Name: reading reaction progress with integrated laws
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 39 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.7

IPC.7.F

the-integrated-rate-law-the-dependence-of-concentration-on-time

The Integrated Rate Law: The Dependence of Concentration on Time

反応物の濃度と速度定数から反応速度を決定するために使用される速度法則は、反応速度が反応物の濃度と時間に依存することを示す速度法則に変換できます。
これらの速度法則は、反応物がどれだけゆっくりとまたは速く消費されるか、または反応物の半分の濃度に達するのに必要な時間を研究するために使用できます。
まず、特定の時間間隔での反応物濃度の変化として反応速度を表す微分速度法則を調べます。この法則の統合は、反応物の初期濃度と特定の期間後のその濃度との関係として反応速度を表す統合速度の法則につながります。
積分率法則は、全体的な反応順序に依存するため、反応タイプごとに異なります。ただし、全体的な順序に関係なく、すべての積分レート法則は、異なる y、m、x、b 成分を持つ標準線形方程式の形式を取り、プロットして直線を生成できます。
ゼロ次積分率法則では、[A]tは時間tでの反応物濃度、kは速度定数、tは時間、[A]0は初期反応物濃度です。
ゼロ次反応の場合、反応物濃度を時間の関数としてプロットすると、直線が生成されます。傾きは速度定数の負の値であり、y切片は初期反応物濃度です。
一次反応では、時間の関数としてプロットされた反応物濃度の自然対数が直線になります。傾きは速度定数の負の値に対応し、y切片は初期反応物濃度の自然対数を与えます。
2 次積分率の法則によれば、反応物濃度の逆数対時間比のプロットは直線になります。傾きは速度定数に等しく、y 切片は初期反応物濃度の逆数を表します。
全体的な反応順序は、実験速度論データを使用して、さまざまな積分速度則をプロットすることにより特定できます。線形グラフのプロットのみが、正しい全体的な反応順序に対応します。その後の分析により、任意の時点での速度定数と反応物濃度を決定できます。

積分速度則：反応濃度と時間

微分速度則が速度と反応物濃度に関係するのに対し、積分速度則と呼ばれる第2の速度論は、反応物濃度と時間に関係します。積分速度則は、一定時間後に存在する反応物や生成物の量を決定したり、反応がある程度進行するのに必要な時間を推定したりするのに使用できます。例えば、放射性物質の放射能が安全なレベルまで減衰するために保管しなければならない期間を決定する際に、積分速度則が役立ちます。
 微積分を用いて、化学反応の微分速度則を時間に対して積分すると、反応物・生成物の量と反応の経過時間を関係付ける式が得られます。
 一次反応
 単純な一次反応（反応速度= k[A]）の反応速度式を積分すると、反応物濃度の経時変化を表す方程式が得られます。
   <img alt = "Eq1" src = "/ files / ftp_upload / 11377 / 11377_Equation 1.png" style = "height:50px;" />
 ここで、[A] tは任意の時点tにおけるAの濃度、[A]0はAの初期濃度、kは一次速度定数です。数学的に扱いやすくするため、濃度の線形依存性を示す式に変更すると次のようになります。（y = mx + b）:         
   <img alt = "Eq2" src = "/ files / ftp_upload / 11377 / 11377_Equation 2.png" style = "height:50px;" />
 この方程式は、1次のln[A]tとtのプロットを示しています。反応は、傾きが−kでy切片がln[A]0の直線です。一連の速度データをこの方法でプロットしても直線状にならない場合、反応はAの1次ではありません。
 二次反応
 単純な二次反応の微分速度則は、rate = k[A]2,であり、積分速度則は、次の通りです。
 <img alt = "Eq3" src = "/ files / ftp_upload / 11377 / 11377_Equation 3.png" style = "text-align:center; height:70px;" />
 二次の積分速度則もまた、直線の方程式の形をとります。この式によれば、二次反応の1/[A]t対tのプロットは、傾きがk、y切片が1/[A]0の直線となります。プロットが直線でない場合は、その反応は二次反応ではありません。
 ゼロ次反応             
 ゼロ次反応の場合、微分速度則はrate = kです。ゼロ次反応は、反応物の濃度に関係なく、一定の反応速度を示します。ゼロ次反応速度は、特定の条件下における一部の反応でのみ観察されます。これらの反応は、特定の条件が満たされない場合に異なる速度論的挙動を示します。このため、より慎重な用語である疑似ゼロ次反応という語が使用されることもあります。             &# 160;                
 ゼロ次反応の積分式も線形関数であり、y = mx + bの形式をとります。             &# 160;    
   <img alt = "Eq4" src = "/ files / ftp_upload / 11377 / 11377_Equation 4.png" style = "height:50px;" />
 ゼロ次反応の[A] vs. 時間tのプロットは、傾きが− kかつ[A]0のyの切片を持つ直線です。
 上記の文章は以下から引用しました。 <a href="https://openstax.org/books/chemistry-2e/pages/12-4-integrated-rate-laws">Openstax, Chemistry 2e, Section 12.4: Integrated Rate Laws.</a>

