Name: reading reaction progress with integrated laws
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 39 s
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K12 Standards

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IPC.7

IPC.7.F

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The Integrated Rate Law: The Dependence of Concentration on Time

Una legge di velocità usata per determinare la velocità di reazione, partendo dalle concentrazioni dei reagenti, e dalle costanti di velocità, può essere convertita in leggi di velocità che dimostrano la dipendenza della velocità di reazione dalla concentrazione e dal tempo dei reagenti. Queste leggi di velocità possono essere usate per studiare quanto lentamente o velocemente venga consumato un reagente, o quanto tempo serva per raggiungere la metà della concentrazione di un reagente. Per iniziare, esaminiamo la legge della velocità differenziale, che esprime la velocità di reazione come una variazione della concentrazione dei reagenti durante un intervallo di tempo specifico.

L'integrazione di questa legge porta alla legge della velocità integrata, che esprime la velocità di reazione come una relazione fra la concentrazione iniziale di un reagente e la sua concentrazione dopo una durata specifica. La legge della velocità integrata dipende dall'ordine di reazione generale e, dunque, varia per ogni tipo di reazione. Tuttavia, indipendentemente dall'ordine generale, tutte le leggi delle velocità integrate assumono la forma di un'equazione lineare standard, con componenti y, m, x e b distinte, e possono essere tracciate per generare una linea retta.

In una legge della velocità integrata di ordine zero, _t è la concentrazione del reagente al momento t, k è la costante di velocità, t è il tempo, e _0 è la concentrazione iniziale del reagente. Per una reazione di ordine zero, un grafico della concentrazione dei reagenti in funzione del tempo genera una linea retta. La pendenza è il valore negativo della costante di velocità, e l'intercetta y è la concentrazione iniziale del reagente.

In una reazione del primo ordine, il log naturale della concentrazione dei reagenti tracciato in funzione del tempo fornisce una linea retta. La pendenza corrisponde al valore negativo della costante di velocità, mentre l'intercetta su y fornisce il log naturale della concentrazione iniziale del reagente. Secondo la legge della velocità integrata del secondo ordine, un grafico dell'inverso della concentrazione dei reagenti rispetto al tempo, produce una linea retta.

La pendenza è uguale alla costante di velocità e l'intercetta sull'asse delle y rappresenta l'inverso della concentrazione iniziale del reagente. L'ordine di reazione globale può essere identificato utilizzando dati cinetici sperimentali, tracciando le diverse leggi di velocità integrate. Solo il grafico lineare corrisponde all'ordine corretto della reazione globale.

L'analisi successiva consente di determinare la costante di velocità e la concentrazione del reagente in un preciso momento.

la legge della cinetica integrata: la dipendenza della concentrazione nel tempo

Mentre la legge sulla velocit differenziale mette in relazione la velocit e le concentrazioni dei reagenti, una seconda forma di legge sulla velocit chiamata legge sulla velocit integrata mette in relazione le concentrazioni dei reagenti e il tempo. Le leggi sulla velocit integrata possono essere utilizzate per determinare la quantit di reagente o prodotto presente dopo un periodo di tempo o per stimare il tempo necessario affinch una reazione proceda in una certa misura. Ad esempio, una legge sui tassi integrata aiuta a determinare il periodo di tempo in cui un materiale radioattivo deve essere immagazzinato affinch la sua radioattivit decada a un livello sicuro.

Utilizzando il calcolo infinitesimale, la legge sulla velocit differenziale di una reazione chimica pu essere integrata rispetto al tempo per fornire un'equazione che mette in relazione la quantit di reagente/prodotto con il tempo trascorso della reazione.

Reazioni del primo ordine

L'integrazione della legge sulla velocit per una semplice reazione del primo ordine (velocit = k[A]) d come risultato un'equazione che descrive la variazione della concentrazione dei reagenti nel tempo:

 <img alt="Eq1" src="/files/ftp_upload/11377/11377_Equation 1.png" style="height: 50px;" />

Qui, [A]_t la concentrazione di A in qualsiasi momento t, [A]_0 la concentrazione iniziale di A e k la costante di velocit del primo ordine. Per comodit matematica, questa equazione riorganizzata in un formato che mostra una dipendenza lineare della concentrazione dal tempo che assume la forma di un'equazione lineare (y = mx + b):

 <img alt="Eq2" src="/files/ftp_upload/11377/11377_Equation 2.png" style="height: 50px;" />

L'equazione suggerisce che un grafico di ln[A]_t rispetto a t per una reazione del primo ordine una linea retta con una pendenza di ?k e un'intercetta y di ln[A]_0. Se una serie di dati sulla velocit vengono tracciati in questo modo ma non risultano in una linea retta, la reazione non del primo ordine in A.

Reazioni del secondo ordine

La legge sulla velocit differenziale per una reazione semplice del secondo ordine velocit = k[A]_2, e la legge sulla velocit integrata :

<img alt="Eq3" src="/files/ftp_upload/11377/11377_Equation 3.png" style="text-align: center; height: 70px;" />

Anche la legge tariffaria integrata del secondo ordine assume la forma dell'equazione di una linea retta. Secondo l'equazione, un grafico di 1/[A]_t rispetto a t per una reazione del secondo ordine una linea retta con una pendenza di k e un'intercetta y di 1/[A]_0. Se la trama non una linea retta, la reazione non di secondo ordine.

Reazioni di ordine zero

Per le reazioni di ordine zero, la legge sulla velocit differenziale velocit = k. Una reazione di ordine zero presenta una velocit di reazione costante, indipendentemente dalla concentrazione dei suoi reagenti. La cinetica di ordine zero si osserva per alcune reazioni solo in determinate condizioni specifiche. Queste stesse reazioni mostrano comportamenti cinetici diversi quando le condizioni specifiche non sono soddisfatte e, per questo motivo, a volte viene utilizzato il termine pi prudente pseudo-ordine zero.

Anche la legge sulla velocit integrata per una reazione di ordine zero una funzione lineare, assumendo la forma di y = mx + b:

 <img alt="Eq4" src="/files/ftp_upload/11377/11377_Equation 4.png" style="height: 50px;" />

Un grafico di [A] rispetto al tempo t per una reazione di ordine zero una linea retta con una pendenza di ?k e un'intercetta y di [A]_0.

Questo testo adattato da <a href="https://openstax.org/books/chemistry-2e/pages/12-4-integrated-rate-laws">Openstax, Chemistry 2e, Section 12.4: Integrated Rate Laws.</a>

La legge della cinetica integrata: la dipendenza della concentrazione nel tempo

Mentre la legge del tasso differenziale mette in relazione il tasso e le concentrazioni dei reagenti, una seconda forma di legge del tasso chiamata legge del tasso integrato si riferisce ...

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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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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...

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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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