Name: finding rate law from initial rates
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 53 s
Channel: JoVE

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Determining Order of Reaction

Per una reazione chimica, la legge della velocità esprime la relazione fra la velocità della reazione e la concentrazione del reagente. Gli esponenti delle concentrazioni dei reagenti influenzano individualmente la velocità di reazione e sono detti ordini di reazione. L'ordine di reazione è determinato sperimentalmente usando il metodo delle velocità iniziali, in cui una reazione chimica viene ripetuta più volte con concentrazioni di reagenti variabili per misurare le velocità di reazione iniziali.

Un aumento della concentrazione del reagente, che produce un aumento linearmente proporzionale della velocità di reazione, caratterizza una reazione di primo ordine. Se raddoppiando la concentrazione del reagente la velocità iniziale quadruplica, si osserva una reazione di secondo ordine. Tuttavia, se la variazione delle concentrazioni dei reagenti non influisce sui valori della velocità iniziale, allora si osserva una reazione di ordine zero.

Quando i dati delle velocità iniziali ottenuti presentano una relazione indiscernibile fra la variazione della concentrazione iniziale di reagenti e la velocità corrispondente, si calcola un rapporto delle leggi di velocità. Qui, due qualsiasi valori di concentrazione del reagente e le loro corrispondenti velocità di reazione sono utilizzati per determinare l'ordine di reazione. E per quanto riguarda le reazioni con più reagenti?

Innanzitutto, utilizzando il metodo delle velocità iniziali, l'ordine di reazione di ciascun reagente è determinato individualmente. Poi, i singoli ordini di reazione sono espressi come esponenti delle rispettive concentrazioni di reagenti per formulare la legge della velocità. Infine, la somma dei singoli esponenti dalla legge della velocità determina l'ordine complessivo della reazione.

Mentre l'ordine della reazione rappresenta la dipendenza della velocità di reazione dalla concentrazione del reagente, una misura diretta della velocità di reazione relativa è indicata dalla costante di velocità. La costante di velocità k è il coefficiente di proporzionalità che collega la velocità di reazione al prodotto delle concentrazioni dei reagenti. L'unità di una costante di velocità dipende dall'ordine di reazione generale e può essere determinata riorganizzando la legge della velocità per risolvere la costante di velocità.

Per una reazione di ordine zero, k ha la molarità unitaria per secondi. L'unità per una reazione di primo ordine è uno su secondi, e per una reazione di secondo ordine è uno su molarità-secondi. Una costante di velocità elevata indica una reazione rapida.

Al contrario, una costante di velocità più piccola indica una reazione lenta. Un valore di zero indica l'assenza di qualsiasi reazione chimica.

determinazione dell'ordine di reazione

Le leggi sulla velocit descrivono la relazione tra la velocit di una reazione chimica e la concentrazione dei suoi reagenti. In una legge di velocit, la costante di velocit k e l'ordine di reazione vengono determinati sperimentalmente osservando come cambia la velocit di reazione al variare della concentrazione dei reagenti. Un approccio sperimentale comune alla determinazione dellequazione cinetica il metodo delle tariffe iniziali. Questo metodo prevede la misurazione delle velocit di reazione per pi prove sperimentali effettuate utilizzando diverse concentrazioni iniziali dei reagenti. Confrontando le velocit misurate per queste prove possibile determinare gli ordini di reazione e, successivamente, la costante di velocit, che insieme vengono utilizzati per formulare una legge sulla velocit.

Per esempio, la velocit di una reazione che coinvolge l'ossido nitrico con l'ozono [NO (g) + O_3 (g) ? NO_2 (g) + O_2 (g)] pu essere determinata dai dati sperimentali del metodo delle velocit iniziali, nel laboratorio.

<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">  Trial     </td>
			<td style="color: black; border: 1px solid black; text-align: center;"> [NO] (mol/L)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">[O3] (mol/L)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">  Δ[NO2]/Δt (mol/L·s)  </td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">1</td>
			<td style="color: black; border: 1px solid black; text-align: center;">     1.00 × 10−6      </td>
			<td style="color: black; border: 1px solid black; text-align: center;">   3.00 × 10−6    </td>
			<td style="color: black; border: 1px solid black; text-align: center;">    6.60 × 10−5     </td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">2</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.00 × 10−6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">6.00 × 10−6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.32 × 10−4</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">3</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.00 × 10−6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">9.00 × 10−6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.98 × 10−4</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">4</td>
			<td style="color: black; border: 1px solid black; text-align: center;">2.00 × 10−6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">9.00 × 10−6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">3.96 × 10−4</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">5</td>
			<td style="color: black; border: 1px solid black; text-align: center;">3.00 × 10−6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">9.00 × 10−6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">5.94 × 10−4</td>
		</tr>
	</tbody>
</table>

Dai dati tariffari, una generica legge tariffaria; tasso = k[NO]^m[O_3]^n formulato. I valori degli ordini di reazione m e n e la costante di velocit k sono determinati dai dati sperimentali utilizzando un processo in tre parti:

Nel passaggio 1, il valore di m viene determinato dai dati in cui [NO] varia e [O_3] costante. Nelle prove 3, 4 e 5, [NO] varia mentre [O_3] rimane costante. Quando [NO] raddoppia dalla prova 3 alla 4, la velocit raddoppia, e quando [NO] triplica dalla prova 3 alla 5, anche la velocit triplica. Pertanto, anche la velocit direttamente proporzionale a [NO] e m nella legge sulla velocit uguale a 1.

