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

A taxa de uma reação química é altamente sensível às mudanças de temperatura. Esta dependência de temperatura é matematicamente explicada utilizando a equação de Arrhenius;que exprime a relação entre a taxa constante, a temperatura absoluta, o fator de frequência e a energia de ativação. A energia de ativação e o fator de frequência também podem ser determinados graficamente convertendo a Equação de Arrhenius numa forma não-exponencial.Utilizando os logaritmos naturais de ambos os lados, pode ser criada uma equação para uma função linear. O valor do declive corresponde ao valor negativo da energia de ativação sobre a constante gasosa, e a intercessão y corresponde ao logaritmo natural do fator de frequência. Esta equação pode ser utilizada para criar um gráfico chamado a teoria de Arrhenius, no qual o logaritmo natural da taxa constante é indicado como sendo uma função do inverso da temperatura em kelvin.Dados cinéticos das experiências e reações podem ser ilustrados e analisados utilizando a teoria de Arrhenius. Neste exemplo, o gráfico produz uma linha reta. O valor de declive dado em kelvin é igual ao valor negativo da energia de ativação sobre R.Depois de atribuir o valor à constante gasosa e de resolver a energia de ativação, é obtido um valor de 93, 1 kilojoules por mol.Além disso, a intercessão y de 26, 8 é igual ao logaritmo natural do fator de frequência. Assim, a solução de A dá o valor de 4, 36 10¹¹ com a unidade um sobre molaridade por segundo a mesma unidade que a taxa constante. Em casos de dados de cinética limitada ou dificuldades na representação gráfica, pode ser utilizado um modelo de dois pontos da equação de Arrhenius para calcular a energia de ativação de uma forma não gráfica.Nesses casos, a forma não-exponencial da equação de Arrhenius é modificada para incluir constantes em duas temperaturas diferentes. A posterior subtração e reorganização da expressão produz o modelo de dois pontos da equação de Arrhenius, que é utilizada para calcular a energia de ativação das taxas constantes criadas experimentalmente a duas temperaturas diferentes. Ao substituir os valores, a energia de ativação para esta reação é de 145 kilojoules por mol.

equação de arrhenius

A equação de Arrhenius relaciona a energia de ativação e a constante de velocidade, k, para reações químicas. Na equação de Arrhenius, k = Ae−Ea/RT, R é a constante de gás ideal, que tem um valor de 8,314 J/mol·K, T é a temperatura na escala de kelvin, Ea é a energia de ativação em J/mole, e é a constante 2,7183, e A é uma constante chamada de factor de frequência, que está relacionada com a frequência de colisões e com a orientação das moléculas reativas.
A equação de Arrhenius pode ser utilizada para calcular a energia de ativação de uma reação a partir de dados cinéticos experimentais. Uma abordagem conveniente para determinar a Ea para uma reação envolve a medição de k a duas ou mais temperaturas diferentes. Ela utiliza uma versão modificada da equação de Arrhenius que assume a forma de uma equação linear:
 <img alt="Eq1" src="/files/ftp_upload/11380/11380_Equation_1.png" style="height: 200px;" />
Um gráfico de ln k versus 1/T é linear com um declive igual a −Ea/R e intercepção y igual a ln A.
Considere a seguinte reação:
 <img alt="Eq2" src="/files/ftp_upload/11380/11380_Equation_2.png" style="height: 50px;" />
A energia de ativação desta reação pode ser determinada se a variação na constante da velocidade com a temperatura for conhecida a partir dos dados cinéticos da reação, conforme mostrado.
<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 velocidade (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>
Os dados fornecidos podem ser utilizados para derivar os valores do inverso da temperatura (1/T) e do log natural 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;" />
Ao representar graficamente os pontos de dados derivados com ln k versus 1/T, é gerado um gráfico de linha exibindo uma relação linear entre ln k e 1/T, como mostrado.
O declive da linha, que corresponde à energia de ativação, pode ser estimado usando dois pares de dados experimentais.              
 <img alt="Eq3" src="/files/ftp_upload/11380/11380_Equation_3.png" style="height: 350px;" />
Uma abordagem alternativa ao derivar energia de ativação envolve a utilização da constante de velocidade a duas temperaturas diferentes. Nesta abordagem, a equação de Arrhenius é reorganizada em um formato conveniente de dois pontos:
 <img alt="Eq4" src="/files/ftp_upload/11380/11380_Equation_4v2.png" style="height: 75px;" />
Ao reorganizar a equação, é gerada uma expressão para a energia de ativação.
 <img alt="Eq5" src="/files/ftp_upload/11380/11380_Equation_5.png" style="height: 75px;" />
Ao substituir quaisquer dois pares de dados e fazendo outros cálculos, obtém-se o valor da energia de ativação em joules por mole ou quilojoules por mole.
 <img alt="Eq6" src="/files/ftp_upload/11380/11380_Equation_6.png" style="height: 135px;" />
Esta abordagem alternativa de dois pontos produz o mesmo resultado que a abordagem gráfica. No entanto, na prática, a abordagem gráfica normalmente fornece resultados mais fiáveis ao trabalhar com dados experimentais reais.
Este texto é adaptado de <a href="https://openstax.org/books/chemistry-2e/pages/12-5-collision-theory">Openstax, Chemistry 2e, Section 12.5: Collision Theory</a>.

Equação de Arrhenius

A equação de Arrhenius relaciona a energia de ativação e a constante de taxa, k, para reações químicas. Na equação de Arrhenius, k = Ae−Ea/RT, R é ...

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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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