Name: reading reaction progress with integrated laws
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 39 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.7

IPC.7.F

the-integrated-rate-law-the-dependence-of-concentration-on-time

The Integrated Rate Law: The Dependence of Concentration on Time

قانون حساب المعدل المُستخدم لتحديد معدل سرعة التفاعل،من خلال تركيز المادة المتفاعلة و ثوابت معدل السرعة،يمكن أن يتحول إلى قوانين،تُظهر اعتماد معدل التفاعل على تركيز المادة المتفاعلة،وعلى الزمن. قوانين حساب المعدل هذه،يمكن استخدامها لدراسة مدى بطء أو سرعة استهلاك مادة متفاعلة،أو الوقت اللازم للوصول إلى نصف تركيز المادة المتفاعلة. بدايةًلنتأمل القانون التفاضلي لحساب المعدل،والذي يعبر عن معدل التفاعل على أنه تغير في تركيز المادة المتفاعلة أثناء فترة زمنية محددة.تكامل هذا القانون يؤدي إلى قانون المعدل التكاملي،الذي يعبر عن معدل التفاعل كعلاقة بين التركيز الأولي لمادة متفاعلة،وبين تركيزها بعد مدة محددة. قانون المعدل التكاملي يعتمد على درجة التفاعل الإجمالية،وبالتالي،يختلف من نوع تفاعل إلى آخر. غير أنه بغض النظر عن الدرجة الإجمالية،قوانين المعدل التكاملية تأخذ شكل معادلة خطية قياسية مع اختلاف في قيمة المكونات y،m،x و b،ويمكن تمثيلها بيانيًا لتعطي خطًا مستقيمًا.في قانون معدل تكاملي من الدرجة الصفرية،ترمز t-إلى تركيز المادة المتفاعلة في زمن t،فيما ترمز k إلى ثابت معدل السرعة،وترمز t إلى الزمن،وترمز A0 إلى التركيز الأولي للمادة المتفاعلة. وفي تفاعل من الدرجة الصفرية،يعطي تمثيل بياني لتركيز المادة الفاعلة كدالّة على الزمن خطًا مستقيمًا. الانحدار هو القيمة السالبة لثابت معدل السرعة،ونقطة التقاطع مع محور y هي التركيز الأولي للمادة المتفاعلة.في تفاعل من الدرجة الأولى،إذا وضع اللوغاريتم الطبيعي لتركيز المادة المتفاعلة في مخطط كدالّة على الزمن،سيعطي خطًا مستقيمًا. الانحدار يتوافق مع القيمة السالبة لثابت معدل السرعة،فيما يعطي التقاطع مع محور y اللوغاريتم الطبيعي للتركيز الأولي للمادة المتفاعلة. وفقًا للقانون التكاملي لمعدل تفاعل من الدرجة الثانية،مخطط عكس تركيز المادة المتفاعلة،مقابل الزمن يعطي خطًا مستقيمًا.الانحدار يعادل ثابت معدل السرعة،فيما يمثل تقاطع محور y عكس التركيز الأولي للمادة المتفاعلة. يمكن التعرف على درجة التفاعل الإجمالية،باستخدام بيانات حركية تجريبية بتمثيل بياني لقوانين المعدل المختلفة. فقط المخطط،ذو الرسم البياني الخطي،يطابق درجة التفاعل الإجمالية الصحيحة.التحليل التالي يسمح بتحديد ثابت معدل السرعة وتركيز المادة المتفاعلة في أي زمن معين.

