Name: reading reaction progress with integrated laws
Uploaded: 2020-09-24T15:06:50.000Z
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The Integrated Rate Law: The Dependence of Concentration on Time

Une loi de vitesse utilisée pour déterminer la vitesse de réaction des concentrations de réactif et constantes de taux peuvent être convertis en lois de taux démontrant la dépendance de la vitesse de réaction à la concentration du réactif et au temps. Ces lois de taux peuvent être utilisées pour étudier a lenteur ou la rapidité de combustion d'un réactif ou le temps nécessaire pour atteindre la moitié de la concentration d'un réactif. Pour commencer, examinez la loi de vitesse différentielle différentiel, qui définit la vitesse de réaction comme une variation de la concentration du réactif pendant un intervalle de temps spécifique.L'intégration de cette loi conduit à la loi tarifaire intégrée, qui traduit la vitesse de réaction en tant que relation entre la concentration réactive initiale et sa concentration après une durée spécifique. La loi de vitesse intégrée dépend de l'ordre global de la réaction et, par conséquent, varie pour chaque type de réaction. Cependant, quel que soit l'ordre général, toutes les lois de vitesse intégrées prennent la forme d'une équation linéaire standard avec y, m, x, et b composants et peuvent être représentées par une ligne droite sur un graphe.Dans une loi de vitesse intégrée d'ordre zéro, _t est la concentration du réactif au temps t, k est la constante de vitesse, t est le temps, et _0 est la concentration initiale du réactif. Pour une réaction d'ordre zéro, le graphe de la concentration de réactif en fonction du temps présente une ligne droite. La pente est la valeur négative de la constante de vitesse, et l'ordonnée à l'origine est la concentration initiale du réactif.Dans une réaction de premier ordre, le log naturel de la concentration de réactif représenté sur un graphe en fonction du temps donne une ligne droite. La pente correspond à la valeur négative du constante de vitesse, tandis que l'ordonnée à l'origine donne le log naturel de la concentration initiale du réactif. Selon la loi des vitesses intégrés de second ordre, un graphe de l'inverse de la concentration de réactif en fonction du temps donne une ligne droite.La pente correspond à la constante de vitesse, et l'ordonnée à l'origine représente l'inverse de la concentration initiale du réactif. L'ordre de réaction global peut être identifié en utilisant des données cinétiques expérimentales en traçant sur un graphe les différentes lois de vitesse intégrées. Seul le graphique avec un courbe linéaire correspond à l'ordre de réaction global correct.Une analyse ultérieure permet de déterminer la constante de vitesse et la concentration de réactif à un instant donné.

loi de vitesse intégrée : dépendance de la concentration sur le temps

Alors que la loi de vitesse différentielle relie la vitesse et les concentrations de réactifs, une seconde forme de la loi de vitesse appelée loi de vitesse intégrée relie les concentrations de réactifs et le temps. Les lois de vitesse intégrées peuvent être utilisées pour déterminer la quantité de réactif ou de produit présente au bout d'une période de temps ou pour estimer le temps nécessaire pour qu'une réaction se poursuive jusqu'à un certain point. Par exemple, une loi de vitesse intégrée permet de déterminer la durée de stockage d'une matière radioactive pour que sa radioactivité diminue à un niveau qui soit sûr. 
 En utilisant le calcul, la loi de vitesse différentielle pour une réaction chimique peut être intégrée par rapport au temps pour donner une équation reliant la quantité de réactif/produit au temps écoulé de la réaction. 
 Réactions de premier ordre 
 L'intégration de la loi de vitesse pour une réaction simple de premier ordre (vitesse = k[A]) conduit à une équation décrivant la variation de la concentration du réactif avec le temps : 
  <img alt="Eq1" src="/files/ftp_upload/11377/11377_Equation 1.png" style="height: 50px;" />
 Ici, [A]t est la concentration de A à tout moment t, [A]0 est la concentration initiale de A et k est la constante de vitesse de premier ordre. Pour des raisons mathématiques, cette équation est réorganisée dans un format montrant une dépendance linéaire entre la concentration et le temps qui prend la forme de l'équation d'une ligne droite (y = mx + b) :         
  <img alt="Eq2" src="/files/ftp_upload/11377/11377_Equation 2.png" style="height: 50px;" />
 L'équation indique qu'un tracé de ln[A]t par rapport à t pour une réaction de premier ordre est une ligne droite avec une pente de −k et un y à l'origine de ln[A]0. Si un ensemble de données de vitesse est tracé de cette façon mais ne donne pas par une ligne droite, la réaction n'est pas du premier ordre pour A. 
 Réactions de deuxième ordre 
 La loi de vitesse différentielle pour une simple réaction de deuxième ordre est vitesse = k[A]2, et la loi de vitesse intégrée est : 
 <img alt="Eq3" src="/files/ftp_upload/11377/11377_Equation 3.png" style="text-align: center; height: 70px;" />
 La loi de vitesse intégrée de deuxième ordre prend également la forme de l'équation d'une ligne droite. Selon l'équation, un tracé de 1/[A]t par rapport à t pour une réaction de deuxième ordre est une ligne droite avec une pente de k et une ordonnée à l'origine de 1/[A]0. Si le tracé n'est pas une ligne droite, la réaction n'est pas du deuxième ordre. 
 Réactions d'ordre zéro            
 Pour les réactions d'ordre zéro, la loi de vitesse différentielle est vitesse = k. Une réaction d'ordre zéro présente une vitesse de réaction constante, quelle que soit la concentration de son ou de ses réactifs. Des cinétiques d'ordre zéro sont observées pour certaines réactions seulement dans certaines conditions spécifiques. Ces mêmes réactions présentent des comportements cinétiques différents lorsque les conditions spécifiques ne sont pas remplies, et pour cette raison, le terme plus prudent de pseudo-ordre zéro est parfois utilisé.                            
 La loi de vitesse intégrée pour une réaction d'ordre zéro est également une fonction linéaire, qui prend la forme de y = mx + b :                 
  <img alt="Eq4" src="/files/ftp_upload/11377/11377_Equation 4.png" style="height: 50px;" />
 Un tracé de [A] par rapport au temps t pour une réaction d'ordre zéro est une ligne droite avec une pente de −k et un y à l'origine de [A]0. 
 Ce texte est adapté de<a href="https://openstax.org/books/chemistry-2e/pages/12-4-integrated-rate-laws"> Openstax, Chimie 2e, Section 12.4 : Lois de vitesse intégrées. </a>

Loi de vitesse intégrée : dépendance de la concentration sur le temps

Alors que la loi différentielle de vitesse relie le taux et les concentrations de réactifs, une deuxième forme de loi de vitesse appelée loi de vitesse intégrée relie ...

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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

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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...

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

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Reading Reaction Progress with Integrated Laws

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