# Kinetics

**Kinetics** is the study of the rate at which compounds react. This depends on several factors, including the area of contact between the materials, their concentrations, and the

temperature at which the reaction takes place. For a

reaction *k* A +

*m* B → C + D, the rate is typically something of the form

- d[C]/dt =
*k(T)*[A]^{k'}[B]^{m'}

Here [X] denotes, for a reaction between liquids, gases, or solutes, the

concentration of X; for a reaction taking place at a boundary it would denote something like moles per area of X. k(T) is a rate constant that depends on temperature. The exponents

*k'* and

*m'* are called

*orders* and depend on the reaction mechanism, ie the sequence of steps (collisions) that the reaction takes place by, and in fact kinetics is one of the main ways of studying these. For a single-step reaction we would have

- d[C]/dt =
*ke*^{-Ea/RT}[A]^{k}[B]^{m}

Here

*E*_{a} is the

activation energy, the energy per mole it is necessary for the molecules to have to react. Since at temperature

*T* the molecules have energies according to a

Boltzmann distribution, one can expect the proportion of collisions with energy greater than Ea to vary with

*e*^{-Ea/RT}.

*K* has to do with stuff like the probability that molecules are in the right orientation, and of course dimensions.

For most multi-step reactions the rate is determined primarily by a single slow step, with preceding steps proceeding quickly to a state of rough equilibrium. In general, concentrations of species are never determined solely by a single process, and as reactions occur the products begin to undergo the reverse reaction to some extent. Thus reactions never proceed to 100% completion but rather to a state of chemical equilibrium where every step occurs at the same rate as its reverse.

The Arrhenius equation gives the quantitative basis of the relationship between the activation energy and the rate at which a reaction proceeds.