قانون المعدّل المتكامل: اعتماد التركيز على الوقت

بينما يتعلق قانون المعدل التفاضلي بمعدل وتركيزات المواد المتفاعلة، فإن الشكل الثاني من قانون المعدل المسمّى قانون المعدل المتكامل يتعلق بتركيزات المواد المتفاعلة والوقت. يمكن استخدام قوانين المعدل المتكامل لتحديد كمية المادة المتفاعلة أو المنتج الموجود بعد فترة زمنية أو لتقدير الوقت اللازم لحدوث رد فعل ما إلى حد معين. على سبيل المثال ، يساعد قانون المعدل المتكامل في تحديد المدة الزمنية التي يجب تخزين المادة المشعة فيها حتى يتحلل نشاطها الإشعاعي إلى مستوى آمن. باستخدام حساب التفاضل والتكامل ، يمكن دمج قانون المعدل التفاضلي لتفاعل كيميائي فيما يتعلق بالوقت لإعطاء معادلة تتعلق بكمية المادة المتفاعلة / المنتج بالوقت المنقضي للتفاعل. ردود الفعل من الدرجة الأولى ينتج عن تكامل قانون المعدل لتفاعل بسيط من الدرجة الأولى (المعدّل = k[A]) معادلة تصف التباين في تركيز المادة المتفاعلة مع الوقت:  <img alt="Eq1" src="/files/ftp_upload/11377/11377_Equation 1.png" style="height: 50px;" /> هنا، [A] t هو تركيز A في أي وقت t، ويكون [A]0 هو التركيز الأولي لـ A، و k هو ثابت معدل الدرجة الأولى. لتسهيل العمليات الحسابية، تمت إعادة ترتيب هذه المعادلة إلى تنسيق يوضح اعتماداً خطياً للتركيز على الوقت الذي يأخذ شكل معادلة خط مستقيم (y = mx + b):         <img alt="Eq2" src="/files/ftp_upload/11377/11377_Equation 2.png" style="height: 50px;" /> تقترح المعادلة أن مخطط ln[A]t مقابل t بالنسبة إلى تفاعل من الدرجة الأولى هو خط مستقيم بميل −k and a y-مَيل من ln[A]0. إذا تم رسم مجموعة من بيانات المعدلات بهذه الطريقة ولم ينتج عنها خط مستقيم، فإن التفاعل ليس من الدرجة الأولى في A. التفلاعلات من الدرجة الثانية قانون المعدل التفاضلي لتفاعل بسيط من الدرجة الثانية هو: المعدّل = k[A]2, وقانون المعدّل المتكامل هو: <img alt="Eq3" src="/files/ftp_upload/11377/11377_Equation 3.png" style="text-align: center; height: 70px;" /> يأخذ قانون المعدل المتكامل من الدرجة الثانية أيضًا شكل معادلة الخط المستقيم. وفقًا للمعادلة ، فإن الرسم البياني 1/[A]t مقابل t للتفاعل من الدرجة الثانية هو خط مستقيم بمَيل k وتقاطع 1/[A]0. إذا لم يكن المخطط خطاً مستقيماً، فإن التفاعل ليس من الدرجة الثانية. ترتيب صفري Reactions            بالنسبة للتفاعلات الصفرية، يكون قانون المعدل التفاضلي هو: المعدّل = k. A يُظهر التفاعل الصفري معدل تفاعل ثابتًا، بغض النظر عن تركيز المادة (المواد) المتفاعلة. لوحظت حركيات الترتيب الصفري لبعض التفاعلات فقط في ظل ظروف معينة محددة. تظهر هذه التفاعلات نفسها سلوكيات حركية مختلفة عندما لا’ تتحقق الشروط المحددة ، ولهذا السبب ، يتم استخدام المصطلح الأكثر حكمة أحيانًا الترتيب شبه الصفري.                             قانون المعدل المتكامل للتفاعل الصفري هو أيضًا دالة خطية ، تتخذ شكل y = mx + b:                  <img alt="Eq4" src="/files/ftp_upload/11377/11377_Equation 4.png" style="height: 50px;" /> مخطط [A] مقابل الوقت t للتفاعل الصفري هو خط مستقيم بميل −k و y-تقاطع [A]0.هذا النص مقتبس من <a href="https://openstax.org/books/chemistry-2e/pages/12-4-integrated-rate-laws">Openstax, Chemistry 2e, Section 12.4: Integrated Rate Laws.</a>

بينما يتعلق قانون المعدل التفاضلي بمعدل وتركيزات المواد المتفاعلة ، فإن شكلا ثانيا من قانون المعدل يسمى قانون المعدل المتكامل يتعلق ...

Education

JoVE Core

Chemistry

الكيمياء

واحد

Chemical Kinetics

الحركية الكيميائية

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

reading reaction progress with integrated laws

Integrated rate laws connect reaction concentration to time. They help show how much reactant or product is present after a certain period. They can also help estimate how long a reaction must run to reach a given extent. A common use is finding how long radioactive material must be stored before its radioactivity drops to a safe level.

These equations come from the differential rate law after it is integrated with respect to time. For a first-order reaction, where rate = k[A], the integrated form relates the concentration of A at time t to the initial concentration [A]0 and the first-order rate constant k. The equation can be rearranged into the straight-line form y = mx + b. That means a plot of ln[A]t versus t should be linear. The slope is −k, and the y-intercept is ln[A]0. If the data do not make a straight line, the reaction is not first order in A.

Second-order reactions follow a different pattern. For a simple second-order reaction, the differential rate law is rate = k[A]2. Its integrated rate law also gives a straight-line relationship. A plot of 1/[A]t versus time t should be linear, with slope k and y-intercept 1/[A]0. If the plot is not straight, the reaction is not second order.

