Order of reaction
In chemical kinetics, the order of reaction with respect to a given substance (such as reactant, catalyst or product) is defined as the index, or exponent, to which its concentration term in the rate equation is raised.^{[1]} For the typical rate equation of form r\; =\; k[\mathrm{A}]^x[\mathrm{B}]^y..., where [A], [B], ... are concentrations, the reaction orders (or partial reaction orders) are x for substance A, y for substance B, etc. The overall reaction order is the sum x + y + ....
For example, the chemical reaction between mercury (II) chloride and oxalate ion
 2 HgCl_{2}(aq) + C_{2}O_{4}^{2}(aq) → 2 Cl^{}(aq) + 2 CO_{2}(g) + Hg_{2}Cl_{2}(s)
has the observed rate equation^{[2]}
 r = k[HgCl_{2}]^{1}[C_{2}O_{4}^{2}]^{2}
In this case, the reaction order with respect to the reactant HgCl_{2} is 1 and with respect to oxalate ion is 2; the overall reaction order is 1 + 2 = 3. As is true for many reactions, the reaction orders (here 1 and 2 respectively) differ from the stoichiometric coefficients (2 and 1). Reaction orders can be determined only by experiment. Their knowledge allows conclusions to be drawn about the reaction mechanism, and may help to identify the ratedetermining step.
Elementary (singlestep) reactions do have reaction orders equal to the stoichiometric coefficients for each reactant, but complex (multistep) reactions may or may not have reaction orders equal to their stoichiometric coefficients.
Orders of reaction for each reactant are often positive integers, but they may also be zero, fractional, or negative.
A reaction can also have an undefined reaction order with respect to a reactant if the rate is not simply proportional to some power of the concentration of that reactant; for example, one cannot talk about reaction order in the rate equation for a bimolecular reaction between adsorbed molecules:
 r=k \frac{K_1K_2C_AC_B}{(1+K_1C_A+K_2C_B)^2}. \,
Contents
 Method of initial rates 1
 First order 2
 Second order 3
 Pseudofirst order 4
 Zero order 5
 Fractional order 6
 Mixed order 7
 Negative order 8
 See also 9
 References 10
 External links 11
Method of initial rates
The order of a reaction for each reactant can be estimated^{[3]} from the variation in initial rate with the concentration of that reactant, using the natural logarithm of the typical rate equation
 \ln r = \ln k + x\ln[A] + y\ln[B] + ...
For example the initial rate can be measured in a series of experiments at different initial concentrations of reactant A with all other concentrations [B], [C], ... kept constant, so that
 \ln r = x\ln[A] + \textrm{constant}
The slope of a graph of \ln r as a function of \ln [A] then corresponds to the order x with respect to reactant A.
However this method is not always reliable because
 measurement of the initial rate requires accurate determination of small changes in concentration in short times (compared to the reaction halflife) and is sensitive to errors, and
 the rate equation will not be completely determined if the rate also depends on substances not present at the beginning of the reaction, such as intermediates or products.
The tentative rate equation determined by this method is therefore normally verified by comparing the concentrations measured over a longer time (several halflives) with the integrated form of the rate equation.
First order
If a reaction rate depends on a single reactant and the value of the exponent is one, then the reaction is said to be first order. In organic chemistry, the class of S_{N}1 (nucleophilic substitution unimolecular) reactions consists of firstorder reactions. For example,^{[4]} in the reaction of aryldiazonium ions with nucleophiles in aqueous solution ArN_{2}^{+} + X^{−} → ArX + N_{2}, the rate equation is r = k[ArN_{2}^{+}], where Ar indicates an aryl group.
Another class of firstorder reactions is radioactive decay processes which are all first order. These are, however, nuclear reactions rather than chemical reactions.
Second order
A reaction is said to be second order when the overall order is two. The rate of a secondorder reaction may be proportional to one concentration squared r= k [A]^2\, , or (more commonly) to the product of two concentrations r= k[A][B]\, . As an example of the first type, the reaction NO_{2} + CO → NO + CO_{2} is secondorder in the reactant NO_{2} and zero order in the reactant CO. The observed rate is given by r= k [NO_2]^2\, , and is independent of the concentration of CO.^{[5]}
The second type includes the class of S_{N}2 (nucleophilic substitution bimolecular) reactions, such as the alkaline hydrolysis of ethyl acetate:^{[4]}

