Kinetics: every key term you need (+ practice quiz)

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• Atomic Structure & Properties
• Compound Structure & Properties
• Intermolecular Forces & Properties
• Chemical Reactions

Thermodynamics Overview

The study of energy transfer and transformation in chemical systems; includes heat, work, and entropy.

First Law of Thermodynamics

Energy is conserved; ΔE = q + w, where q is heat and w is work. The total energy of a system is constant.

Enthalpy (H)

A state function measuring the heat content of a system; ΔH = ΔE + ΔPV. Used to describe heat flow at constant pressure.

Exothermic Reactions

Reactions that release energy to surroundings; ΔH < 0. Examples: combustion, condensation, freezing.

Endothermic Reactions

Reactions that absorb energy from surroundings; ΔH > 0. Examples: melting, evaporation, photosynthesis.

Hess's Law

The enthalpy change of a reaction is the same regardless of the pathway; ΔH_rxn = Σ ΔH_products - Σ ΔH_reactants.

Standard Enthalpy of Formation (ΔH_f°)

The enthalpy change when one mole of a compound is formed from its elements in their standard states.

Calorimetry

Experimental technique measuring heat transfer; q = m × c × ΔT, where m is mass, c is specific heat, ΔT is temperature change.

Specific Heat Capacity

The amount of heat required to raise the temperature of 1 gram of substance by 1°C; units: J/(g·°C).

Heat of Combustion

The enthalpy change when one mole of substance burns completely in oxygen; typically large negative values.

Entropy (S)

A measure of disorder or randomness in a system; increases with higher temperature, more particles, and phase changes.

Second Law of Thermodynamics

In any spontaneous process, the entropy of the universe increases; ΔS_univ = ΔS_sys + ΔS_surr > 0.

Third Law of Thermodynamics

The entropy of a perfect crystal at absolute zero (0 K) is zero; entropy of all substances > 0 above 0 K.

Standard Entropy (S°)

The entropy of one mole of a substance at 25°C and 1 atm; used to calculate ΔS_rxn = Σ S°_products - Σ S°_reactants.

Gibbs Free Energy (G)

ΔG = ΔH - TΔS; determines spontaneity of a reaction. ΔG < 0 means spontaneous, ΔG > 0 means non-spontaneous.

ΔG and Spontaneity

ΔG < 0: spontaneous; ΔG = 0: equilibrium; ΔG > 0: non-spontaneous. Temperature affects the sign of ΔG.

ΔG and Equilibrium

ΔG° = -RT ln(K); relates standard free energy to the equilibrium constant; used to calculate K or predict reaction favorability.

Temperature Dependence of Spontaneity

For reactions with ΔH < 0, ΔS > 0: spontaneous at all temperatures. For ΔH > 0, ΔS < 0: non-spontaneous at all temperatures.

High Temperature, High Entropy Systems

When TΔS dominates (high T), entropy-driven processes favor disorder; useful for understanding dissolution and diffusion.

Low Temperature, High Enthalpy Systems

When T is low, ΔH dominates; enthalpy-driven processes favor strong bonding and low energy states.

Bond Dissociation Energy

The energy required to break a bond; used to calculate ΔH_rxn = Σ BDE_bonds broken - Σ BDE_bonds formed.

Lattice Energy

The energy required to separate one mole of an ionic solid into gaseous ions; high values indicate strong ionic bonding.

Solvation Energy

The enthalpy change when a solute dissolves; ΔH_solv = ΔH_hydration + ΔH_separation (for ionic compounds).

Born-Haber Cycle

A thermochemical cycle used to calculate lattice energies by summing enthalpy changes from ionization, electron affinity, and other steps.

Phase Diagrams

Graphs showing conditions (T, P) where phases (solid, liquid, gas) are stable; includes triple point and critical point.

Triple Point

The unique condition (T, P) where all three phases (solid, liquid, gas) coexist in equilibrium.

Critical Point

The highest temperature and pressure at which a liquid and gas can coexist; above this, the substance is a supercritical fluid.

Heat of Fusion

The enthalpy change when one mole of solid melts to liquid at its melting point; endothermic (ΔH > 0).

Heat of Vaporization

The enthalpy change when one mole of liquid vaporizes to gas at its boiling point; typically larger than ΔH_fus.

Heat of Sublimation

The enthalpy change when solid converts directly to gas; ΔH_sub = ΔH_fus + ΔH_vap.

Clausius-Clapeyron Equation

ln(P₂/P₁) = -ΔH_vap/R × (1/T₂ - 1/T₁); relates vapor pressure to temperature.

