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rate determining step wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 example reaction no 2 co toggle example reaction no 2 co subsection 1 1 first step rate determining 1 2 pre equilibrium if the second step were rate determining 2 nucleophilic substitution 3 composition of the transition state 4 reaction coordinate diagram 5 chain reactions 6 diffusion control 7 see also 8 references toggle the table of contents rate determining step 23 languages العربية català کوردی čeština dansk deutsch español eesti فارسی suomi français magyar bahasa indonesia italiano 日本語 한국어 nederlands português română simple english slovenčina ไทย 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia redirected from rate limiting step slowest step of a chemical reaction rate limiting step redirects here for the biochemistry term see rate limiting step biochemistry in chemical kinetics the overall rate of a reaction is often approximately determined by the slowest step known as the rate determining step rds or rd step 1 or r d step 2 3 or rate limiting step for a given reaction mechanism the prediction of the corresponding rate equation for comparison with the experimental rate law is often simplified by using this approximation of the rate determining step in principle the time evolution of the reactant and product concentrations can be determined from the set of simultaneous rate equations for the individual steps of the mechanism one for each step however the analytical solution of these differential equations is not always easy and in some cases numerical integration may even be required 4 the hypothesis of a single rate determining step can greatly simplify the mathematics in the simplest case the initial step is the slowest and the overall rate is just the rate of the first step also the rate equations for mechanisms with a single rate determining step are usually in a simple mathematical form whose relation to the mechanism and choice of rate determining step is clear the correct rate determining step can be identified by predicting the rate law for each possible choice and comparing the different predictions with the experimental law as for the example of no 2 and co below the concept of the rate determining step is very important to the optimization and understanding of many chemical processes such as catalysis and combustion example reaction no 2 co edit as an example consider the gas phase reaction no 2 co no co 2 if this reaction occurred in a single step its reaction rate r would be proportional to the rate of collisions between no 2 and co molecules r k no 2 co where k is the reaction rate constant and square brackets indicate a molar concentration another typical example is the zel dovich mechanism first step rate determining edit in fact however the observed reaction rate is second order in no 2 and zero order in co 5 with rate equation r k no 2 2 this suggests that the rate is determined by a step in which two no 2 molecules react with the co molecule entering at another faster step a possible mechanism in two elementary steps that explains the rate equation is no 2 no 2 no no 3 slow step rate determining no 3 co no 2 co 2 fast step in this mechanism the reactive intermediate species no 3 is formed in the first step with rate r 1 and reacts with co in the second step with rate r 2 however no 3 can also react with no if the first step occurs in the reverse direction no no 3 2 no 2 with rate r 1 where the minus sign indicates the rate of a reverse reaction the concentration of a reactive intermediate such as no 3 remains low and almost constant it may therefore be estimated by the steady state approximation which specifies that the rate at which it is formed equals the total rate at which it is consumed in this example no 3 is formed in one step and reacts in two so that d no 3 d t r 1 r 2 r 1 0 displaystyle frac d ce no3 dt r_ 1 r_ 2 r_ 1 approx 0 the statement that the first step is the slow step actually means that the first step in the reverse direction is slower than the second step in the forward direction so that almost all no 3 is consumed by reaction with co and not with no that is r 1 r 2 so that r 1 r 2 0 but the overall rate of reaction is the rate of formation of final product here co 2 so that r r 2 r 1 that is the overall rate is determined by the rate of the first step and almost all molecules that react at the first step continue to the fast second step pre equilibrium if the second step were rate determining edit the other possible case would be that the second step is slow and rate determining meaning that it is slower than the first step in the reverse direction r 2 r 1 in this hypothesis r 1 r 1 0 so that the first step is almost at equilibrium the overall rate is determined by the second step r r 2 r 1 as very few molecules that react at the first step continue to the second step which is much slower such a situation in which an intermediate here no 3 forms an equilibrium with reactants prior to the rate determining step is described as a pre equilibrium 6 for the reaction of no 2 and co this hypothesis can be rejected since it implies a rate equation that disagrees with experiment no 2 no 2 no no 3 fast step no 3 co no 2 co 2 slow step rate determining if the first step were at equilibrium then its equilibrium constant expression permits calculation of the concentration of the intermediate no 3 in terms of more stable and more easily measured reactant and product species k 1 no no 3 no 2 2 displaystyle k_ 1 frac ce no no3 ce no2 2 no 3 k 1 no 2 2 no displaystyle ce no3 k_ 1 frac ce no2 2 ce no the overall reaction rate would then be r r 2 k 2 no 3 co k 2 k 1 no 2 2 co no displaystyle r r_ 2 k_ 2 ce no3 co k_ 2 k_ 1 frac ce no2 2 co ce no which disagrees with the experimental rate law given above and so disproves the hypothesis that the second step is rate determining for this reaction however some other reactions are believed to involve rapid pre equilibria prior to the rate determining step as shown below nucleophilic substitution edit another example is the unimolecular nucleophilic substitution s n 1 reaction