Chemical kinetics (kinetics): The study of the rates of chemical reactions and the steps by which they occur.

Rate: Rapidity of change, a property involving time.

Some chemical reactions are very fast and appear instantaneous to the eye on mixing the reactants, while others are very slow and the products only form over minutes, hours or even longer.

In this example the numerical value of the rate depends on which reactant or product concentration is being measured. To overcome this it is possible to express the rate of reaction defined by its chemical equation.

Most chemical reactions take place in a series of elementary reactions (steps).

Elementary reaction: A one step reaction. There are three classes of elementary reaction.

Molecularity: The number of particles (molecules, ions or radicals) taking part in an elementary reaction;
1 for unimolecular, 2 for bimolecular and 3 for termolecular.

Reaction mechanism: The sequential elementary steps of a reaction.

A + B X
X + C P + Q
The overall reaction is A + B + C P + Q
The species X is called a reaction intermediate.

Reaction intermediate: A species produced in one step of a chemical reaction but which is consumed in a later step. It is not a product of the overall reaction, and hence does not appear in the overall equation.

Rate-determining step: The slowest elementary step which effectively determines the overall rate of a reaction.

Rate equation (law): A mathematical equation relating the instantaneous rate of the reaction to the concentrations of reactants, products, or any other permanent species (such as catalysts) taking part in the reaction at that instance
Example: for the reaction
 H₂O₂(aq) + 2H⁺(aq) + 2I¯(aq) I₂(aq) + 2H₂O at pH of 7
the rate law is found by experiment to be:  v = k[H₂O₂][I¯]

Rate coefficient (constant): Constant of proportionality in a rate law.
Example: k in the above rate law.

Reaction order:
(a) With respect to a single species - the power to which the concentration of a single species is raised in a rate law.
Example: the above reaction is first-order in H₂O₂ and first-order in I¯.
(b) Overall - the sum of the powers of the species in the rate law.
Example: the above reaction is second-order overall . k is a second-order rate constant.

For a reaction between two species to occur they must collide, and most reactions take place in a series of bimolecular collisions, i.e. by a series of bimolecular elementary steps. If the step involves two different species, A and B, the rate of collision, and therefore the rate of reaction, is proportional to the concentrations of A and B. Thus for the elementary bimolecular reaction
   A + B C + D
rate of reaction = k[A][B] where k is called a bimolecular rate constant. A bimolecular rate constant is clearly a 2nd order rate constant. For elementary reactions the order of the reactions are the same as the molecularity. As the units for rate of reaction are mol L⁻¹ s⁻¹ it follows from the rate laws that the units of 1st order, 2nd order and 3rd order rate constants are respectively s⁻¹, L mol⁻¹ s⁻¹ and L² mol⁻² s⁻¹ .

As bonds are often broken in elementary reactions not all collisions between reactant species lead to reaction, only those which collide with sufficient energy to overcome the activation energy barrier.

Activation energy: Symbol E_a. The minimum energy needed for colliding species to react, or cross the barrier. The magnitude of k depends on the height of the barrier, i.e. on the activation energy. The greater the E_a, the smaller the k, and the slower the reaction. The activation energy, E_a, is determined from an Arrhenius plot.

Arrhenius plot: A plot of ln k or ln rate against 1/T where T is the absolute temperature (temperature in kelvin). The slope of an Arrhenius plot equals -E_a/R where R is the universal gas constant. This follows from the Arrhenius equation.

Arrhenius equation: k = Aexp(−E_a/RT) where A is called the Arrhenius pre-exponential factor.

The kinetic energy of molecules, and hence the fraction of collisions with energy in excess of E_a increases with increasing temperature. Therefore the rate of a reaction, and the magnitude of k, increase with temperature. The greater the E_a, the more sensitive the rate and rate constant to changes in temperature.

Unlike equilibrium constant expressions, the rate law for a reaction cannot be derived from inspection of the overall chemical equation but must be determined experimentally. Only for elementary reactions (i.e. one step reactions) can the rate law be deduced directly from the equation (as explained above).

Information on reaction mechanisms can be obtained from experimentally obtained rate laws. While a rate law for a reaction can be derived for a postulated mechanism (because the rate law for each elementary step can be written), agreement between the experimental rate law and postulated mechanism does not prove the mechanism. Different mechanisms can lead to the same rate law.

Integrated rate equation: A mathematical equation which relates the concentration of a species at a given time to its initial concentration and the time, and which involves the rate constant
Example: For the 1st order reaction A Products [A]_t = [A]_oe^−kt where [A]_t and [A]_o are the concentrations of reactant A at time t and at the beginning of the reaction respectively.

Half-life: Symbol t_½, the time for the amount of a reactant in limiting amount (i.e. not in excess) to fall to half its original value. Commonly applied to radioactive isotopes
Example: The half-life of cobalt-60, ⁶⁰Co, is 5.3 years. Thus a sample of radioactive Co-60 would have lost half of its radioactivity at the end of 5.3 years.

Mean life-time: Symbol τ, the time for the amount of a reactant in limiting amount (i.e. not in excess) to fall to 0.368 (1/e) of its original value. This is the average time a molecule must wait before undergoing reaction.

Chain reaction: A reaction in which an intermediate formed in an initiation step produces further reactive intermediates in the propagation steps until removed in a termination step.

Chain length: The average number of propagating cycles between initiation and termination.

Catalyst: A substance which increases the rate of a reaction without being consumed in the overall reaction. It provides an alternative pathway or mechanism which increases the rate of the overall reaction. The catalyst is involved in the new pathway but if it is consumed in one step it is regenerated in a later step.

Homogeneous catalysis: The catalyst is in the same phase as the reactants.
Examples:
Sulfuric acid in the esterification of an organic acid and alcohol.
The catalysis of the decomposition of hydrogen peroxide by potassium iodide.

Heterogeneous catalysis: The catalyst is in a different phase from the reactants. A solid catalyst adsorbs reacting species onto its surface where the reaction takes place.
Example:
Solid V₂O₅ in the reaction of gaseous SO₂ and O₂ to form SO₂.
An important step in the manufacture of sulphuric acid.