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

Скорость химической реакции очень чувствительна к изменениям температуры. Эта температурная зависимость математически описывается с помощью уравнения Аррениуса, которое выражает взаимосвязь между константой скорости, абсолютной температурой, стерическим фактором и энергией активации. Энергию активации и стерический фактор также можно определить графически, преобразовав уравнение Аррениуса в неэкспоненциальную форму.Используя натуральные логарифмы с обеих сторон, получаем уравнение линейной функции. Величина наклона соответствует отрицательному значению энергии активации, деленному на газовую постоянную, а точка пересечения оси y соответствует натуральному логарифму стерического фактора. Это уравнение можно использовать для построения графика, называемого графиком Аррениуса, на котором натуральный логарифм константы скорости обозначается как функция, обратная температуре в кельвинах.Кинетические данные экспериментов и реакций можно проиллюстрировать и проанализировать с помощью этого графика Аррениуса. В этом примере график представляет собой прямую линию. Величина наклона, указанная в кельвинах, задается равной отрицательному значению энергии активации, деленному на R.После присвоения значения газовой постоянной и решения уравнения энергии активации получается значение 93, 1 килоджоуля на моль.Кроме того, точка пересечения по оси игрек, 26, 8, равна натуральному логарифму стерического фактора. Таким образом, решение для A дает значение 4, 36 10¹¹ с единицей измерения один на моль в секунду той же единицей, что и у константы скорости. В случаях ограниченных кинетических данных или трудностей с графическим представлением, для вычисления энергии активации неграфическим способом может форма прямой, проходящей через две точки"уравнения Аррениуса.В таких случаях неэкспоненциальная форма уравнения Аррениуса модифицируется для включения констант скорости при двух различных температурах. Последующее вычитание и перестановка выражения приводят к нужной форме уравнения Аррениуса, которая используется для расчета энергии активации на основе экспериментально полученных констант скорости при двух различных температурах. Подставляя значения, можно рассчитать, что энергия активации этой реакции составляет 145 килоджоулей на моль.

Графики Аррениуса

Уравнение Аррениуса соотносит энергию активации и константу скорости, k, для химических реакций. В уравнении Аррениуса k = AE-EA/RT, R — идеальная газовая константа, которая имеет значение 8.314 Дж/моль·K, T — температура на шкале Кельвина, EA — энергия активации в Дж/моле, e — константа 2.7183, а A — константа, называемая частотным коэффициентом, которая связана с частотой столкновений и ориентацией реагирующих молекул. 
 Уравнение Аррениуса можно использовать для вычисления энергии активации реакции на экспериментальных кинетических данных. Удобный подход к определению EA для реакции предполагает измерение k при двух или более различных температурах. В ней используется модифицированная версия уравнения Аррениуса, которая принимает форму линейного уравнения: 
  <img alt="Eq1" src="/files/ftp_upload/11380/11380_Equation_1.png" style="height: 200px;" />
 График ln k в сравнении с 1/T линейный с уклоном, равным -a/R и y-отсекаемый равным ln A. 
 Рассмотрим следующую реакцию: 
  <img alt="Eq2" src="/files/ftp_upload/11380/11380_Equation_2.png" style="height: 50px;" />
 Энергия активации этой реакции может быть определена, если изменение постоянной скорости с температурой известно из кинетических данных реакции, как показано на рисунке. 
 <table style="margin-left: auto; margin-right: auto;">
 <tbody>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">Температура (K) </td>
 <td style="color: black; border: 1px solid black; text-align: center;">Постоянная скорости (л/моль/с) </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>
 Предоставленные данные могут быть использованы для получения значений обратной от температуры (1/T) и природного лога 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;" />
 На графике производных точек данных с ln k по сравнению с 1/T создается линейный график, показанный линейной зависимостью между ln k и 1/T, как показано на рисунке. 
 Наклон линии, соответствующий энергии активации, можно оценить с помощью двух экспериментальных пар данных.              
  <img alt="Eq3" src="/files/ftp_upload/11380/11380_Equation_3.png" style="height: 350px;" />
 Альтернативный подход к извлечению энергии активации предполагает использование постоянной скорости при двух различных температурах. При таком подходе уравнение Аррениуса переупорядочено до удобной двухточечной формы: 
  <img alt="Eq4" src="/files/ftp_upload/11380/11380_Equation_4v2.png" style="height: 75px;" />
 При перестановке уравнения генерируется выражение для энергии активации. 
  <img alt="Eq5" src="/files/ftp_upload/11380/11380_Equation_5.png" style="height: 75px;" />
 Подстановка двух пар данных и дальнейшие расчеты дают значение энергии активации в джоулях на моль или киложоулях на моль. 
  <img alt="Eq6" src="/files/ftp_upload/11380/11380_Equation_6.png" style="height: 135px;" />
 Этот альтернативный двухточечный подход дает тот же результат, что и графический подход. Однако на практике графический подход обычно обеспечивает более надежные результаты при работе с фактическими экспериментальными данными. 
 Этот текст адаптирован из<a href="https://openstax.org/books/chemistry-2e/pages/12-5-collision-theory"> Openstax, Химия 2е изд., раздел 12.5: Теория столкновений</a>.

Уравнение Аррениуса связывает энергию активации и постоянную скорости k, для химических реакций. В уравнении Аррениуса k = Ae−Ea/RT, R равно ...

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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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