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# Order of reaction

Main article: Rate equation

The Order of reaction [1] with respect to a certain reactant is defined, in chemical kinetics, as the power to which its concentration term in the rate equation is raised.

For example, given a chemical reaction A + 2B → C with a rate equation r = k[A]1[B]2, the reaction order with respect to A would be 1 and with respect to B would be 2, the total reaction order would be 2+1=3. It is not necessary that the order of a reaction is a whole number - zero and fractional values of order are possible - but they tend to be integers. Reaction orders can be determined only by experiment. Their knowledge allows conclusions about the reaction mechanism.

The reaction order is not necessarily related to the stoichiometry of the reaction, unless the reaction is elementary. Complex reactions may or may not have reaction orders equal to their stoichiometric coefficients

For example [2]:

CH3COOC2H5 + OH- → CH3COO- + C2H5OH.
It has the following rate equation: r = k[CH3COOC2H5][OH]
• The rate equation for imidazole catalyzed hydrolysis is
r = k [imidazole][CH3COOC2H5]
although no imidazole is present in the stoichiometric chemical equation
• In the reaction of aryldiazonium ions with nucleophiles in aqueous solution ArN2+ + X- → ArX + N2 the rate equation is
r = k[ArN2+]

Reactions can also have an undefined reaction order with respect to a reactant, for example one can not talk about reaction order in the rate equation found when dealing with a bimolecular reaction between adsorbed molecules:

$r=k \frac{K_1K_2C_AC_B}{(1+K_1C_A+K_2C_B)^2}$ .

If the concentration of one of the reactants remains constant (because it is a catalyst or it is in great excess with respect to the other reactants) its concentration can be included in the rate constant, obtaining a pseudo constant: if B is the reactant whose concentration is constant then r = k[A][B] = k'[A]. The second order rate equation has been reduced to a pseudo first order rate equation. This makes the treatment in order to obtain an integrated rate equation much easier.

Zero-order reactions are often seen for thermal chemical decompositions where the reaction rate is independent of the concentration of the reactant (changing the concentration has no effect on the speed of the reaction):

In broken-order reactions the order is a non-integer typical of reactions with a complex reaction mechanism. For example the chemical decomposition of ethanal into methane and carbon monoxide proceeds with an order of 1.5 with respect to ethanal. The decomposition of phosgene to carbon monoxide and chlorine has order 1 with respect to phosgene itself and order 0.5 with respect to chlorine.

In a mixed-order reaction the order of a reaction changes in the course of a reaction as a result of changing variables such as pH. An example is the oxidation of an alcohol to a ketone by a ruthenate (RuO42-) and a hexacyanoferrate, the latter serving as the sacrificial catalyst converting Ru(IV) back to Ru(VI) [3]: the disappearing-rate of the ferrate is zero-order with respect to the ferrate at the onset of the reaction (when its concentration is high and the ruthenium catalyst is quickly regenerated) but changes to first-order when its concentration decreases.

Negative order reactions are rare, for example the conversion of ozone (order 2) to oxygen (order -1).

## References

1. ^ IUPAC's Goldbook definition of order of reaction
2. ^ Kenneth A. Connors Chemical Kinetics, the study of reaction rates in solution, 1990, VCH Publishers
3. ^ Ruthenium(VI)-Catalyzed Oxidation of Alcohols by Hexacyanoferrate(III): An Example of Mixed Order Mucientes, Antonio E,; de la Peña, María A. J. Chem. Educ. 2006 83 1643. Abstract