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

可以将用于根据反应物浓度和速率常数 确定反应速率的速率定律 转换为表明反 应速率依赖于反应物浓度和 时间的速率定律。这些速率定律可以用来研究 反应物消耗的速度有多慢或多快，或者需要多少时间才能达到 反应物浓度的一半。首先，看一下微分 速率定律，它将反应速率 表示为特定时间间隔内 反应物浓度的变化。积分该定律可得到积分速率定律，它利用反应物初始浓度 与特定时间后浓度 之间的关系 来表示反应速率。积分速率定律取决于 总反应级数，因此，对于每种反应类型都是不同的。但是，无论总级数如何，所有积分速率定律都采用 具有不同 y、m、x 和 b 分量的标准线性方程式的形式，并且可以绘制成 一条直线。在零级积分速率定律中，_t 是时刻 t 时的反应物浓度，k 是速率常数，t 是时间，_0 是初始反应物浓度。对于零级反应，将反应物浓度作为时间函数绘图 会生成一条直线。斜率是速率常数的负值，y 截距是初始反应物浓度。在一级反应中，将反应物浓度的自然对数 作为时间函数绘图 会给出一条直线。斜率对应于速率常数的负值，而 y 截距给出 初始反应物浓度的自然对数。根据二级积分速率定律，反应物浓度的倒数 与时间的关系曲线为一条直线。斜率等于速率常数，y 截距表示 初始反应物浓度的倒数。通过绘制不同的积分速率定律，可以使用实验动力学数据 确定总反应级数。只有带有线性图的绘图 对应正确的总反应级数。随后的分析可确定 速率常数以及任何给定时刻的反应物浓度。

积分速率定律：浓度对时间的依赖

差分速率定律与反应物的速率和浓度有关，而速率定律的第二种形式称为综合速率法则，与反应物的浓度和时间有关。积分速率定律可用于确定一段时间后存在的反应物或生成物的数量，或估算某种反应在某种程度上进行所需的时间。 例如，积分速率定律有助于确定放射性物质必须存放多久才能使其放射性衰减到安全水平。 
 使用微积分，化学反应的差分速率定律可以结合时间来提供一个方程，将反应剂 / 产品数量与反应的经过时间相关。 
 一阶反应 
 通过集成速率定律进行简单的一阶反应 (率值 = k[A]) ，方程会随时间描述反应物浓度中的变化： 
  <img alt="Eq1" src="/files/ftp_upload/11377/11377_Equation 1.png" style="height: 50px;" />
 在这里，[A]t 是A任何时候的浓度 t ，[A]0 是的初始浓度， k 是第一个率值常量。 为了便于计算，此方程被重新排列为显示浓度对时间的线性依赖的格式，格式为直线方程 (y = mx + b):        
  <img alt="Eq2" src="/files/ftp_upload/11377/11377_Equation 2.png" style="height: 50px;" />
 该等式表明，一阶ln [ A ] t 与 t 的关系图 反应是一条斜率为＆＃8722; k 且ln [ A ] 0 。 如果以这种方式绘制一组速率数据但未得出直线，则该反应不是 A 中的一阶。
 二阶反应 
 用于简单二阶反应的差分速率定律为率值 =k[A]2, 积分速率定律为： 
 <img alt="Eq3" src="/files/ftp_upload/11377/11377_Equation 3.png" style="text-align: center; height: 70px;" />
 二阶积分率定律也采用直线方程的形式。 根据等式，二阶反应的1 / [A] t 与 t 的图是一条直线，斜率为 k 和y截距1 / [A] 0 。 如果该图不是直线，则反应不是二阶的。
 零阶反应            
 对于零阶反应，差分速率定律为率值 = K 零阶反应显示恒定反应率值，而不管其反应剂的浓度如何。 只有在特定条件下，才会观察到一些反应的零阶动力学。 当特定条件未得到满足时，这些相同的反应会表现出不同的动能行为，因此，有时会使用更谨慎的”伪零阶”术语。                            
 零阶反应的积分速率定律也是一个线性函数，其形式为y = mx + b:                 
  <img alt="Eq4" src="/files/ftp_upload/11377/11377_Equation 4.png" style="height: 50px;" />
 零级反应的[A]与时间 t 的关系图是一条直线，其斜率为＆＃8722; k 和 y -[ A ] 0 的截距。
 本文改编自<a href="https://openstax.org/books/chemistry-2e/pages/12-4-integrated-rate-laws"> Openstax, 化学 2e, 第12.4节：积分速率定律。 </a>

尽管微分速率定律描述了反应速率与反应物浓度之间的关系，但另一种称为积分速率定律的速率定律则描述了……

Education

教育

JoVE Core

Chemistry

化学

Chemical Kinetics

化学动力学

KEY TERMS AND CONCEPTS

关键术语与概念

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

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arrhenius plots

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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...

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 化学通过简单明了且通俗易懂的动画视频课程，将普通化学概念带入到现实生活当中。此外，在科学家行动视频中，我们演示了在实验室中进行的经典和原始研究实验。

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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IPC.7.C

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IPC.7.D

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IPC.7.E

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

Reading Reaction Progress with Integrated Laws

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