 CH_{3}COOC_{2}H_{5} + OH^{−} → CH_{3}COO^{−} + C_{2}H_{5}OH.
This reaction is firstorder in each reactant and secondorder overall: r = k[CH_{3}COOC_{2}H_{5}][OH^{−}]
If the same hydrolysis reaction is catalyzed by imidazole, the rate equation becomes^{[4]} r = k[imidazole][CH_{3}COOC_{2}H_{5}]. The rate is firstorder in one reactant (ethyl acetate), and also firstorder in imidazole which as a catalyst does not appear in the overall chemical equation.
Pseudofirst order
If the concentration of a reactant 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–firstorder (or occasionally pseudo–secondorder) rate equation. For a typical secondorder reaction with rate equation r = k[A][B]\, , if the concentration of reactant B is constant then r = k [A][B] = k'[A] \, , where the pseudo–firstorder rate constant k' = k [B] \, . The secondorder rate equation has been reduced to a pseudo–firstorder rate equation, which makes the treatment to obtain an integrated rate equation much easier.
For example, the hydrolysis of sucrose in acid solution is often cited as a firstorder reaction with rate r = k[sucrose]\, . The true rate equation is thirdorder, r = k[sucrose][H^+][H_2O]\, ; however, the concentrations of both the catalyst H^{+} and the solvent H_{2}O are normally constant, so that the reaction is pseudo–firstorder.^{[6]}
Zero order
For zeroorder reactions, the reaction rate is independent of the concentration of a reactant, so that changing its concentration has no effect on the speed of the reaction. This is true for many enzymecatalyzed reactions, provided that the reactant concentration is much greater than the enzyme concentration which controls the rate. For example, the biological oxidation of ethanol to acetaldehyde by the enzyme liver alcohol dehydrogenase (LADH) is zero order in ethanol.^{[7]}
Fractional order
In fractional order reactions, the order is a noninteger, which often indicates a chemical chain reaction or other complex reaction mechanism. For example, the pyrolysis of ethanal (CH_{3}CHO) into methane and carbon monoxide proceeds with an order of 1.5 with respect to ethanal: r = k[CH_{3}CHO]^{3/2}.^{[8]} The decomposition of phosgene (COCl_{2}) to carbon monoxide and chlorine has order 1 with respect to phosgene itself and order 0.5 with respect to chlorine: r = k[COCl_{2}] [Cl_{2}]^{1/2}.
The order of a chain reaction can be rationalized using the steady state approximation for the concentration of reactive intermediates such as free radicals. For the pyrolysis of ethanal, the RiceHerzfeld mechanism is^{[8]}
 Initiation CH_{3}CHO → •CH_{3} + •CHO

Propagation •CH_{3} + CH_{3}CHO → CH_{3}CO• + CH_{4}



 CH_{3}CO• → •CH_{3} + CO



 Termination 2 •CH_{3} → C_{2}H_{6}
where • denotes a free radical. To simplify the theory, the reactions of the •CHO to form a second •CH_{3} are ignored.
In the steady state, the rates of formation and destruction of methyl radicals are equal, so that \frac{d[CH_3]}{dt} = k_i[CH_3CHO]k_t[\cdot CH_3]^2 = 0,
so that the concentration of methyl radical [\cdot CH_3] \quad\alpha \quad[CH_3CHO]^{1/2}.
The reaction rate equals the rate of the propagation steps which form the main reaction products CH_{4} and CO:
 v = \frac{d[CH_4]}{dt} = k_p[\cdot CH_3][CH_3CHO] \quad\alpha \quad[CH_3CHO]^{3/2}
in agreement with the experimental order of 3/2.^{[8]}
Mixed order
More complex rate laws have been described as being mixed order if they approximate to the laws for more than one order at different concentrations of the chemical species involved. For example, a rate law of the form r = k_1[A]+k_2[A]^2 represents concurrent first order and second order reactions (or more often concurrent pseudofirst order and second order) reactions, and can be described as mixed first and second order.^{[9]} For sufficiently large values of [A] such a reaction will approximate second order kinetics, but for smaller [A] the kinetics will approximate first order (or pseudofirst order). As the reaction progresses, the reaction can change from second order to first order as reactant is consumed.
Another type of mixedorder rate law has a denominator of two or more terms, often because the identity of the ratedetermining step depends on the values of the concentrations. An example is the oxidation of an alcohol to a ketone by hexacyanoferrate (III) ion [Fe(CN)_{6}^{3−}] with ruthenate (VI) ion (RuO_{4}^{2−}) as catalyst.^{[10]} For this reaction, the rate of disappearance of hexacyanoferrate (III) is r = \frac{k_\alpha + k_\beta[Fe(CN)_6]^{2}}
This is zeroorder with respect to hexacyanoferrate (III) at the onset of the reaction (when its concentration is high and the ruthenium catalyst is quickly regenerated), but changes to firstorder when its concentration decreases and the regeneration of catalyst becomes ratedetermining.
Negative order
A reaction rate can have a negative partial order with respect to a substance. For example the conversion of ozone (O_{3}) to oxygen follows the rate equation r=k\frac \, in an excess of oxygen. This corresponds to second order in ozone and order (1) with respect to oxygen.^{[11]}
When a partial order is negative, the overall order is usually considered as undefined. In the above example for instance, the reaction is not described as first order even though the sum of the partial orders is 2 + (1) = 1, because the rate equation is more complex than that of a simple firstorder reaction.
See also
References
 ^ IUPAC's Goldbook definition of order of reaction
 ^ Petrucci R.H., Harwood W.S. and Herring F.G. General Chemistry (8th ed., PrenticeHall 2002), p.5856
 ^ P. Atkins and J. de Paula, Physical Chemistry (W.H. Freeman, 8th ed. 2006), p.7978
 ^ ^{a} ^{b} ^{c} Kenneth A. Connors Chemical Kinetics, the study of reaction rates in solution, 1990, VCH Publishers
 ^ Whitten K.W., Galley K.D. and Davis R.E. General Chemistry (4th edition, Saunders 1992), p.6389
 ^ I. Tinoco, K. Sauer and J.C. Wang Physical Chemistry. Principles and Applications in Biological Sciences. (3rd ed., PrenticeHall 1995) p.3289
 ^ Tinoco, Sauer and Wang p.331
 ^ ^{a} ^{b} ^{c} P. Atkins and J. de Paula, Physical Chemistry 8th ed.(W.H. Freeman 2006), p.830
 ^ Espenson J.H. Chemical Kinetics and Reaction Mechanisms (2nd ed., McGrawHill 2002), p.34 and p.60
 ^ 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
 ^ Laidler K.J. Chemical Kinetics (3rd ed., Harper & Row 1987), p.305
External links
 Chemical kinetics, reaction rate, and order (needs flash player)
 Reaction kinetics, examples of important rate laws (lecture with audio).
 Rates of Reaction