律速段階

関: rate-limiting step

WordNet

walk a short distance to a specified place or in a specified manner; "step over to the blackboard"
a short distance; "its only a step to the drugstore" (同)stone''s throw
move or proceed as if by steps into a new situation; "She stepped into a life of luxury"; "he wont step into his fathers footsteps"
support consisting of a place to rest the foot while ascending or descending a stairway; "he paused on the bottom step" (同)stair
a solid block joined to the beams in which the heel of a ships mast or capstan is fixed
the act of changing location by raising the foot and setting it down; "he walked with unsteady steps"
put down or press the foot, place the foot; "For fools rush in where angels fear to tread"; "step on the brake" (同)tread
cause (a computer) to execute a single command
furnish with steps; "The architect wants to step the terrace"
move with ones feet in a specific manner; "step lively"
place (a ships mast) in its step
shift or move by taking a step; "step back"
be worthy of or have a certain rating; "This bond rates highly"
amount of a charge or payment relative to some basis; "a 10-minute phone call at that rate would cost $5" (同)charge per unit
a magnitude or frequency relative to a time unit; "they traveled at a rate of 55 miles per hour"; "the rate of change was faster than expected"
a quantity or amount or measure considered as a proportion of another quantity or amount or measure; "the literacy rate"; "the retention rate"; "the dropout rate"
assign a rank or rating to; "how would you rank these students?"; "The restaurant is rated highly in the food guide" (同)rank, range, order, grade, place
estimate the value of; "How would you rate his chances to become President?"; "Gold was rated highly among the Romans" (同)value
give (hair) the appearance of being fuller by using a rat
a pad (usually made of hair) worn as part of a womans coiffure
any of various long-tailed rodents similar to but larger than a mouse
catch rats, especially with dogs
desert ones party or group of friends, for example, for ones personal advantage
employ scabs or strike breakers in
standing or position on a scale
the course along which a person has walked or is walking in; "I followed in his steps"; "he retraced his steps"; "his steps turned toward home"

PrepTutorEJDIC

『一歩』,歩み;一歩の距離,歩幅;短い距離 / (階段・はしごの)『段』,踏み段;《複数形で》『階段』 / (目的・目標への)『一歩』,一段階《+『to』(『toward』)+『名』》 / 足音 / 足跡 / 『歩調』,足取り;(ダンスの)ステップ / (目標に近づく)『手段』,方法,処置 / 階級,昇級 / (音楽で)音程 / (温度計などの)目盛り / 《方向を表す副詞[句]を伴って》(…の方へ)『歩む』,一歩踏み出す,行く / (…を)踏みつける《+『on』+『名』》 / 〈足〉‘を'踏み出す;〈ダンス〉‘の'ステップを踏む / …‘を'歩測する《+『off』(『out』)+『名』,+『名』+『off』(『out』)》 / 〈段〉‘を'切り込む
〈C〉『割合』,『率』 / 〈C〉《the~,a~》『速度』(speed),進度 / 〈C〉『値段』,『相場』;料金 / 〈U〉等級(class),(…)等 / 《複数形ぃ》《英》地方税 / (…の金額に)…‘の'『値段を決める』,見積もる《+『名』+『at』+『名』》 / …‘を'『評価する』,みなす / 《米話》…‘に'値する,‘の'価値がある / 『評価される』;みなされる
…‘を'どなりつける
『ネズミ』 / ひきょう者,裏切り者 / ネズミをつかまえる / 《話》(人を)裏切る,密告する《+『on』+『名』〈人〉》
〈C〉〈U〉（品質・技量などによる）格づけ,評価 / 〈C〉（個人・会社の経済的な）信用度 / 〈C〉(トン・馬力による)(船舶・車)の等級 / 〈C〉(テレビ・ラジオの)視聴率

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/05/28 22:20:26」(JST)

wiki en

[Wiki en表示]

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 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.^[1] 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 NO₂ 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.

