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

معدل سرعة التفاعل الكيميائي،بالغ الحساسية للتغيرات في درجة الحرارة. هذه التبعية لدرجات الحرارة،تُوضّح رياضيًا باستخدام معادلة أرينيوس التي تعبّر عن العلاقة بين ثابت معدل السرعة،ودرجة الحرارة المطلقة،ومُعامل التردد،وطاقة التنشيط. طاقة التنشيط ومُعامل التردد يمكن تحديدهما كذلك بيانيًا بتحويل معادلة أرينيوس إلى صيغة غير أسّية.باستخدام اللوغاريتمات طبيعية على طرفي المعادلة،تنشأ لدينا معادلة ذات دلالة خطية. قيمة ميل المنحنى تتطابق مع القيمة السالبة لطاقة التنشيط مقسومة على ثابت الغازات العام،والالتقاء عند محور Y يتطابق مع اللوغاريتم الطبيعي لمُعامل التردد. يمكن استخدام هذه المعادلة لإنشاء مخطط بياني يُسمى مخطط أرينيوس،ويشار فيه إلى اللوغاريتم الطبيعي لثابت معدل التفاعل كدالّة على معكوس درجة الحرارة بوحدة الكلفن.البيانات الحركية للتجارب والتفاعلات يمكن شرحها وتحليلها باستخدام مخطط أرينيوس. في هذا المثال،يعطي الرسم البياني خطًا مستقيمًا. قيمة ميل المنحنى المعطاة بالكلفن توضع مساوية للقيمة السالبة لطاقة التنشيط مقسومة على R.وبعد تحديد قيمة ثابت الغازات العام وإيجاد قيمة طاقة التنشيط،نحصل على 93.1 كيلو جول لكل مول.إلى جانب ذلك،تكون قيمة نقطة التقاطع مع محورY هو 26.8 مساوية للوغاريتم الطبيعي لمُعامل التردد. وعليه فبحلّالمعادلة تكون قيمة A تساوي ناتج 4.36 10¹¹ وتكون الوحدة واحد على مول لكل ثانية وهي ذات الوحدة التي يقاس بها ثابت المعدل. في حالات البيانات الحركية المحدودة أو الصعوبات في التمثيل البياني،يمكن استخدام صيغة ذات متغيرين لمعادلة أرينيوس لحساب طاقة التنشيط بأسلوب غير بياني.في مثل هذه الحالات،يتم تعديل الصيغة غير الأسّية لمعادلة أرينيوس لتشمل ثابت المعدل عند درجتي حرارة مختلفتين. عملية الطرح التالية وإعادة ترتيب العبارة الجبرية يعطي صيغة ذات متغيرين لمعادلة أرينيوس،والتي تُستخدم لحساب طاقة التنشيط،من ثوابت المعدل الناتجة تجريبيًا،عند درجتي حرارة مختلفتين. باستبدال القيم،تُحسب طاقة التنشيط لهذا التفاعل لتكون 145 كيلو جول لكل مول.

