence.
Polanyi rule (early/late barrier)
Translational energy efficient for early barrier; vibrational for late barrier; predicts mode-selective reactivity.
Autocatalysis and BZ reaction
Rate proportional to product concentration; Belousov–Zhabotinsky oscillations; Field–Körös–Noyes model; chemical waves.