Zero-order reactions behave differently again. For these reactions, the rate is rate = k, so the reaction rate stays constant even when reactant concentration changes. Some reactions show zero-order kinetics only under certain conditions, so the term pseudo-zero-order is sometimes used. The integrated rate law is also linear here. A plot of [A] versus time t is a straight line with slope −k and y-intercept [A]0.

Reading Reaction Progress with Integrated Laws

reading-reaction-progress-with-integrated-laws

reaction rate

Measuring Reaction Rates

Measuring reaction rates shows how fast reactants are used up or products are formed over time. The rate of reaction is the change in the amount of a reactant or product per unit time. Because of that, scientists measure how a property changes as the reaction proceeds and connect that change to reactant or product amounts. For reactions that make or use a gas, the rate can be followed by changes in volume or pressure. A rate expression is the mathematical way to write how concentration changes...

measuring reaction rates

Tracking Reaction Kinetics with Light and Pressure

Reaction kinetics can be tracked with polarimetry, spectrometry, and pressure measurements. These methods let scientists follow a reaction without disturbing the sample. They also help determine how reactant or product concentrations change over time. Polarimetry is used for optically active substances. These substances rotate the plane of polarized light, which is called optical rotation. The effect comes from molecular structure. Normal monochromatic light is unpolarized, but after it passes...

concentration and rate law

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...

determining order of reaction

Finding Rate Law from Initial Rates

Rate laws connect the speed of a chemical reaction to the concentration of its reactants. The rate constant, k, and the reaction orders are not taken from the chemical equation. They are found experimentally by watching how the rate changes when the reactant concentrations change. One common way to do this is the method of initial rates. In this method, several trials are run with different starting concentrations. The measured rates are then compared to determine the reaction orders and,...

the integrated rate law: the dependence of concentration on time

Integrated rate laws connect reaction concentration to time. They help show how much reactant or product is present after a certain period. They can also help estimate how long a reaction must run to reach a given extent. A common use is finding how long radioactive material must be stored before its radioactivity drops to a safe level. These equations come from the differential rate law after it is integrated with respect to time. For a first-order reaction, where rate = k[A], the integrated...

half-life of a reaction

Reaction Half-Life in Kinetics

Reaction half-life is the time needed for half of a reactant to be consumed. After each half-life, half of the remaining reactant is used up. A hydrogen peroxide decomposition example shows this pattern clearly. The concentration drops from 1.000 M to 0.500 M in the first 6.00 hours, then to 0.250 M in the next 6.00 hours, and then to 0.125 M in the third period. Each later 6.00-hour interval removes half of what is left. For first-order reactions, the half-life does not depend on the reactant...

temperature dependence on reaction rate

Collision Theory and Reaction Speed

Collision theory explains why reaction speed depends on how particles collide. Atoms, molecules, or ions must come close together before they can react. The theory says the reaction rate depends on the collision rate, the orientation of the colliding species, and whether the collision has enough energy for bonds to change. A gas-phase reaction between carbon monoxide and oxygen shows why orientation matters. The molecules can collide in more than one way. If the oxygen side of carbon monoxide...

arrhenius plots

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...

reaction mechanisms

Elementary Steps in Reaction Mechanisms

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...

rate-determining steps

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...

catalysis

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...

enzymes

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...

key terms and concepts

Learn how integrated rate laws connect concentration and time for first-order, second-order, and zero-order reactions, including straight-line plots and slopes.

Reading Reaction Progress with Integrated Laws | JoVE K12

chemistry

JoVE Core Chemistry brings general chemistry concepts to life using concise and easy-to-understand animated video lessons. Plus, in the scientist-in-action videos, we demonstrate classical and original research experiments performed in today's laboratories worldwide.

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Matter and its Interactions

PS.Chm.5.1

Pennsylvania State Academic Standards

Physical Science

Chemical Reactions

3.2.9-12.D

3.2.9-12.E

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Interactions Of Matter

Chemical reactions

Virginia  Standards of Learning

HIgh School

CH.7

CH.7.e

Alabama Course of Study Science

Matter and Its Interactions: Energy

9-12.C.3.3.d

Next Generation Science Standards

Matter and Its Interactions

HS-PS1-4

HS-PS1-5

Florida Department of Education

SC.912.P.12

SC.912.P.12.12

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Chemical Reactions

HS-PS1-5.

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IPC.7.B

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Reading Reaction Progress with Integrated Laws

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