مخطّطات أرهينيوس

تتعلق معادلة أرهينيوس بطاقة التنشيط وثابت المعدل، k، للتفاعلات الكيميائية. في معادلة أرهينيوس ، k = Ae−Ea/RT, R هو ثابت الغاز المثالي، الذي تبلغ قيمته8.314 J/mol·K ، T هي درجة الحرارة على مقياس كلفن، Ea هي طاقة التنشيط في جول/مول، e هي الثابت 2.7183، و A هو ثابت يسمى عامل التردد، والذي يرتبط بتكرار التصادمات واتجاه الجزيئات المتفاعلة. يمكن استخدام معادلة أرهينيوس لحساب طاقة التنشيط لتفاعل من البيانات الحركية التجريبية. تتضمن الطريقة الملائمة لتحديد Ea للتفاعل قياس k عند درجتين أو أكثر من درجات الحرارة المختلفة. يستخدم نسخة معدلة من معادلة أرهينيوس التي تأخذ شكل معادلة خطية: p style="text-align: center"> <img alt="Eq1" src="/files/ftp_upload/11380/11380_Equation_1.png" style="height: 200px;" /> مخطط ln k مقابل 1/T هو خطي بميل يساوي −Ea/R وتقاطع يساوي ln A. ضع في اعتبارك التفاعل التالي:  <img alt="Eq2" src="/files/ftp_upload/11380/11380_Equation_2.png" style="height: 50px;" /> يمكن تحديد طاقة التنشيط لهذا التفاعل إذا كان التباين في معدل ثابت مع درجة الحرارة معروفًا من البيانات الحركية للتفاعل، كما هو موضح. <table style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="color: black; border: 1px solid black; text-align: center;">درجة الحرارة (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> يمكن استخدام البيانات المقدمة لاشتقاق قيم معكوس درجة الحرارة (1/T) واللوغاريثم الطبيعي لـ 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;" /> عند رسم نقاط البيانات المشتقة باستخدام ln k مقابل 1/T، يتم إنشاء بيان خطّي يعرض علاقة خطية بينln k و 1/T، كما هو موضح. يمكن تقدير ميل الخط الذي يتوافق مع طاقة التنشيط باستخدام أي زوج من أزواج البيانات التجريبية.               <img alt="Eq3" src="/files/ftp_upload/11380/11380_Equation_3.png" style="height: 350px;" /> تتضمن الطريقة البديلة في اشتقاق طاقة التنشيط استخدام معدل ثابت عند درجتي حرارة مختلفتين. في هذا النهج، يتم إعادة ترتيب معادلة أرهينيوس إلى شكل مناسب من نقطتين:  <img alt="Eq4" src="/files/ftp_upload/11380/11380_Equation_4v2.png" style="height: 75px;" /> عند إعادة ترتيب المعادلة، يتم إنشاء تعبير عن طاقة التنشيط.  <img alt="Eq5" src="/files/ftp_upload/11380/11380_Equation_5.png" style="height: 75px;" /> من خلال استبدال أي زوجي بيانات وإجراء المزيد من العمليات الحسابية ، ينتج عن ذلك قيمة طاقة التنشيط بالجول لكل مول أو الكيلوجول لكل مول.  <img alt="Eq6" src="/files/ftp_upload/11380/11380_Equation_6.png" style="height: 135px;" /> ينتج عن هذا النهج البديل المكون من نقطتين نفس نتيجة النهج الرسومي. ومع ذلك، من الناحية العملية، عادةً ما يوفر النهج الرسمي نتائج أكثر موثوقية أثناء العمل مع البيانات التجريبية الفعلية. هذا النص مقتبس من <a href="https://openstax.org/books/chemistry-2e/pages/12-5-collision-theory">Openstax, Chemistry 2e, Section 12.5: Collision Theory</a>.

تربط معادلة أرهينيوس طاقة التنشيط وثابت المعدل k للتفاعلات الكيميائية. في معادلة أرهينيوس ، k = Ae−Ea / RT ، R هو ...

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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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reaction rate

Measuring Reaction Rates

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Reaction Order from Concentration

Reaction order from concentration shows how reactant amounts affect reaction rate. Rate laws, also called differential rate laws or rate equations, are mathematical expressions that connect reaction rate with the concentrations of reactants. For a generic reaction a A + b B → products, the rate law can be written using the reactant concentrations [A] and [B] and a rate constant k. In a rate law, k is the rate constant for one specific reaction at one specific temperature. The exponents m and n...

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Reading Reaction Progress with Integrated Laws

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Reaction Half-Life in Kinetics

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Collision Theory and Reaction Speed

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arrhenius plots

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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Chemical reactions can happen in steps, and a balanced equation does not show the full path at the molecular level. A reaction mechanism, also called a reaction path, gives the step-by-step process that explains how reactants become products. The decomposition of ozone is one example of a reaction that can be described by a sequence of steps. Each step in a mechanism is an elementary reaction. These elementary reactions happen in order, and when they are added together, they give the balanced...

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Reaction Bottlenecks in Chemical Kinetics

Reaction bottlenecks help explain rate-determining steps in multistep reaction mechanisms. In a mechanism with several elementary steps, one step is often much slower than the others. That slowest step is called the rate-limiting step, or rate-determining step. A reaction cannot move faster than its slowest step, so this step controls the overall reaction rate. The idea is like traffic on a four-lane freeway with one lane closed. Cars can only move as fast as the bottleneck allows. In the same...

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Catalyst Action in Reaction Rates

Catalysts change the rate of a chemical reaction by giving it a faster path. A catalyst increases reaction rate without being consumed during the process. Its effect is often explained with reaction mechanisms and energy diagrams. For an endothermic reaction, the reactants and products start and end at the same energies in both cases. The uncatalyzed path is a one-step mechanism with one transition state. The catalyzed path follows a different mechanism with two transition states and a lower...

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Enzyme Action and Inhibition

Enzymes are biological catalysts that speed up many reactions in living organisms. They help control cellular metabolism by lowering the activation energy needed for biochemical reactions. When activation energy drops, reaction rates can increase. Enzyme problems can also lead to serious disease. A genetic abnormality that causes G6PD, or glucose-6-phosphate dehydrogenase, deficiency can disrupt the pathway that supplies NADPH to cells. In red blood cells, this can reduce glutathione and...

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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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Explain how atomic energy levels and emission spectra present evidence for the wave particle duality.

IPC.7.E

Science concepts. The student knows that relationships exist between the structure and properties of matter. The student is expected to:

Determining Activation Energy from Temperature

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