Chemical Kinetics

The One Thing

Chemical kinetics explains reaction speed by relating changes in concentration to time and identifying how concentration, temperature, activation energy, catalysts, and reaction mechanisms affect the rate. Rate laws and experimental data determine reaction order, while the Arrhenius equation relates the rate constant to temperature and activation energy.

Reactions, Processes and Experiments

Key Terms

• Chemical kinetics: The branch of chemistry concerned with reaction rates, reaction mechanisms, and factors affecting reaction speed.
• Rate of reaction: The change in concentration of a reactant or product per unit time. For aA + bB → cC + dD, rate = -(1/a)d[A]/dt = -(1/b)d[B]/dt = (1/c)d[C]/dt = (1/d)d[D]/dt.
• Average rate: The change in concentration over a finite time interval: average rate = change in concentration/change in time.
• Instantaneous rate: The reaction rate at a particular instant, represented by the slope of the concentration-time curve at that instant.
• Rate law: An equation showing how reaction rate depends on reactant concentrations, such as rate = k[A]^m[B]^n.
• Rate constant: The proportionality constant $k$ in a rate law. It depends on temperature and the nature of the reaction, but not usually on reactant concentrations.
• Order of reaction: The sum of the powers of concentration terms in the experimentally determined rate law. For rate = k[A]^m[B]^n, order = m + n.
• Zero-order reaction: A reaction whose rate is independent of reactant concentration: rate = k.
• First-order reaction: A reaction whose rate is proportional to the first power of reactant concentration: rate = k[A].
• Second-order reaction: A reaction commonly described by rate = k[A]^2 or rate = k[A][B].
• Molecularity: The number of reacting species colliding simultaneously in a single elementary reaction step.
• Elementary reaction: A single-step reaction for which molecularity can be stated directly from the reacting particles.
• Complex reaction: A reaction occurring through two or more elementary steps.
• Activation energy: The minimum extra energy that reacting particles must possess for an effective collision and successful reaction.
• Arrhenius equation: The relationship k = A e^(-Ea/RT), where $k$ is the rate constant, $A$ is the frequency factor, $E_a$ is activation energy, $R$ is the gas constant, and $T$ is absolute temperature.
• Logarithmic Arrhenius equation: The equation log k = log A - Ea/(2.303RT).
• Two-temperature Arrhenius equation: The relation log(k2/k1) = Ea/(2.303R) × (T2 - T1)/(T1T2).
• Collision theory: The theory that reactions occur when particles collide with sufficient energy and suitable orientation.
• Catalyst: A substance that changes reaction rate by providing an alternative pathway with lower activation energy without being permanently consumed.
• Pseudo-first-order reaction: A higher-order reaction that behaves as first order because one reactant is present in very large excess and its concentration remains nearly constant.
• Rate-determining step: The slowest significant step in a multistep reaction mechanism, which often strongly influences the observed rate law.
• Frequency factor, $A$: The factor in the Arrhenius equation associated with collision frequency and suitable orientation.
• Gas constant, $R$: The constant used in the Arrhenius equation; R = 8.314 J mol^-1 K^-1.
• Absolute temperature, $T$: Temperature expressed in kelvin when used in the Arrhenius equation.
• Units of rate: Concentration time${}^{-1}$, commonly mol L^-1 s^-1.
• Units of $k$: For rate = k[A]^n, the units are (concentration)^(1-n) time^-1.

Easily Confused

• Order and molecularity: Order is determined experimentally and may be zero, fractional, integral, or, in special cases, negative; molecularity applies only to an elementary step and is always a positive whole number.
• Overall complex reaction and elementary reaction: Molecularity is not assigned to an overall complex reaction, whereas it can be assigned directly to an elementary reaction.
• Rate law and balanced overall equation: The order cannot generally be predicted from the balanced overall equation; it must be obtained from experimental rate data.
• Reactant and product rate terms: Reactant terms carry a negative sign because reactant concentration decreases; product terms carry a positive sign because product concentration increases.
• Average and instantaneous rate: Average rate applies over a finite interval; instantaneous rate applies at one particular instant and is represented by a curve’s tangent slope.
• First-order and zero-order half-life: The first-order half-life is independent of initial concentration, whereas the zero-order half-life is t1/2 = [A]0/(2k).
• First-order and second-order integrated plots: A first-order reaction gives a straight-line plot of $\ln [A]$ against time; a second-order reaction of the type rate = k[A]^2 gives a straight-line plot of $1/[A]$ against time.
• Catalyst and equilibrium position: A catalyst lowers activation energy for both forward and reverse reactions and changes the rate of reaching equilibrium, but it does not change the equilibrium constant or equilibrium composition.
• Activation energy and overall enthalpy change: A catalyst lowers activation energy but does not alter the overall enthalpy change.
• Temperature and concentration effects: Increasing concentration generally increases collision frequency, whereas increasing temperature increases the fraction of molecules with energy equal to or greater than the activation energy.

What Gets Asked

• Calculating reaction rate from stoichiometry: Use rate = -(1/a)d[A]/dt = -(1/b)d[B]/dt = (1/c)d[C]/dt = (1/d)d[D]/dt; omitting stoichiometric coefficients or using the wrong sign costs marks.
• Determining order from rate data: Use the experimentally determined rate law rather than the balanced overall equation; assigning order from overall stoichiometric coefficients is a common error.
• Using integrated rate equations and plots: Match zero order with [A] versus time, first order with ln[A] versus time, and second order of the type rate = k[A]^2 with 1/[A] versus time.
• Calculating half-life: Use t1/2 = [A]0/(2k) for zero order, t1/2 = 0.693/k for first order, and t1/2 = 1/(k[A]0) for second order; confusing the dependence on initial concentration loses marks.
• Distinguishing order from molecularity: State that order is experimental and may be zero or fractional, whereas molecularity belongs only to an elementary step and is a positive integer.
• Applying the Arrhenius equation: Use kelvin for $T$, R = 8.314 J mol^-1 K^-1, and the correct logarithmic form; using Celsius or confusing -Ea/R with -Ea/(2.303R) gives an incorrect result.