Name: reaction bottlenecks in chemical kinetics
Uploaded: 2020-09-24T15:06:50.000Z
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Rate-Determining Steps

La maggior parte delle reazioni chimiche procede in un meccanismo di reazione a più fasi. Ma come si determina un meccanismo di reazione? I meccanismi di reazione vengono ipotizzati basandosi sulle loro equazioni chimiche bilanciate e sulle leggi di velocità determinate sperimentalmente, per ogni passaggio elementare.

Ciascuna fase ha una velocità di reazione, una costante di velocità e un'energia di attivazione specifiche. La fase più lenta è detta fase determinante la velocità e che influenza la velocità di reazione netta. Può essere utilizzata per verificare la legge di velocità per la reazione complessiva e per convalidare un meccanismo di reazione proposto.

Considerate la decomposizione del protossido di azoto in azoto e ossigeno. La legge della velocità, determinata sperimentalmente, non corrisponde all'espressione della velocità di una reazione a fase singola, che è confermata dalla presenza osservata di atomi di ossigeno in un intermedio di reazione. Pertanto, avviene attraverso un meccanismo di reazione in cui tutti i passaggi si accumulano per fornire la reazione complessiva.

Innanzitutto, le costanti di velocità indicano che il primo passaggio è il passaggio di limitazione della velocità. È il più lento e pertanto influenza la velocità di reazione complessiva. Una legge sulla velocità proposta tramite questo passaggio può essere impostata ugualmente alla legge sulle velocità complessive.

Questa legge di velocità proposta, derivata direttamente dalla concentrazione molecolare del reagente elementare, corrisponde alla legge di velocità sperimentale e verifica il meccanismo di reazione previsto. Tuttavia, molte reazioni iniziano con una fase iniziale rapida, seguita da una fase di determinazione della velocità. In questi casi, come possono essere proposti meccanismi di reazione?

Considerate la formazione del bromuro di nitrosile. La legge della velocità sperimentale è del secondo ordine per l'ossido nitrico, e del primo per il bromo molecolare. Il primo passaggio è un rapido passaggio di equilibrio con uguale velocità di reazione avanti e indietro, seguito da una seconda fase di determinazione della velocità, che contiene un intermedio di reazione.

Di conseguenza, la legge sui tassi proposta, manterrà l'intermedio di reazione. Pertanto, un confronto diretto fra la legge di velocità proposta, contenente l'intermedio di reazione ad una concentrazione sconosciuta, e la legge di velocità sperimentale, che accoglie i reagenti di partenza, è difficile. Tuttavia, supponendo che il primo stadio sia in equilibrio, la concentrazione intermedia può essere impostata come uguale alle concentrazioni dei reagenti.

Sostituendo questa relazione nella legge di velocità proposta, e combinando le costanti di velocità in una costante di velocità complessiva, si genera un'espressione consistente con la legge di velocità sperimentale. Combinando i passaggi elementari si ottiene l'equazione bilanciata complessiva, che soddisfa il secondo requisito per un meccanismo di reazione. Pertanto, il meccanismo di reazione a due fasi proposto per la formazione del bromuro di nitrosile è valido.

passaggi di determinazione della velocità

Relativi meccanismi di reazione

In un meccanismo di reazione multistadio, uno degli stadi elementari procede significativamente più lentamente degli altri. Questa fase più lenta è chiamata fase di limitazione della velocità (o fase di determinazione della velocità). Una reazione non può procedere più velocemente della fase più lenta e, quindi, la fase che determina la velocità limita la velocità complessiva della reazione.

Il concetto di determinazione della velocità può essere compreso dall'analogia di un'autostrada a 4 corsie con un breve tratto di strozzatura del traffico causata dalla chiusura della corsia. Come il collo di bottiglia che influenza la velocità complessiva alla quale i veicoli potrebbero viaggiare, il passo elementare più lento influenza la velocità di reazione netta.