Vapor Pressure

The pressure of a gas in equilibrium with its liquid; increases with temperature and is compound-specific.

Sublimation Pressure

The pressure exerted by solid in equilibrium with its vapor; dry ice and naphthalene sublime at standard conditions.

Heating Curves

Graphs showing temperature vs. heat added; flat regions indicate phase changes (ΔT = 0 during melting/boiling).

Cooling Curves

Reverse of heating curves; show temperature decrease as heat is removed; used to identify phase transitions.

Supercritical Fluids

Substances above their critical point; have properties of both liquids (density) and gases (diffusivity); used as solvents.

Thermal Energy Distribution

At higher temperatures, molecules have greater average kinetic energy; more energetic collisions and faster reaction rates.

Activation Energy (Ea)

The minimum energy required for a reaction to proceed; lowers for catalyzed reactions without changing ΔG.

Arrhenius Equation

k = A × e^(-Ea/RT); relates rate constant to temperature and activation energy; exponential temperature dependence.

Temperature Coefficient (Q₁₀)

Approximate rule: reaction rates roughly double for every 10°C increase (applies when Ea is moderate).

Collision Theory

Reaction rate depends on collision frequency, orientation, and energy; only collisions with E ≥ Ea lead to reaction.

Reaction Coordinate Diagram

Energy diagram showing reactants, transition state (highest point), and products; helps visualize activation energy.

Catalysts and Energy

Catalysts lower Ea by providing alternative pathways; speeds up both forward and reverse reactions equally.

Enzyme Catalysis

Biological catalysts (enzymes) form enzyme-substrate complexes, lowering Ea; highly specific and efficient.

Surface Area Effect

Increasing surface area (grinding solids, stirring) increases collision frequency; speeds up reaction rates.

Concentration Effect on Rate

Higher concentrations increase collision frequency; rate often follows rate laws determined experimentally.

Pressure Effect on Gases

Higher pressure (for gases) increases concentration and collision frequency; liquids/solids minimally affected.

Reaction Order

Zero order: rate = k; first order: rate = k[A]; second order: rate = k[A]² or k[A][B]. Determined experimentally.

Half-Life (t₁/₂)

Time for reactant concentration to decrease to half; for first-order reactions, t₁/₂ = 0.693/k (independent of concentration).

Integrated Rate Laws

Mathematical expressions showing concentration vs. time; first-order: ln[A] = ln[A]₀ - kt; second-order: 1/[A] = 1/[A]₀ + kt.

Pre-Exponential Factor (A)

In Arrhenius equation, represents collision frequency and orientation factor; larger A means faster reaction.

Temperature Jump

Rapid temperature increase triggers instant equilibrium shifts; used to study fast reactions kinetically.

Coupled Reactions

Unfavorable reactions (ΔG > 0) can be driven by favorable ones; ΔG_total = ΔG₁ + ΔG₂ must be negative.

Cell Potential and Spontaneity

In electrochemistry, E°_cell > 0 means spontaneous (ΔG < 0); E°_cell < 0 means non-spontaneous (ΔG > 0).

Work and Thermodynamics

Electrical work (wₑ = -nFE) and mechanical work (w = -PΔV) are both forms of energy transfer from chemical reactions.

Gibbs Energy and Electrochemistry

ΔG° = -nFE°; combines thermodynamics and electrochemistry to predict spontaneity of redox reactions.

Period 5 Big Picture

Thermodynamics and kinetics together determine if and how fast reactions occur. Spontaneity (ΔG), energy (ΔH), disorder (ΔS), and activation barriers (Ea) are interconnected in predicting and controlling chemical change.

Method of Initial Rates

Compare experiments where one concentration changes: if doubling [A] doubles rate, order 1; quadruples, order 2; no change, order 0. Sum gives overall order.

Units of k

Zero order: M/s; first order: s⁻¹; second order: M⁻¹s⁻¹. The units reveal the overall order of a rate law.

Integrated Rate Law Plots

Linear plots identify order: [A] vs t (zero), ln[A] vs t (first, slope −k), 1/[A] vs t (second, slope +k).

First-Order Half-Life

t½ = 0.693/k, independent of concentration; radioactive decay follows this. Second-order half-life = 1/(k[A]₀), lengthening as reactant depletes.

Rate-Determining Step

The slowest elementary step controls the overall rate; the rate law is written from that step's molecularity, substituting for intermediates if needed.

Intermediates vs. Catalysts

An intermediate is produced then consumed (appears in steps, not overall); a catalyst is consumed then regenerated and lowers activation energy.

