Name: determining activation energy from temperature
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 34 s
Channel: JoVE

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Arrhenius Plots

La vitesse d'une réaction chimique est très sensible aux changements en température. Cette dépendance à la température est mathématiquement expliquée en utilisant l'équation d'Arrhenius;ce qui exprime la relation entre la vitesse constante, la température absolue, le facteur de fréquence et l'énergie d'activation. L'énergie d'activation et le facteur de fréquence peuvent également être déterminé graphiquement en convertissant l'équation d'Arrhenius sous une forme non exponentielle.En utilisant les logarithmes naturels des deux côtés, une équation pour une fonction linéaire est générée. La valeur de la pente correspond à la valeur négative d'énergie d'activation par rapport à la constante de gaz, et l'ordonnée à l'origine correspond au logarithme naturel du facteur de fréquence. Cette équation peut être utilisée pour générer un graphe appelé le graphe d'Arrhenius, dans lequel le logarithme naturel du taux constante est notée en fonction de l'inverse de la température en kelvin.Données cinétiques d'expérimentations et de réactions peuvent être illustrées et analysées à l'aide de ce graphique d'Arrhenius. Dans cet exemple, le graphe donne une ligne droite. La valeur de pente donnée en kelvin est réglé égal à la valeur négative de l'énergie d'activation sur R.Après avoir attribué la valeur de la constante de gaz et la résolution de l'énergie d'activation, une valeur de 93, 1 kilojoules par mole est obtenue.De plus, l'ordonnée à l'origine de 26, 8 est égal au logarithme naturel du facteur de fréquence. Ainsi, la résolution de A donne la valeur de 4, 36 10¹¹ avec l'unité une sur la molarité-secondes la même unité que la constante de vitesse. En cas de données cinétiques limitées ou de difficultés avec représentation graphique, une forme en deux points de l'équation d'Arrhenius peut être utilisée pour calculer l'énergie d'activation de manière non graphique.Dans de tels cas, la forme non exponentielle de l'équation d'Arrhenius est modifiée pour inclure des constantes de vitesse à deux températures différentes. Soustraction et réarrangement ultérieurs de l'expression donnent la forme à deux points de l'équation d'Arrhenius, qui est utilisé pour calculer l'énergie d'activation de constantes de taux générées expérimentalement à deux températures différentes. En substituant les valeurs, l'énergie d'activation pour cette réaction est calculée à 145 kilojoules par mole.