L’equazione cinetica può essere derivata direttamente dalle equazioni chimiche bilanciate per le reazioni elementari. Tuttavia, questo non è il caso della maggior parte delle reazioni chimiche, dove le equazioni bilanciate spesso rappresentano il cambiamento complessivo nel sistema chimico, risultante da meccanismi di reazione a più fasi. Pertanto, l’equazione cinetica dev’essere determinata dai dati sperimentali e il meccanismo di reazione successivamente dedotto dall’equazione cinetica.

Ad esempio, consideriamo la reazione di NO2 e CO:

<img alt="Eq1" src="/files/ftp_upload/11382/11382_Equation_1.png" style="text-align: center; height: 50px;" />

La legge sperimentale sulla velocità per questa reazione a temperature superiori a 225 °C è:

<img alt="Eq2" src="/files/ftp_upload/11382/11382_Equation_2.png" style="text-align: center; height: 50px;" />

Secondo la l’equazione cinetica, la reazione è del primo ordine rispetto a NO_2 e del primo ordine rispetto a CO. Ciò è coerente con un meccanismo bimolecolare a stadio singolo ed è possibile che questo meccanismo di reazione sia valido per questo processo chimico a alte temperature.

Tuttavia, a temperature inferiori a 225 °C, la reazione è descritta da un’equazione cinetica diversa e di secondo ordine rispetto a NO_2:

<img alt="Eq3" src="/files/ftp_upload/11382/11382_Equation_3.png" style="text-align: center; height: 50px;" />

Questa equazione cinetica non è coerente con il meccanismo a fase singola, ma è coerente con il seguente meccanismo a due fasi:

<img alt="Eq4" src="/files/ftp_upload/11382/11382_Equation_4.png" style="text-align: center; height: 70px;" />

La fase di determinazione della velocità (più lenta) fornisce un’equazione cinetica che mostra una dipendenza di secondo ordine dalla concentrazione di NO_2, e la somma delle due equazioni elementari fornisce la reazione netta complessiva.

In generale, quando la fase che determina la velocità (più lenta) è la prima fase del meccanismo di reazione, l’equazione cinetica per la reazione complessiva è la stessa dell’equazione cinetica per questa fase. Tuttavia, quando la fase che determina la velocità è preceduta da una fase elementare che comporta una reazione rapidamente reversibile, l’equazione cinetica per la reazione complessiva può essere più difficile da ricavare, spesso a causa della presenza di intermedi di reazione.

In tali casi, è possibile utilizzare il concetto che una reazione reversibile è all'equilibrio quando le velocità dei processi diretti e inversi sono uguali.

Ad esempio, consideriamo la reazione elementare reversibile in cui NO dimerizza per produrre una specie intermedia N_2O_2. Quando questa reazione è all'equilibrio:

<img alt="Eq5" src="/files/ftp_upload/11382/11382_Equation_5.png" style="text-align: center; height: 115px;" />

Questa espressione può essere riorganizzata per esprimere la concentrazione dell'intermedio in termini di reagente NO:

<img alt="Eq6" src="/files/ftp_upload/11382/11382_Equation_6.png" style="text-align: center; height: 75px;" />

Questo approccio può essere utilizzato nella formulazione di equazioni cinetiche per reazioni complessive quando sono presenti intermedi di reazione.

Esempio di derivazione dell’equazione cinetica da un meccanismo di reazione

Consideriamo una reazione tra monossido di azoto e cloro molecolare, per la quale viene proposto un meccanismo in due fasi come mostrato:

<img alt="Eq7" src="/files/ftp_upload/11382/11382_Equation_7.png" style="text-align: center; height: 70px;" />

Questo meccanismo può essere utilizzato per derivare l'equazione e prevedere l’equazione cinetica per la reazione complessiva. Inizialmente, sommando le due reazioni elementari, si ottiene l'equazione della reazione complessiva.

