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 velocidad de una reacción química es muy sensible a los cambios de temperatura. Esta dependencia de la temperatura se explica matemáticamente mediante la ecuación de Arrhenius;que expresa la relación entre la constante de velocidad, la temperatura absoluta, el factor de frecuencia y la energía de activación. La energía de activación y el factor de frecuencia también se pueden determinar gráficamente convirtiendo la ecuación de Arrhenius en una forma no exponencial.Utilizando los logaritmos naturales en ambos lados, se genera una ecuación para una función lineal. El valor de la pendiente corresponde al valor negativo de la energía de activación sobre la constante del gas, y la intersección con el eje y corresponde al logaritmo natural del factor de frecuencia. Esta ecuación se puede utilizar para generar una gráfica llamada gráfica de Arrhenius, en la que el logaritmo natural de la constante de velocidad se designa como una función de la inversa de la temperatura en kelvins.Los datos cinéticos de experimentos y reacciones se pueden ilustrar y analizar utilizando este gráfico de Arrhenius. En este ejemplo, el gráfico produce una línea recta. El valor de la pendiente dado en kelvins se iguala al valor negativo de la energía de activación sobre R.Después de asignar el valor de la constante de gas y despejar la energía de activación, se obtiene un valor de 93, 1 kilojulios por mol.Además, la intersección con el eje y de 26, 8 es igual al logaritmo natural del factor de frecuencia. Por lo tanto, la solución para A da el valor de 4, 36 10¹¹ con la unidad de uno sobre molaridad-segundos, la misma unidad que la constante de velocidad. En casos de datos cinéticos limitados o dificultades con la representación gráfica, se puede utilizar una forma de dos puntos de la ecuación de Arrhenius para calcular la energía de activación de una manera no gráfica.En tales casos, la forma no exponencial de la ecuación de Arrhenius se modifica para incluir constantes de velocidad a dos temperaturas diferentes. La substracción y el reordenamiento subsiguientes de la expresión producen la forma de dos puntos de la ecuación de Arrhenius, que se utiliza para calcular la energía de activación a partir de constantes de velocidad generadas experimentalmente a dos temperaturas diferentes. Cuando se substituyen los valores, se calcula que la energía de activación para esta reacción es de 145 kilojulios por mol.

los gráficos de arrhenius

La ecuación de Arrhenius relaciona la energía de activación y la constante de velocidad, k, para las reacciones químicas. En la ecuación de Arrhenius, −Ea/RT, donde R es la constante de gas ideal, que tiene un valor de 8,314 J/mol·K,T es la temperatura en la escala kelvin, Ea es la energía de activación en J/mol, e es la constante 2,7183, y A es una constante llamada factor de frecuencia, que está relacionado con la frecuencia de las colisiones y la orientación de las moléculas que reaccionan.
 La ecuación de Arrhenius se puede utilizar para calcular la energía de activación de una reacción a partir de datos cinéticos experimentales. Un enfoque conveniente para determinar la Ea para una reacción implica la medición de k a dos o más temperaturas diferentes. Utiliza una versión modificada de la ecuación de Arrhenius que toma la forma de una ecuación lineal:
  <img alt="Eq1" src="/files/ftp_upload/11380/11380_Equation_1.png" style="height: 200px;" />
 Un gráfico de lnk frente a 1/T es lineal con una pendiente igual a −Ea/R y una intercepción y igual a lnA.
 Considere la siguiente reacción:
  <img alt="Eq2" src="/files/ftp_upload/11380/11380_Equation_2.png" style="height: 50px;" />
 La energía de activación de esta reacción se puede determinar si la variación en la constante de velocidad con la temperatura se conoce a partir de los datos cinéticos de la reacción, como se muestra.
 <table style="margin-left: auto; margin-right: auto;">
 <tbody>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">Temperatura (K)</td>
 <td style="color: black; border: 1px solid black; text-align: center;">Constante de velocidad (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>
 Los datos proporcionados pueden utilizarse para obtener los valores de la inversa de la temperatura (1/T) y el registro natural de k (lnk).
 <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;">nk</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;" />
 Al trazar los puntos de datos obtenidos con ln k frente a 1/T, se genera un gráfico de líneas que muestra una relación lineal entre lnk y 1/T, como se muestra.
 La pendiente de la línea, que corresponde a la energía de activación, puede estimarse utilizando dos pares de datos experimentales cualesquiera.              
  <img alt="Eq3" src="/files/ftp_upload/11380/11380_Equation_3.png" style="height: 350px;" />
 Un enfoque alternativo para obtener la energía de activación implica la utilización de la constante de velocidad a dos temperaturas diferentes. En este enfoque, la ecuación de Arrhenius se reorganiza en una forma conveniente de dos puntos:
  <img alt="Eq4" src="/files/ftp_upload/11380/11380_Equation_4v2.png" style="height: 75px;" />
 Al reorganizar la ecuación, se genera una expresión para la energía de activación.
  <img alt="Eq5" src="/files/ftp_upload/11380/11380_Equation_5.png" style="height: 75px;" />
 Al sustituir dos pares de datos cualesquiera y realizando los cálculos adicionales se obtiene el valor de la energía de activación en jules por mol o kilojules por mol.
  <img alt="Eq6" src="/files/ftp_upload/11380/11380_Equation_6.png" style="height: 135px;" />
 Este enfoque alternativo de dos puntos produce el mismo resultado que el enfoque gráfico. Sin embargo, en la práctica, el enfoque gráfico normalmente proporciona resultados más fiables mientras se trabaja con datos experimentales reales.
 Este texto es adaptado de<a href="https://openstax.org/books/chemistry-2e/pages/12-5-collision-theory"> Openstax, Química 2e, Sección 12.5: Teoría de las Colisiones</a>.

Los Gráficos de Arrhenius

La ecuación de Arrhenius relaciona la energía de activación y la constante de velocidad, k, para las reacciones químicas. En la ecuación de Arrhenius, k = Ae−Ea/RT, R es ...

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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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