tracés d'arrhenius

La loi d'Arrhénius relie l'énergie d'activation et la constante de vitesse, k, pour les réactions chimiques. Dans l'équation d'Arrhénius, k = Ae−Ea/RT, R est la constante du gaz parfait, qui a une valeur de 8,314 J/mol·K, T est la température sur l'échelle de Kelvin, Ea est l'énergie d'activation en J/mole, e est la constante 2,7183 et A est une constante appelée le facteur de fréquence, qui est lié à la fréquence des chocs et à l'orientation des molécules qui réagissent. 
 L'équation d'Arrhénius peut être utilisée pour calculer l'énergie d'activation d'une réaction à partir de données cinétiques expérimentales. Une approche pratique pour déterminer l'Ea d'une réaction implique la mesure de k à deux ou plusieurs températures différentes. Elle utilise une version modifiée de l'équation d'Arrhénius qui prend la forme d'une équation linéaire : 
  <img alt="Eq1" src="/files/ftp_upload/11380/11380_Equation_1.png" style="height: 200px;" />
 Un tracé de ln k par rapport à 1/T est linéaire, avec une pente égale à −Ea/R et une ordonnée à l'origine égale à ln A. 
 Réfléchissez à la réaction suivante : 
  <img alt="Eq2" src="/files/ftp_upload/11380/11380_Equation_2.png" style="height: 50px;" />
 L'énergie d'activation de cette réaction peut être déterminée si la variation de la constante de vitesse avec la température est connue à partir des données cinétiques de la réaction, comme illustré. 
 <table style="margin-left: auto; margin-right: auto;">
 <tbody>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">Température (K) </td>
 <td style="color: black; border: 1px solid black; text-align: center;">Constante de vitesse (L/mol/s) </td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">555 </td>
 <td style="color: black; border: 1px solid black; text-align: center;">3,52 × 10–7 </td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">575 </td>
 <td style="color: black; border: 1px solid black; text-align: center;">1,22 × 10–6 </td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">645 </td>
 <td style="color: black; border: 1px solid black; text-align: center;">8,59 × 10–5 </td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">700 </td>
 <td style="color: black; border: 1px solid black; text-align: center;">1,16 × 10–3 </td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">781 </td>
 <td style="color: black; border: 1px solid black; text-align: center;">3,95  × 10–2 </td>
 </tr>
 </tbody>
 </table>
 Les données fournies peuvent être utilisées pour déduire les valeurs de l'inverse de la température (1/T) et du logarithme népérien de k (ln k). 
 <table style="margin-left: auto; margin-right: auto;">
 <tbody>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">1/T (K–1) </td>
 <td style="color: black; border: 1px solid black; text-align: center;">ln k</td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">   1,80 × 10–3    </td>
 <td style="color: black; border: 1px solid black; text-align: center;">    –14,860    </td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">1,74 × 10–3 </td>
 <td style="color: black; border: 1px solid black; text-align: center;">–13,617 </td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">1,55 × 10–3 </td>
 <td style="color: black; border: 1px solid black; text-align: center;">–9,362 </td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">1,43 × 10–3 </td>
 <td style="color: black; border: 1px solid black; text-align: center;">–6,759 </td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">1,28 × 10–3 </td>
 <td style="color: black; border: 1px solid black; text-align: center;">–3,231 </td>
 </tr>
 </tbody>
 </table>
  <img alt="Image1" src="/files/ftp_upload/11380/11380_Image 1.png" style="height: 350px;" />
 En traçant les points déduits des données avec ln k par rapport à 1/T, un graphe linéaire présentant une relation linéaire entre ln k et 1/T est généré, comme illustré. 
 La pente de la droite, qui correspond à l'énergie d'activation, peut être estimée à l'aide de deux des paires de données expérimentales.              
  <img alt="Eq3" src="/files/ftp_upload/11380/11380_Equation_3.png" style="height: 350px;" />
 Une autre approche pour déduire l'énergie d'activation implique l'utilisation de la constante de vitesse à deux températures différentes. Pour cette approche, l'équation d'Arrhenius est réorganisée sous une forme à deux points pratique : 
  <img alt="Eq4" src="/files/ftp_upload/11380/11380_Equation_4v2.png" style="height: 75px;" />
 Lors de la réorganisation de l'équation, une expression pour l'énergie d'activation est générée. 
  <img alt="Eq5" src="/files/ftp_upload/11380/11380_Equation_5.png" style="height: 75px;" />
 En substituant deux paires de données et en effectuant davantage de calculs, on obtient la valeur de l'énergie d'activation en joules par mole ou kilojoules par mole. 
  <img alt="Eq6" src="/files/ftp_upload/11380/11380_Equation_6.png" style="height: 135px;" />
 Cette autre approche à deux points donne le même résultat que l'approche graphique. Cependant, dans la pratique, l'approche graphique fournit généralement des résultats plus fiables tout en travaillant avec des données expérimentales réelles. 
 Ce texte est adapté de<a href="https://openstax.org/books/chemistry-2e/pages/12-5-collision-theory"> Openstax, Chimie 2e, Section 12.5 : Théorie des collisions</a>.

Tracés d'Arrhenius

L’équation d’Arrhenius relie l’énergie d’activation et la constante de vitesse, k, pour les réactions chimiques. Dans l’équation d’Arrhenius, k = Ae−Ea/RT, R est ...

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determining activation energy from temperature

The Arrhenius equation links activation energy and the rate constant, k, for chemical reactions. It is written as k = Ae−Ea/RT. In this equation, R is the ideal gas constant with a value of 8.314 J/mol·K, T is the temperature on the kelvin scale, Ea is the activation energy in J/mole, e is the constant 2.7183, and A is the frequency factor. The frequency factor depends on collision frequency and the orientation of reacting molecules.

Experimental kinetic data can be used to find the activation energy of a reaction. One practical method is to measure k at two or more temperatures. The Arrhenius equation can then be rewritten in a linear form. A plot of ln k versus 1/T gives a straight line. The slope equals −Ea/R, and the y-intercept equals ln A.

For example, a reaction with known rate constants at 555 K, 575 K, 645 K, 700 K, and 781 K can be analyzed this way. The rate constants are 3.52 × 10−7, 1.22 × 10−6, 8.59 × 10−5, 1.16 × 10−3, and 3.95 × 10−2 L/mol/s, respectively. These values can be converted to 1/T and ln k. The resulting data set can then be plotted to show the linear relationship between ln k and 1/T.

The slope of the line gives the activation energy. It can be estimated from any two experimental data pairs on the graph. Another option is the two-point form of the Arrhenius equation. This rearranged equation uses rate constants at two temperatures to calculate Ea directly. Both methods give the same result. In practice, the graphical method is often more reliable when working with real experimental data.

Determining Activation Energy from Temperature

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The Arrhenius equation links activation energy and the rate constant, k, for chemical reactions. It is written as k = Ae−Ea/RT. In this equation, R is the ideal gas constant with a value of 8.314 J/mol·K, T is the temperature on the kelvin scale, Ea is the activation energy in J/mole, e is the constant 2.7183, and A is the frequency factor. The frequency factor depends on collision frequency and the orientation of reacting molecules. Experimental kinetic data can be used to find the activation...

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Determining Activation Energy from Temperature

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