Reaction Coordinate Diagram

Given a reaction coordinate (energy diagram), the rate determining step can be determined by taking the largest energy difference between any starting material or intermediate on the diagram and any transition state that comes after it. That transition state will then be the rate-determining step of a given reaction. The transition state with highest absolute energy may not necessarily correspond to the rate determining step.

Example reaction: NO
2 + CO

As an example, consider the gas-phase reaction NO
2 + CO → NO + CO₂. 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.

First step rate-determining

In fact, however, the observed reaction rate is second order in NO
2 and zero order in CO,^[2] 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 which 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 r₁ and reacts with CO in the second step with rate r₂. 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 ${\frac {{d}{\ce {[NO3]}}}{dt}}=r_{1}-r_{2}-r_{-1}\approx 0$

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 ≪ r₂, so that r₁ – r₂ ≈ 0. But the overall rate of reaction is the rate of formation of final product (here CO₂), so that r = r₂ ≈ r₁. That is, the overall rate is determined by the rate of the first step, and (almost) all molecules which react by the first step continue to the second step which is just as fast.

If the second step were rate-determining

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: r₂ ≪ r_-1. In this hypothesis, r₁ – r_-1 ≈ 0, so that the first step is (almost) at equilibrium. The overall rate is determined by the second step, r = r₂ ≪ r₁, as very few molecules which react by the first step continue to the second step which is much slower. However this hypothesis can be rejected (for the example reaction) since it implies a rate equation which disagrees with experiment.

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

The overall reaction rate would then be

,

which disagrees with the experimental rate law given above, and so disproves the hypothesis that the second step is rate-determining.

Nucleophilic substitution

Another example is the unimolecular nucleophilic substitution (S_N1) 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
4H
9Br) by aqueous sodium hydroxide. The mechanism has two steps (where R denotes the tert-butyl radical t-C
4H
9)

Formation of a carbocation R-Br → R+
+ Br−
Nucleophilic attack by one water molecule R+
+ OH−
→ ROH.

This reaction is found to be first-order with rate = k[RBr], 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
3Br) is a bimolecular nucleophilic substitution (S_N2) reaction in a single bimolecular step. Its rate law is second-order, rate = k[RBr][OH−
].

Composition of the transition state

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.^[3] For the NO
2-CO reaction above, the rate depends on [NO
2]² so that the activated complex has composition N
2O
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
2C
2O
4 + Cl
2 → 2 CO₂ + 2 H+
+ 2 Cl−
.^[3] The observed rate law is

,

which implies an activated complex in which the reactants lose 2H+
+ Cl−
before the rate-determining step. The formula of the activated complex is Cl
2 + H
2C
2O
4 – 2 H+
– Cl−
+ x H
2O, or C
2O
4Cl(H
2O)–
x (An unknown number of water molecules are added because the possible dependence of the reaction rate on H
2O 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 known to be rapid is^[3]

Cl
2 + H
2O ⇌ HOCl + Cl−
+ H+

H
2C
2O
4 ⇌ H+
+ HC
2O−
4

HOCl + HC
2O−
4 → H
2O + Cl−
+ 2 CO₂

Diffusion control

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.

References

^ Steinfeld J.I., Francisco J.S. and Hase W.L. Chemical Kinetics and Dynamics (2nd ed., Prentice-Hall 1999) chap. 2
^ Whitten K.W., Galley K.D. and Davis R.E. General Chemistry (4th edition, Saunders 1992), p.638-9
^ ^a ^b ^c Espenson, J.H. (2002). Chemical Kinetics and Reaction Mechanisms (2nd ed.). McGraw-Hill. pp. 127–132. ISBN 0072883626.

Zumdahl, Steven S. (2005). Chemical Principles (5th ed.). Houghton Mifflin. pp. 727–8. ISBN 0618372067.

