Unit 5: Kinetics

Kinetics

The study of reaction rates and the factors that affect how fast reactions occur.

Reaction rate

How quickly reactants are consumed or products are formed; based on change in concentration over time (typical units: M s⁻¹).

Average rate

The change in concentration over a time interval divided by the time elapsed (Δ[ ]/Δt).

Instantaneous rate

The reaction rate at a specific moment; the slope of the tangent line to a concentration vs. time curve.

Rate of disappearance

Rate for a reactant being consumed, defined with a negative sign to make the rate positive: rate = −Δ[A]/Δt.

Rate of appearance

Rate for a product being formed: rate = Δ[B]/Δt (positive as concentration increases).

Stoichiometric rate relationship

Using coefficients to relate species rates in a reaction aA + bB → cC + dD: rate = −(1/a)Δ[A]/Δt = −(1/b)Δ[B]/Δt = (1/c)Δ[C]/Δt = (1/d)Δ[D]/Δt.

Spectrophotometry

A rate-measurement method where color intensity (absorbance) is monitored to track concentration of a colored reactant or product.

Initial rate

The reaction rate measured at the very beginning of a reaction, used to determine rate laws from concentration changes.

Method of initial rates

An experimental strategy that compares initial rates from trials with different initial concentrations to determine reaction orders and k.

Rate law

An experimentally determined equation relating rate to reactant concentrations, e.g., rate = k[A]^m[B]^n.

Rate constant (k)

The proportionality constant in a rate law; depends on the reaction and conditions (especially temperature, activation energy, and catalysts).

Reaction order (with respect to a reactant)

The exponent on a reactant concentration term in the rate law; shows how rate changes when that concentration changes.

Overall reaction order

The sum of exponents in the rate law (e.g., m + n + …).

Zero-order reaction

A reaction where rate does not depend on reactant concentration (rate = k).

First-order reaction

A reaction where rate is proportional to the first power of a reactant concentration (rate = k[A]).

Second-order reaction

Commonly refers to rate = k[A]² (or overall order 2); rate depends on concentration squared (doubling [A] quadruples rate in k[A]²).

Units of the rate constant

Depend on overall order: [k] = M^(1−overall order) s⁻¹ (e.g., order 1: s⁻¹; order 2: M⁻¹ s⁻¹).

Integrated rate law

An equation that relates reactant concentration to time (concentration–time relationship) for a specific reaction order.

Zero-order integrated rate law

For rate = k: [A]t = [A]0 − kt (a plot of [A] vs. t is linear).

First-order integrated rate law

For rate = k[A]: ln[A]t = ln[A]0 − kt (equivalently, [A]t = [A]0 e^(−kt)).

Second-order integrated rate law (for rate = k[A]²)

1/[A]t = 1/[A]0 + kt (a plot of 1/[A] vs. t is linear).

Linearized plot

A graph that becomes a straight line after transforming concentration data (e.g., ln[A] vs t for first order) to diagnose reaction order and find k.

Slope (kinetics linear plots)

Connects directly to k: zero-order [A] vs t slope = −k; first-order ln[A] vs t slope = −k; second-order 1/[A] vs t slope = +k.

Half-life (t1/2)

The time required for a reactant concentration to decrease to half its current value.

First-order half-life equation

For first-order reactions, half-life is constant: t1/2 = (ln 2)/k (independent of [A]0).

Zero-order half-life equation

For zero-order reactions: t1/2 = [A]0/(2k) (depends on starting concentration).

Second-order half-life equation (for rate = k[A]²)

For second-order reactions of the form k[A]²: t1/2 = 1/(k[A]0) (depends on starting concentration).

Collision theory (molecular collision model)

Explains reaction rates by requiring collisions, sufficient energy to overcome Ea, and proper orientation for bonds to break/form.

Activation energy (Ea)

The minimum energy required for reactants to reach the transition state (the energy barrier to reaction).

Transition state (activated complex)

A high-energy, unstable arrangement of atoms at the top of the energy barrier; not an isolable substance.

Potential energy (reaction energy) diagram

A graph of potential energy vs reaction progress showing reactant energy, product energy, the peak (transition state), Ea, and ΔH.

Enthalpy change (ΔH)

The energy difference between products and reactants on an energy diagram; distinct from activation energy (Ea).

Arrhenius equation

Relates k to temperature: k = A e^(−Ea/RT), where A is the frequency factor and T is in kelvins.

Frequency factor (A)

The Arrhenius pre-exponential factor representing collision frequency and orientation probability (how often effective collisions occur).

Arrhenius linear plot

A plot of ln k vs 1/T that is linear with slope −Ea/R and intercept ln A.

Two-temperature Arrhenius form

ln(k2/k1) = −(Ea/R)(1/T2 − 1/T1), used to compute Ea or predict k at a new temperature.

Reaction mechanism

A proposed sequence of elementary steps that adds up to the overall balanced chemical reaction.

Elementary step

A single molecular event in a mechanism; its rate law follows directly from the step’s reactant particles.

Intermediate

A species produced in one step and consumed in a later step; cancels out and does not appear in the net overall equation.

Molecularity

The number of reacting particles in an elementary step (unimolecular, bimolecular, or termolecular).

Unimolecular step

An elementary step involving one reacting particle (e.g., A → products); rate law: rate = k[A].

Bimolecular step

An elementary step involving collisions of two particles (e.g., A + B → products); rate law: rate = k[A][B].

Termolecular step

An elementary step involving three particles colliding simultaneously; rare in practice.

Rate-determining step (RDS)

The slowest step in a multi-step mechanism; acts as the bottleneck that limits the overall reaction rate.

Fast equilibrium approximation

A common mechanism pattern where a fast reversible step sets an intermediate concentration (e.g., [I] = K[A][B]) used to eliminate intermediates from the rate law.

Catalyst

A substance that increases reaction rate without being permanently consumed by providing an alternate pathway with lower Ea; changes k but not ΔH or the equilibrium constant.

Homogeneous catalyst

A catalyst in the same phase as the reactants; participates in steps and is regenerated later in the mechanism.

Heterogeneous catalyst

A catalyst in a different phase (often a solid surface); reactants adsorb, react, and desorb; higher surface area typically increases rate.

Enzyme

A biological catalyst (usually a protein) that binds substrates at an active site, orients them, and stabilizes the transition state; sensitive to temperature and pH (denaturation lowers activity).