The goal of reaction kinetics is to derive and parameterise a mathematical expression for the rate of change of a species $\rm A$ in a reacting environment. Once a rate law

$$\dot r = \frac{\partial [{\rm A}]}{\partial t} = f(T,[\dots])$$ is estabished, the evolution of the reacting system—and hence the change in concentrations $[{\rm \dots}]$ with time—can be calculated.

The rate $\dot r$ of an elementary reaction

$$n{\rm A} + m{\rm B} + \dots \rightarrow k[{\rm C}] + l[{\rm D}] + \dots$$ can be written as $$\dot r = \frac{\partial_t [{\rm A}]}{n} = \frac{\partial_t [{\rm B}]}{m} = \frac{\partial_t [{\rm C}]}{k} = \frac{\partial_t [{\rm D}]}{l} = k\cdot [{\rm A}]^\alpha [{\rm B}]^\beta…$$

Elementary reactions

A number of achetypical elementary reactions are easily defined.

name	reaction	rate law
first order	$[{\rm A}] \rightarrow [{\rm products}]$	$\dot r = [{\rm A}]$
second order	$[{\rm A}]+[{\rm A}] \rightarrow [{\rm products}]$	$\dot r = [{\rm A}]^2$
	$[{\rm A}]+[{\rm B}] \rightarrow [{\rm products}]$	$\dot r = [{\rm A}][{\rm B}]$

The stoichiometric factor is reflected in the rate law for an elementary reaction, which can be written as:

$$n{\rm A} + m{\rm B} + … \xrightarrow{\rm elementary} {\rm products} \quad\therefore\quad \dot r = [{\rm A}]^n[{\rm B}]^m…$$

Achetypical reaction mechanisms

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