in organic chemistry where it is the first rate determining step that is unimolecular a specific case is the basic hydrolysis of tert butyl bromide t c 4 h 9 br by aqueous sodium hydroxide the mechanism has two steps where r denotes the tert butyl radical t c 4 h 9 formation of a carbocation r br r br nucleophilic attack by hydroxide ion r oh roh this reaction is found to be first order with r k r br which indicates that the first step is slow and determines the rate the second step with oh is much faster so the overall rate is independent of the concentration of oh in contrast the alkaline hydrolysis of methyl bromide ch 3 br is a bimolecular nucleophilic substitution s n 2 reaction in a single bimolecular step its rate law is second order r k r br oh composition of the transition state edit a useful rule in the determination of mechanism is that the concentration factors in the rate law indicate the composition and charge of the activated complex or transition state 7 for the no 2 co reaction above the rate depends on no 2 2 so that the activated complex has composition n 2 o 4 with 2 no 2 entering the reaction before the transition state and co reacting after the transition state a multistep example is the reaction between oxalic acid and chlorine in aqueous solution h 2 c 2 o 4 cl 2 2 co 2 2 h 2 cl 7 the observed rate law is v k cl 2 h 2 c 2 o 4 h 2 cl displaystyle v k frac ce cl2 h2c2o4 ce h 2 ce cl which implies an activated complex in which the reactants lose 2 h cl before the rate determining step the formula of the activated complex is cl 2 h 2 c 2 o 4 2 h cl x h 2 o or c 2 o 4 cl h 2 o x an unknown number of water molecules are added because the possible dependence of the reaction rate on h 2 o was not studied since the data were obtained in water solvent at a large and essentially unvarying concentration one possible mechanism in which the preliminary steps are assumed to be rapid pre equilibria occurring prior to the transition state is 7 cl 2 h 2 o hocl cl h h 2 c 2 o 4 h hc 2 o 4 hocl hc 2 o 4 h 2 o cl 2 co 2 reaction coordinate diagram edit in a multistep reaction the rate determining step does not necessarily correspond to the highest gibbs energy on the reaction coordinate diagram 8 6 if there is a reaction intermediate whose energy is lower than the initial reactants then the activation energy needed to pass through any subsequent transition state depends on the gibbs energy of that state relative to the lower energy intermediate the rate determining step is then the step with the largest gibbs energy difference relative either to the starting material or to any previous intermediate on the diagram 8 9 also for reaction steps that are not first order concentration terms must be considered in choosing the rate determining step 8 6 chain reactions edit not all reactions have a single rate determining step in particular the rate of a chain reaction is usually not controlled by any single step 8 diffusion control edit in the previous examples the rate determining step was one of the sequential chemical reactions leading to a product the rate determining step can also be the transport of reactants to where they can interact and form the product this case is referred to as diffusion control and in general occurs when the formation of product from the activated complex is very rapid and thus the provision of the supply of reactants is rate determining see also edit product determining step rate limiting step biochemistry references edit kozuch sebastian martin jan june 2011 the rate determining step is dead long live the rate determining state chemphyschem 12 8 1413 1418 doi 10 1002 cphc 201100137 pmid 21523880 organic chemistry volume 1 6 e by finar aliphatic organic chemistry by amit arora steinfeld j i francisco j s hase w l chemical kinetics and dynamics 2nd ed prentice hall 1999 ch 2 whitten k w galley k d davis r e general chemistry 4th edition saunders 1992 p 638 639 1 2 3 peter atkins and julio de paula physical chemistry 8th ed w h freeman 2006 p 814 815 isbn 0 7167 8759 8 1 2 3 espenson j h 2002 chemical kinetics and reaction mechanisms 2nd ed mcgraw hill pp 127 132 isbn 0072883626 1 2 3 4 keith j laidler chemical kinetics 3rd ed harper and row 1987 p 283 285 isbn 0 06 043862 2 murdoch joseph r 1981 what is the rate limiting step of a multistep reaction journal of chemical education 58 1 32 36 bibcode 1981jched 58 32m doi 10 1021 ed058p32 zumdahl steven s 2005 chemical principles 5th ed houghton mifflin pp 727 8 isbn 0618372067 v t e basic reaction mechanisms nucleophilic substitutions unimolecular nucleophilic substitution s n 1 bimolecular nucleophilic substitution s n 2 nucleophilic internal substitution s n i nucleophilic acyl substitution s n acyl electrophilic substitutions electrophilic aromatic substitution s e ar elimination reactions e1cb elimination e i elimination addition reactions electrophilic addition a e nucleophilic addition a n free radical addition cycloaddition oxidative addition unimolecular reactions intramolecular reaction isomerization photodissociation lindemann mechanism rrkm theory electron proton transfer reactions redox harpoon reaction grotthuss mechanism marcus theory inner sphere electron transfer outer sphere electron transfer medium effects solvent effects cage effect matrix isolation related topics elementary reaction reaction dynamics reactive intermediate radical chemistry molecularity stereochemistry catalysis collision theory arrow pushing potential energy surface more o ferrall jencks plot chemical kinetics rate equation equilibrium constant rate determining step reaction coordinate energy profile chemistry transition state theory activation energy activated complex arrhenius equation eyring equation michaelis menten kinetics diffusion controlled reaction retrieved from https en wikipedia org w index php title rate determining_step oldid 1373382764 category chemical kinetics hidden categories articles with short description short description is different from wikidata this page was last edited on 5 september 2026 at 17 43 utc page was rendered with parsoid text is available 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