Nella fase 2, il valore di n viene determinato dai dati in cui [O_3] varia e [NO] costante. Nelle prove 1,2 e 3, [NO] costante e [O_3] varia. La velocit di reazione cambia in modo direttamente proporzionale alla variazione di [O_3]. Quando [O_3] raddoppia dalla prova 1 alla 2, la velocit raddoppia; quando l'[O_3] triplica dalla prova 1 alla 3, anche la velocit aumenta e triplica. Pertanto, la velocit direttamente proporzionale a [O_3] e n uguale a 1. La legge sulla velocit quindi: velocit = k [NO]^1 [O_3]^1 = k [NO][O_3]

Nella fase 3, il valore di k viene determinato da una serie di concentrazioni (ad esempio, i dati della prova 1) e dalla velocit corrispondente.

<img alt="Eq1" src="/files/ftp_upload/11376/11376_Equation 1.png" style="text-align: center; height: 145px;" />

Nelle reazioni in cui i dati del metodo delle velocit iniziali non implicano direttamente la relazione tra le concentrazioni iniziali e le velocit iniziali, possibile utilizzare un calcolo che coinvolga il rapporto delle leggi di velocit per calcolare l'ordine di reazione e la costante di velocit.

Ad esempio, la legge generale sulla velocit per la reazione 2 NO (g) + Cl_2 (g) ? 2 NOCl (g) espressa come: velocit = k [NO]^m [Cl_2]^n.

I dati derivanti dal metodo delle aliquote iniziali sono:

<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">  Trial    </td>
			<td style="color: black; border: 1px solid black; text-align: center;">  [NO] (mol/L)  </td>
			<td style="color: black; border: 1px solid black; text-align: center;">  [Cl2] (mol/L)  </td>
			<td style="color: black; border: 1px solid black; text-align: center;">  Initial Rate (mol/L·s)     </td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">1</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.10</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.10</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.00300</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">2</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.10</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.15</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.00450</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">3</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.15</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.10</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.00675</td>
		</tr>
	</tbody>
</table>

I valori di m e n possono essere determinati dai dati sperimentali utilizzando un approccio algebrico, in seguito al quale viene determinato il valore di k.

Nella fase 1, il valore di m viene determinato dai dati in cui [NO] varia e [Cl_2] costante. Un rapporto tra lequazione cinetica viene espresso sostituendo i dati di due diversi studi (ad esempio studio 3 e studio 1).

<img alt="Eq2" src="/files/ftp_upload/11376/11376_Equation 2.png" style="text-align: center; height: 260px;" />

Nella fase 2, il valore di n viene determinato dai dati in cui [Cl_2] varia e [NO] costante.

<img alt="Eq4" src="/files/ftp_upload/11376/11376_Equation 4.png" style="text-align: center; height: 120px;" />

Utilizzando i valori calcolati di m e n la legge sulla velocit espressa come velocit = k [NO]2 [Cl_2].

Nella fase 3, il valore numerico della costante di velocit k viene determinato con unit appropriate. Le unit per la velocit di una reazione sono mol/Ls. Le unit per k si concludono sostituendo le unit di tutti gli altri parametri nella legge sui tassi. In questo esempio, le unit di concentrazione sono mol_3/L_3. Le unit per k dovrebbero essere L_2/mol_2s in modo che la velocit sia in termini di mol/Ls. Il valore di k viene determinato una volta risolta l'espressione della legge cinetica, semplicemente sostituendo i valori di una qualsiasi delle prove sperimentali (ad esempio prova 1).

<img alt="Eq5" src="/files/ftp_upload/11376/11376_Equation 5.png" style="text-align: center; height: 70px;" />

Ordine di reazione e unit della costante della velocit

In alcune reazioni, gli ordini di reazione nella legge sulla velocit sono gli stessi dei coefficienti nell'equazione chimica della reazione. Questa solo una coincidenza e molto spesso non cos. Le leggi sulla velocit possono mostrare ordini frazionari per alcuni reagenti e talvolta si osservano ordini di reazione negativi quando un aumento della concentrazione di un reagente provoca una diminuzione della velocit di reazione. Lequazione cinetica sono determinate solo sperimentalmente e non sono previste in modo affidabile dalla stechiometria della reazione.

