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

K12 Standards

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Chemistry and Physics

IPC.7

IPC.7.F

Determining Order of Reaction

Pour une réaction chimique, la loi de vitesse exprime la relation entre la vitesse de réaction et la concentration du réactif. Les exposants des concentrations de réactif influencent individuellement la vitesse de réaction et sont dites les ordres de réaction. L'ordre de réaction est déterminé expérimentalement en utilisant la méthode des taux initiaux, où un produit chimique la réaction est répétée plusieurs fois avec différents concentrations réactives pour mesurer les vitesses de réaction initiales.Une augmentation de la concentration de réactif, produisant une augmentation linéairement proportionnelle dans la vitesse de réaction, qui caractérise une réaction de premier ordre. Si doubler la concentration de réactif multiplie par quatre la vitesse initiale, alors une réaction de second ordre est observée. Cependant, si le changement des concentrations de réactif n'affecte pas les valeurs de taux initiales, alors une réaction d'ordre zéro est observée.Lorsque les données obtenues des taux initiaux présentent une relation indiscernable entre le changement en concentration initiale de réactif et le taux correspondant, un rapport de lois de taux est calculé. Ici, deux valeurs de concentration quelconques du réactif et leurs vitesses de réaction correspondantes sont utilisés pour déterminer l'ordre de réaction. Mais qu'en est-il des réactions avec plusieurs réactifs?Premièrement, en utilisant la méthode des taux initiaux, l'ordre de réaction de chaque réactif est déterminé individuellement. Ensuite, les ordres de réaction individuels sont exprimés en exposants de leur concentrations réactif respectif pour formuler la loi des taux. Enfin, la somme des exposants individuels de la loi de vitesse détermine l'ordre de réaction global.Alors que l'ordre de réaction décrit la dépendance de la vitesse de réaction sur la concentration de réactif, une mesure directe de la vitesse de réaction relative est indiquée par la constante de vitesse. La constante de vitesse k, est le coefficient de proportionnalité reliant la vitesse de réaction au produit des concentrations des réactifs. L'unité d'une constante de vitesse dépend de l'ordre de réaction globale et peut être déterminé en réorganisant la loi des taux pour résoudre la constante de vitesse.Pour une réaction d'ordre zéro, k a l'unité de molarité par seconde. L'unité pour une réaction de premier ordre est une sur secondes, et pour une réaction de second ordre, il est un sur molarité-secondes. Une constante de vitesse élevée indique une réaction rapide.Inversement, une constante de taux plus petite indique une réaction lente. Une valeur de zéro signifie l'absence de toute réaction chimique.

détermination de l'ordre de réaction

Les lois de vitesse décrivent la relation entre la vitesse d'une réaction chimique et la concentration de ses réactifs. Dans une loi de vitesse, la constante de vitesse k et les ordres de la réaction sont déterminés expérimentalement en observant comment la vitesse de réaction change au fur et à mesure que les concentrations des réactifs sont modifiées. Une approche expérimentale courante pour la détermination des lois de vitesse est la méthode des vitesses initiales. Cette méthode consiste à mesurer les vitesses de réaction pour de multiples essais expérimentaux réalisés en utilisant différentes concentrations initiales de réactifs. La comparaison des vitesses mesurées pour ces essais permet de déterminer les ordres de la réaction et, par la suite, la constante de vitesse, qui conjointement servent à formuler une loi de vitesse. 
 La vitesse d'une réaction, par exemple, impliquant l'oxyde nitrique avec l'ozone [NO (g) + O3 (g) ⟶ NO2 (g) + O2 (g)] peut être déterminée à partir des données expérimentales de la méthode des vitesses initiales,  en laboratoire. 
 <table style="margin-left: auto; margin-right: auto;">
 <tbody>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">  Essai    </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>
 À partir des données de vitesse, on formule une loi de vitesse générale ; vitesse = k[NO]m[O3]n. Les valeurs des ordres de réaction m et n et de la constante de vitesse k sont déterminées à partir des données expérimentales en utilisant un procédé en trois parties : 
 À l'étape 1, la valeur de m est déterminée à partir des données dans lesquelles [NO] varie et [O3] est constant. Dans les essais 3, 4 et 5, [NO] varie alors que [O3] reste constant. Lorsque [NO] double de l'essai 3 à 4, la vitesse double, et quand [NO] triple de l'essai 3 à 5, la vitesse triple également. Ainsi, la vitesse est également directement proportionnelle à [NO], et m dans la loi de vitesse est égal à 1. 
 À l'étape 2, la valeur de n est déterminée à partir de données dans lesquelles [Cl2] varie et [NO] est constant. 
 <img alt="Eq4" src="/files/ftp_upload/11376/11376_Equation 4.png" style="text-align: center; height: 120px;" />
 En utilisant les valeurs calculées dem et n, la loi de vitesse est exprimée sous la forme vitesse = k[NO]2[Cl2]. 
 À l'étape 3, la valeur numérique de la constante de vitesse k est déterminée avec les unités appropriées. Les unités de la vitesse d'une réaction sont mol/L·s. Les unités de k sont déduites en substituant les unités de tous les autres paramètres de la loi de vitesse. Dans cet exemple, les unités de concentration sont mol3/L3. Les unités de k doivent être L2/mol2·s de sorte que la vitesse soit en mol/L·s. La valeur de k est déterminée une fois que l'expression de la loi de vitesse a été résolue, en substituant simplement les valeurs de n'importe lequel des essais expérimentaux (par exemple, l'essai 1). 
 <img alt="Eq5" src="/files/ftp_upload/11376/11376_Equation 5.png" style="text-align: center; height: 70px;" />
 Ordre de réaction et unités de la constante de vitesse 
 Dans certaines réactions, il se peut que les ordres de réaction dans la loi de vitesse soient les mêmes que les coefficients dans l'équation chimique de la réaction. Ce n'est qu'une coïncidence et pas le cas très souvent. Les lois de vitesse peuvent présenter des ordres fractionnaires pour certains réactifs, et des ordres de réaction négatifs sont parfois observés lorsqu'une augmentation de la concentration d'un réactif entraîne une diminution de la vitesse de réaction. Les lois de vitesse sont déterminées expérimentalement uniquement et ne sont pas prédites de façon fiable d'après la stœchiométrie de la réaction. 
 Les unités d'une constante de vitesse varient selon l'ordre global de la réaction. L'unité de la constante de vitesse pour une réaction d'ordre zéro est mol/l#183;s (ou M/s) et celle d'une réaction de premier ordre est 1/s. L'unité de la constante de vitesse pour une réaction de deuxième ordre est L/mol#183;s (ou 1/M#183;s) et celle d'une réaction de troisième ordre est L2/mol2#183;s. Bien que les unités spécifiques de concentration et de temps soient indiquées par (mol/L) et (s), toute autre unité valable peut être utilisée pour représenter les propriétés de concentration et de temps. 
 Ce texte est adapté de <a href="https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws#57033"> Openstax, Chimie 2e, Section 12.3 : Lois de vitesse. </a>

Détermination de l'ordre de réaction

Les lois de vitesse décrivent la relation entre la vitesse d’une réaction chimique et la concentration de ses réactifs. Dans une loi de taux, la constante de taux k et ...

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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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determining order of reaction

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,...

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key terms and concepts

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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Finding Rate Law from Initial Rates

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