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

De snelheid van een chemische reactie is zeer gevoelig voor temperatuurveranderingen. Deze temperatuurafhankelijkheid wordt wiskundig verklaard met behulp van de Arrhenius-vergelijking;die de relatie uitdrukt tussen de snelheidsconstante, de absolute temperatuur, de frequentiefactor en de activeringsenergie. De activeringsenergie en frequentiefactor kunnen ook grafisch worden bepaald door de Arrhenius-vergelijking om te zetten in een niet-exponentiële vorm.Met behulp van de natuurlijke logaritmen aan beide zijden wordt een vergelijking voor een lineaire functie gegenereerd. De hellingwaarde komt overeen met de negatieve waarde van activeringsenergie boven gasconstante, en het y-snijpunt komt overeen met de natuurlijke log van de frequentiefactor. Deze vergelijking kan worden gebruikt om een grafiek te genereren die de Arrhenius-grafiek wordt genoemd, waarin de natuurlijke log van de snelheidsconstante wordt aangegeven als een functie van de inverse van de temperatuur in Kelvin.Kinetische gegevens van experimenten en reacties kunnen worden geïllustreerd en geanalyseerd met behulp van deze Arrhenius-grafiek. In dit voorbeeld levert de grafiek een rechte lijn op. De hellingswaarde in Kelvin wordt gelijk gesteld aan de negatieve waarde van activeringsenergie boven R.Na het toekennen van de waarde voor de gasconstante en het oplossen van de activeringsenergie wordt een waarde van 93, 1 kilojoules per mol verkregen.Bovendien is het y-snijpunt van 26, 8 gelijk aan de natuurlijke log van de frequentiefactor. Het oplossen van A geeft dus de waarde van 4, 36 10¹¹ met de eenheid één-gedeeld-door-molariteit-seconden dezelfde eenheid als de snelheidsconstante. In het geval van beperkte kinetische gegevens of problemen met grafische weergave, kan een tweepuntsvorm van de Arrhenius-vergelijking worden gebruikt om de activeringsenergie op een niet-grafische manier te berekenen.In dergelijke gevallen wordt de niet-exponentiële vorm van de Arrhenius-vergelijking gewijzigd om snelheidsconstanten bij twee verschillende temperaturen op te nemen. Daaropvolgende aftrekking en herschikking van de uitdrukking levert de tweepuntsvorm van de Arrhenius-vergelijking op, die wordt gebruikt om de activeringsenergie te berekenen uit experimenteel gegenereerde snelheidsconstanten bij twee verschillende temperaturen. Door de waarden te vervangen, wordt de activeringsenergie voor deze reactie berekend op 145 kilojoules per mol.

arrhenius-vergelijking

De Arrhenius-vergelijking relateert de activeringsenergie en de snelheidsconstante, k, voor chemische reacties. In de vergelijking van Arrhenius, k = Ae−Ea/RT, is R de ideale gasconstante, die een waarde heeft van 8,314 J/mol·K, T is de temperatuur op de Kelvin-schaal, Ea is de activeringsenergie in J/mol, e is de constante 2,7183, en A is een constante die de frequentiefactor wordt genoemd en die verband houdt met de frequentie van botsingen en de oriëntatie van de reagerende moleculen. De Arrhenius-vergelijking kan worden gebruikt om de activeringsenergie van een reactie te berekenen op basis van experimentele kinetische gegevens. Een handige benadering voor het bepalen van de Ea voor een reactie omvat het meten van k bij twee of meer verschillende temperaturen. Het maakt gebruik van een aangepaste versie van de Arrhenius-vergelijking die de vorm aanneemt van een lineaire vergelijking:  <img alt="Eq1" src="/files/ftp_upload/11380/11380_Equation_1.png" style="height: 200px;"> Een grafiek van de ln k versus 1/T is lineair met een helling gelijk aan −Ea/R en een y-snijpunt gelijk aan ln A. Beschouw de volgende reactie:  <img alt="Eq2" src="/files/ftp_upload/11380/11380_Equation_2.png" style="height: 50px;"> De activeringsenergie van deze reactie kan worden bepaald als de variatie in de snelheidsconstante met de temperatuur bekend is uit de kinetische gegevens van de reactie, zoals weergegeven. <table style="margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="color: black; border: 1px solid black; text-align: center;">Temperature (K)</td> <td style="color: black; border: 1px solid black; text-align: center;">Rate constant (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> De verstrekte gegevens kunnen worden gebruikt om de waarden af te leiden van de inverse van temperatuur (1/T) en de natuurlijke log van 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;"> Bij het uitzetten van de afgeleide gegevenspunten met ln k versus 1/T wordt een lijngrafiek gegenereerd die een lineair verband vertoont tussen ln k en 1/T, zoals weergegeven. De helling van de lijn, die overeenkomt met de activeringsenergie, kan worden geschat met behulp van twee van de experimentele dataparen.                <img alt="Eq3" src="/files/ftp_upload/11380/11380_Equation_3.png" style="height: 350px;"> Een alternatieve benadering bij het afleiden van activeringsenergie omvat het gebruik van de snelheidsconstante bij twee verschillende temperaturen. Bij deze benadering wordt de Arrhenius-vergelijking herschikt tot een handige tweepuntsvorm:  <img alt="Eq4" src="/files/ftp_upload/11380/11380_Equation_4v2.png" style="height: 75px;"> Bij het herschikken van de vergelijking wordt een uitdrukking voor de activeringsenergie gegenereerd.  <img alt="Eq5" src="/files/ftp_upload/11380/11380_Equation_5.png" style="height: 75px;"> Door twee willekeurige dataparen te vervangen en verder te berekenen, wordt de waarde voor de activeringsenergie in joule per mol of kilojoule per mol verkregen.  <img alt="Eq6" src="/files/ftp_upload/11380/11380_Equation_6.png" style="height: 135px;"> Deze alternatieve tweepuntsbenadering levert hetzelfde resultaat op als de grafische benadering. In de praktijk levert de grafische benadering echter doorgaans betrouwbaardere resultaten op bij het werken met feitelijke experimentele gegevens.

Arrhenius-vergelijking

The Arrhenius equation relates the activation energy and the rate constant, k, for chemical reactions. In the Arrhenius equation, k = Ae&#8722;Ea/RT, R is ...

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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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Learn how the Arrhenius equation uses temperature and rate constants to find activation energy with a graph or a two-point calculation.

Determining Activation Energy from Temperature | JoVE K12

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Determining Activation Energy from Temperature

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