Le unit per una costante di velocit varieranno in modo appropriato per adattarsi all'ordine generale della reazione. L'unit della costante di velocit per una reazione di ordine zero mol/Ls (o M/s) e quella per una reazione di primo ordine 1/s. L'unit della costante di velocit per una reazione del secondo ordine L/mols (o 1/Ms) e quella per una reazione del terzo ordine L_2/mol_2s. Sebbene le unit specifiche per concentrazione e tempo siano indicate come (mol/L) e (s), qualsiasi altra unit valida pu essere utilizzata per rappresentare le propriet della concentrazione e del tempo.

Questo testo adattato da <a href="https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws#57033">Openstax, Chemistry 2e, Section 12.3: Rate Laws.</a>

Determinazione dell'ordine di reazione

Le leggi di velocità descrivono la relazione tra la velocità di una reazione chimica e la concentrazione dei suoi reagenti. In una legge di velocità, la costante di velocità k e ...

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finding rate law from initial rates

Rate laws connect the speed of a chemical reaction to the concentration of its reactants. The rate constant, k, and the reaction orders are not taken from the chemical equation. They are found experimentally by watching how the rate changes when the reactant concentrations change.

One common way to do this is the method of initial rates. In this method, several trials are run with different starting concentrations. The measured rates are then compared to determine the reaction orders and, after that, the rate constant. These values are used to write the rate law.

For the reaction of nitric oxide with ozone, NO(g) + O3(g) → NO2(g) + O2(g), the data show how this works in the lab. When [NO] is held constant and [O3] changes, the rate changes in the same way. When [O3] doubles, the rate doubles. When [O3] triples, the rate triples. This shows that the reaction is first order in O3. A similar comparison using trials where [O3] stays constant shows that the rate is also directly proportional to [NO], so the reaction is first order in NO as well. The rate law is therefore rate = k[NO][O3].

In other reactions, the orders are found with an algebraic ratio of rate laws. For the reaction 2 NO(g) + Cl2(g) → 2 NOCl(g), the rate law is written as rate = k[NO]m[Cl2]n. Using the trial data, one step gives m = 2 and another gives n = 1. The rate law becomes rate = k[NO]2[Cl2]. The value of k is then found by using one trial and solving for the constant.

The units of the rate constant depend on the overall order of the reaction. Rate is measured in mol/L·s, and the units for k must match the rate law. For this example, the concentration terms give mol3/L3, so k must have units of L2/mol2·s. In general, a zero-order reaction has k in mol/L·s, a first-order reaction has k in 1/s, a second-order reaction has k in L/mol·s, and a third-order reaction has k in L2/mol2·s.

Reaction order does not always match the coefficients in the balanced equation. That match can happen, but it is only a coincidence. Rate laws can also include fractional orders, and some reactants can have negative orders if a higher concentration lowers the reaction rate. Because of this, rate laws are determined by experiment, not by stoichiometry. Although the examples here use mol/L and s, other valid concentration and time units can also be used.

Finding Rate Law from Initial Rates

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Use initial-rate data to find reaction order and the rate constant. Explore examples with NO, ozone, and NOCl, plus how rate constant units change.

Finding Rate Law from Initial Rates | JoVE K12

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Classifying Matter by Composition

Matter: Pure Substances and Mixtures
According to its composition, the matter can be classified into two broad categories &mdash; pure substances and ...

Phase Transitions

Whether solid, liquid, or gas, a substance&#39;s state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the ...

phase-transitions-vaporization-and-condensation

Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize ...

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy ...

phase-transitions-sublimation-and-deposition

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and ...

Melting Points

Melting Points in Organic Chemistry
The melting point of a compound is the temperature at which the solid phase transitions into the liquid phase at a ...

Boiling Points

Source: Lara Al Hariri at the University of Massachusetts Amherst, MA, USA

	Preparation of the LaboratoryExpand
	Here, we show the laboratory preparation ...

Explain how physical and chemical properties of substances are related to their usage in everyday life such as in sunscreen, cookware, industrial applications, and fuels.

IPC.7.C

Emission Spectra

When solids, liquids, or condensed gases are heated sufficiently, they radiate some of the excess energy as light. Photons produced in this manner have a ...

Metal Flame Emission

Metal Flame Emission
Flame testing is an analytical technique where a sample is placed in a flame, and the characteristic flame color is used to identify ...

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution ...

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that ...

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are ...

Explain how electrons can transition from a high energy level to a low energy state, emitting photons at different frequencies for different energy transitions.

IPC.7.D

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a ...

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that ...

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of ...

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy ...

Balmer Series

The Bohr Model
Niels Bohr proposed a model for the hydrogen atom in 1913 that described discrete energy states are associated with a fixed electron orbit ...

Beer's Law

Absorbance and Fluorescence
When light hits a substance, it is either absorbed, transmitted, or reflected. Typically, a substance interacts with a range ...

The Wave Nature of Light

The nature of light has been a subject of inquiry since antiquity. In the seventeenth century, Isaac Newton performed experiments with lenses and prisms ...

Explain how atomic energy levels and emission spectra present evidence for the wave particle duality.

IPC.7.E

Science concepts. The student knows that relationships exist between the structure and properties of matter. The student is expected to:

Finding Rate Law from Initial Rates

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