<img alt="Eq8" src="/files/ftp_upload/11382/11382_Equation_8.png" style="text-align: center; height: 110px;" />

Per derivare un’equazione cinetica da questo meccanismo, si scrivono le equazioni cinetiche per ciascuno dei due passaggi elementari:

<img alt="Eq9" src="/files/ftp_upload/11382/11382_Equation_9.png" style="text-align: center; height: 110px;" />

Secondo il meccanismo di reazione proposto, la fase 2 è quella che determina la velocità. Pertanto, l’equazione cinetica per la reazione complessiva dovrebbe essere la stessa dell’equazione cinetica per questo passaggio elementare. Tuttavia, l’equazione cinetica per la fase 2 contiene una concentrazione di specie intermedia, [NOCl_2]. Per modificare ciò, l’equazione cinetica del primo passaggio elementare viene utilizzata per derivare un'espressione per la concentrazione intermedia in termini di concentrazioni di reagenti.

Supponendo che il passaggio 1 sia all'equilibrio;

<img alt="Eq10" src="/files/ftp_upload/11382/11382_Equation_10.png" style="text-align: center; height: 130px;" />

Sostituendo questa espressione nell’equazione cinetica per il passaggio 2 si ottiene:

<img alt="Eq11" src="/files/ftp_upload/11382/11382_Equation_11v2.png" style="text-align: center; height: 70px;" />

Questo testo è adattato da <a href="https://openstax.org/books/chemistry-2e/pages/12-6-reaction-mechanisms">Openstax, Chemistry 2e, Section 12.6: Reaction Mechanisms.</a>

Passaggi di determinazione della velocità

Meccanismi di reazione correlati
In un meccanismo di reazione a più fasi, una delle fasi elementari progredisce significativamente più lentamente delle altre. Questo più lento ...

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reaction bottlenecks in chemical kinetics

Reaction bottlenecks help explain rate-determining steps in multistep reaction mechanisms. In a mechanism with several elementary steps, one step is often much slower than the others. That slowest step is called the rate-limiting step, or rate-determining step. A reaction cannot move faster than its slowest step, so this step controls the overall reaction rate.

The idea is like traffic on a four-lane freeway with one lane closed. Cars can only move as fast as the bottleneck allows. In the same way, the slowest elementary step sets the pace for the net chemical reaction.

Rate laws can be written directly from balanced equations for elementary reactions. For most reactions, though, the balanced equation shows only the overall change in the system. It does not show each step in the mechanism. For those cases, the rate law must be found from experimental data first, and the mechanism is then tested against that rate law.

The reaction between nitrogen dioxide and carbon monoxide shows this idea well. At temperatures above 225 °C, the experimental rate law is first order in NO2 and first order in CO. That matches a single-step bimolecular mechanism, so that mechanism may apply at high temperature. Below 225 °C, the rate law changes and becomes second order in NO2. That form does not fit the one-step idea, but it does fit a two-step mechanism with a slower first step.

When the rate-determining step is the first step in a mechanism, the overall rate law is the same as the rate law for that step. The rate law can be harder to build when a fast, reversible step happens first. In that case, reaction intermediates can appear. A reversible reaction is at equilibrium when the forward and reverse rates are equal. This idea can be used to rewrite the concentration of an intermediate, such as N2O2 formed when NO dimerizes, in terms of the reactant NO.

The same method works for a reaction between nitrogen monoxide and molecular chlorine. A two-step mechanism is proposed for this reaction, and the two elementary equations are added to get the overall reaction. Step 2 is the rate-determining step, so its rate law describes the overall reaction. Because that rate law includes the intermediate NOCl2, Step 1 is used to express the intermediate concentration in terms of the reactants. Treating Step 1 as an equilibrium step and substituting that result into the rate law for Step 2 gives the final rate law for the overall reaction.

Reaction Bottlenecks in Chemical Kinetics

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Reaction bottlenecks help explain rate-determining steps in multistep reaction mechanisms. In a mechanism with several elementary steps, one step is often much slower than the others. That slowest step is called the rate-limiting step, or rate-determining step. A reaction cannot move faster than its slowest step, so this step controls the overall reaction rate. The idea is like traffic on a four-lane freeway with one lane closed. Cars can only move as fast as the bottleneck allows. In the same...

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Reaction Bottlenecks in Chemical Kinetics | JoVE K12

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Reaction Bottlenecks in Chemical Kinetics

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