External links

The Rate-Limiting Enzyme regulation database (RLEdb)

UpToDate Contents

全文を閲覧するには購読必要です。 To read the full text you will need to subscribe.

1. 分娩前の胎児心拍数評価 antepartum fetal heart rate assessment
2. 心房細動における心拍数のコントロール：薬理療法 control of ventricular rate in atrial fibrillation pharmacologic therapy
3. 分娩第Ⅰ期、Ⅱ期、およびⅢ期の胎児心拍数計測のマネージメント management of intrapartum category i ii and iii fetal heart rate tracings
4. 緊急輪状甲状間膜切開（輪状甲状軟骨切開術） emergent surgical cricothyrotomy cricothyroidotomy
5. 高ナトリウム血症の治療 treatment of hypernatremia

English Journal

Degradation of trichloroethylene by hydrodechlorination using formic acid as hydrogen source over supported Pd catalysts.

Yu X1, Wu T2, Yang XJ2, Xu J2, Auzam J3, Semiat R4, Han YF5.
Journal of hazardous materials.J Hazard Mater.2016 Mar 15;305:178-89. doi: 10.1016/j.jhazmat.2015.11.025. Epub 2015 Dec 1.
An advanced method for the degradation of trichloroethylene (TCE) over Pd/MCM-41 catalysts through a hydrogen-transfer was investigated. Formic acid (FA) was used instead of gaseous H2 as the hydrogen resource. As a model H-carrier compound, FA has proven to yield less by-products and second-hand po
PMID 26685065

Palladium-Catalyzed Dehydrative Cross-Coupling of Allylic Alcohols and N-Heterocycles Promoted by a Bicyclic Bridgehead Phosphoramidite Ligand and an Acid Additive.

Kang K1, Kim J1, Lee A1, Kim WY1, Kim H1,2.
Organic letters.Org Lett.2016 Jan 13. [Epub ahead of print]
A mild and efficient dehydrative cross-coupling reaction between allylic alcohols and N-heterocycles using palladium catalysis is reported. A bicyclic bridgehead phosphoramidite (briphos) ligand together with Pd(dba)2 is a highly efficient catalyst, and an acid additive involved in the rate-determin
PMID 26761609

Theoretical Studies on Palladium-Mediated Enantioselective C-H Iodination.

Zhou M, Yang TL, Dang L.
The Journal of organic chemistry.J Org Chem.2016 Jan 12. [Epub ahead of print]
DFT calculations are carried out to investigate the reaction mechanism for PdII mediated enantioselective C-H iodination. Iodination of aryl ortho C-H bond of benzyl amines catalyzed by PdII diacetate complexes in presence of the L-MPAA ligand experiences three main steps: firstly, C-H bond activati
PMID 26756972

Japanese Journal

Solid–Liquid Extraction and Transport of Metal Ion with the Polymer Inclusion Membrane Using a New Alkylated Pyrrolidinecarboxylic Acid

KANEMARU Shintaro,OSHIMA Tatsuya,BABA Yoshinari
JOURNAL OF CHEMICAL ENGINEERING OF JAPAN 45(10), 816-822, 2012
… Their results suggest that the rate-determining step for the permeability rate at high pH is the mass transfer of a metal complex across the membrane phase. …
NAID 130001858865

CO2 decomposition using electrochemical process in molten salts

Otake Koya,Kinoshita Hiroshi,Kikuchi Tatsuya,Suzuki Ryosuke O
Journal of Physics: Conference Series 379(1), 012038, 2012
… It was found that the rate determining step is the diffusion of oxygen ions into the ZrO2 solid electrolyte. …
NAID 120004650836

In-situ production of PH3 from red phosphorus and atomic hydrogen

Umemoto Hironobu,Nishihara Yushin,Ishikawa Takuma
Chemical Physics Letters 514(1-3), 26-28, 2011-08-12
… These results suggest that the rate-determining step for the production of PH3 is that which produces H atoms. …
NAID 120003339680