微分率法則は反応物の速度と濃度に関連していますが、統合速度法と呼ばれる2番目の形式の速度法則は...

Education

JoVE Core

Chemistry

化学

Chemical Kinetics

化学反応速度論

KEY TERMS AND CONCEPTS

主要用語と概念

reading reaction progress with integrated laws

Integrated rate laws connect reaction concentration to time. They help show how much reactant or product is present after a certain period. They can also help estimate how long a reaction must run to reach a given extent. A common use is finding how long radioactive material must be stored before its radioactivity drops to a safe level.

These equations come from the differential rate law after it is integrated with respect to time. For a first-order reaction, where rate = k[A], the integrated form relates the concentration of A at time t to the initial concentration [A]0 and the first-order rate constant k. The equation can be rearranged into the straight-line form y = mx + b. That means a plot of ln[A]t versus t should be linear. The slope is −k, and the y-intercept is ln[A]0. If the data do not make a straight line, the reaction is not first order in A.

Second-order reactions follow a different pattern. For a simple second-order reaction, the differential rate law is rate = k[A]2. Its integrated rate law also gives a straight-line relationship. A plot of 1/[A]t versus time t should be linear, with slope k and y-intercept 1/[A]0. If the plot is not straight, the reaction is not second order.

Zero-order reactions behave differently again. For these reactions, the rate is rate = k, so the reaction rate stays constant even when reactant concentration changes. Some reactions show zero-order kinetics only under certain conditions, so the term pseudo-zero-order is sometimes used. The integrated rate law is also linear here. A plot of [A] versus time t is a straight line with slope −k and y-intercept [A]0.

Reading Reaction Progress with Integrated Laws

reading-reaction-progress-with-integrated-laws

reaction rate

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the integrated rate law: the dependence of concentration on time

Integrated rate laws connect reaction concentration to time. They help show how much reactant or product is present after a certain period. They can also help estimate how long a reaction must run to reach a given extent. A common use is finding how long radioactive material must be stored before its radioactivity drops to a safe level. These equations come from the differential rate law after it is integrated with respect to time. For a first-order reaction, where rate = k[A], the integrated...

half-life of a reaction

Reaction Half-Life in Kinetics

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reaction mechanisms

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enzymes

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key terms and concepts

Learn how integrated rate laws connect concentration and time for first-order, second-order, and zero-order reactions, including straight-line plots and slopes.

Reading Reaction Progress with Integrated Laws | JoVE K12

chemistry

JoVE Core 化学は、簡潔で理解しやすいアニメーションビデオレッスンを使用して、一般的な化学の概念を生き生きとしたものにします。さらに、活動する科学者のビデオでは、現在世界中の実験室で行われている古典的そして独創的な研究・実験をお見せします。

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North Carolina K-12 Science Standard Course of Study

9-12

Matter and its Interactions

PS.Chm.5.1

Pennsylvania State Academic Standards

Physical Science

Chemical Reactions

3.2.9-12.D

3.2.9-12.E

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Ohio’s Learning Standards and Model Curriculum

Interactions Of Matter

Chemical reactions

Virginia  Standards of Learning

HIgh School

CH.7

CH.7.e

Alabama Course of Study Science

Matter and Its Interactions: Energy

9-12.C.3.3.d

Next Generation Science Standards

Matter and Its Interactions

HS-PS1-4

HS-PS1-5

Florida Department of Education

SC.912.P.12

SC.912.P.12.12

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New York State Science Learning Standards

HS. Chemical Reactions

HS-PS1-5.

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Reading Reaction Progress with Integrated Laws

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