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
strictly limiting the reference of a modified word or phrase; "the restrictive clause in `Each made a list of the books that had influenced him limits the books on the list to only those particular ones defined by the clause"
standing or position on a scale

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〉》
制限する,限定する
〈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）』「2013/07/12 09:30:58」(JST)

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In chemical kinetics, the rate (or velocity) of a reaction mechanism with several steps is often determined by the slowest step, known as the rate-determining step (RDS) or rate-limiting step. The experimental rate equation can help to identify which step is rate-determining.

In a reaction coordinate, the transition state with the highest energy is the rate-determining step of a given reaction.

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: NO₂ + CO[edit]

As an example, consider the gas-phase reaction NO₂ + CO → NO + CO₂. If this reaction occurred in a single step, its reaction rate (r) would be proportional to the rate of collisions between NO₂ and CO molecules r = k[NO₂][CO], where k is the reaction rate constant and square brackets indicate a molar concentration.

First step rate-determining[edit]

In fact, however, the observed reaction rate is second order in NO₂ and zero order in CO,^[1] with rate equation r = k[NO₂]². This suggests that the rate is determined by a step in which two NO₂ 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 NO₃ is formed in the first step with rate r₁ and reacts with CO in the second step with rate r₂. However NO₃ can also react with NO if the first step occurs in the reverse direction (NO + NO₃ → 2 NO₂) with rate r_-1, where the minus sign indicates the rate of a reverse reaction.

The concentration of a reactive intermediate such as [NO₃] 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 NO₃ is formed in one step and reacts in two, so that

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 NO₃ 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[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: 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 NO₃ 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[edit]

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-C₄H₉Br) by aqueous sodium hydroxide. The mechanism has two steps (where R denotes the tert-butyl radical t-C₄H₉)

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 (CH₃Br) is a bimolecular nucleophilic substitution (S_N2) reaction in a single bimolecular step. Its rate law is second-order, rate = k[RBr][OH^-].

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 interact and form the product. This case is referred to as diffusion control and, in general, occurs where the formation of product from the activated complex is very rapid and thus the supply of reactants and their interaction is rate determining.

References[edit]

^ Whitten K.W., Galley K.D. and Davis R.E. General Chemistry (4th edition, Saunders 1992), p.638-9

Zumdahl, Steven S. Chemical Principles. Ed. Boston, Houghton Mifflin Company: 2005, pp 727–728.

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Japanese Journal

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