Fast Equilibrium Pre-Step

If step 1 is a fast equilibrium and step 2 is slow, set forward rate = reverse rate for step 1 to express the intermediate in terms of reactants.

Molecularity

Unimolecular, bimolecular, termolecular elementary steps; termolecular steps are rare because three-body collisions are improbable.

Collision Theory Requirements

Reaction needs a collision with energy ≥ E_a and correct orientation; the fraction with sufficient energy rises exponentially with temperature.

Arrhenius Equation

k = A·e^(−Ea/RT); ln k vs 1/T is linear with slope −Ea/R. Larger E_a means k is more sensitive to temperature.

Two-Point Arrhenius

ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂) lets you find E_a from two rate constants or predict k at a new temperature.

Reaction Energy Profile

Peaks are transition states, valleys between them are intermediates; the tallest barrier from a valley marks the rate-determining step; ΔH is products minus reactants.

Catalysis Types

Homogeneous (same phase, e.g., acid catalysis), heterogeneous (surface adsorption, e.g., Pt in catalytic converters), enzymatic (active site lowers E_a).

Rate Law Is Experimental

Reaction orders cannot be read from overall stoichiometric coefficients — only from data or from a valid mechanism's slow step.

Relative Rates

For aA → bB, rate = −(1/a)Δ[A]/Δt = (1/b)Δ[B]/Δt; a product forming twice as fast as a reactant disappears indicates a 1:2 coefficient ratio.

Temperature and the M-B Curve

Raising T does not change E_a; it increases the fraction of molecules with energy above E_a, so k rises roughly exponentially.

Extracting Orders from Ratios

Divide two rate expressions where only one concentration changes: if tripling [A] multiplies the rate by nine, the order in A is two because 3^m = 9.

Fractional and Zero Orders

A zero-order reactant does not appear in the rate law, which typically means a surface or enzyme is saturated so added reactant cannot increase the rate.

Half-Life Order Diagnostics

Only first-order half-life is constant. Zero-order half-lives shrink as reaction proceeds; second-order half-lives grow, which distinguishes the orders from data.

Linearized Plot Slopes

Zero order gives [A] versus t with slope −k; first order gives ln[A] with slope −k; second order gives 1/[A] with slope +k.

Estimating k from a Half-Life

For a first-order process, k = 0.693 ÷ t½. A 20-minute half-life corresponds to k ≈ 0.0347 min⁻¹ regardless of starting concentration.

Mechanism Validity Tests

A proposed mechanism must sum to the overall equation and its rate-determining step must reproduce the experimental rate law after substituting for intermediates.

Substituting Out an Intermediate

When a fast pre-equilibrium precedes the slow step, set forward and reverse rates equal and solve for the intermediate's concentration in terms of reactants.

Steady-State Intuition

A reactive intermediate stays at low, nearly constant concentration because it is consumed as fast as it forms, which is why it never appears in the final rate law.

Catalyst Signature in a Mechanism

A catalyst is consumed in an early step and regenerated later, so it appears among the reactants of one elementary step and the products of another.

Homogeneous vs. Heterogeneous Catalysis

Homogeneous catalysts share the reactants' phase, as with aqueous acid catalysis, while heterogeneous ones provide a surface, as in a platinum catalytic converter.

Enzyme Specificity and Saturation

Enzymes bind a specific substrate in an active site; once every site is occupied the rate becomes zero order in substrate and depends only on enzyme amount.

Arrhenius Plot Interpretation

Plot ln k against 1/T. The slope equals −Ea/R, so a steeper negative slope means a larger activation energy and greater temperature sensitivity.

Reading a Multi-Step Energy Profile

Each hump is a transition state and each valley between humps is an intermediate. The tallest hump measured from its preceding valley is the rate-determining step.

Why Catalysts Do Not Shift Equilibrium

A catalyst lowers the activation energy of forward and reverse paths equally, speeding both directions and leaving ΔH and the equilibrium position unchanged.

Temperature Effect Magnitude

Rate constants often roughly double per 10 °C rise because the exponential term e^(−Ea/RT) is extremely sensitive to temperature near room conditions.

Orientation Factor

Even sufficiently energetic collisions fail unless the molecules are aligned properly, which is why complex molecules react more slowly than simple ones at equal energy.

Relating Rates of Different Species

For a A + b B → c C, −(1/a)Δ[A]/Δt = −(1/b)Δ[B]/Δt = (1/c)Δ[C]/Δt, so the species with the largest coefficient changes fastest.