Name: reaction order and rate constants
Uploaded: 2020-03-26T07:22:26.000Z
Duration: 4 min 37 s
Channel: JoVE

K12 Standards

Minnesota Academic Standards in Science

9-12

Chemistry

3.2.1 9C.3.1.1.2

Concentration Dependence

反应进行快慢的度量称为反应速率。对于单步反应，反应速率等于各反应物或产物浓度随时间的变化量乘以相应化学计量系数的倒数。可以将浓度随时间的变化理解为时间 t 时的浓度减去初始浓度，再除以 t。反应速率始终为正值，因此反应物的表达式带有负号。在多步反应中，这些速率可能不相等，但我们仍可利用此关系来估算总反应速率。
速率定律，或称速率方程，描述了反应速率与反应物浓度之间的关系。在此方程中，k 为速率常数，A 和 B 是两种反应物，m 和 n 分别是它们的反应级数。反应级数描述了反应物浓度与反应速率之间的关系，且与化学计量关系无关。必须牢记的是，反应级数并不等于配平方程中反应物的化学计量系数。
当一个反应涉及两种或多种反应物时，我们必须考虑每种反应物的反应级数。总反应级数等于各反应物反应级数之和。例如，若反应物 A 为一级反应，反应物 B 为零级反应，则总反应级数为一级。在简单反应中，最常见的反应级数为零级、一级和二级。接下来，我们以单分子反应为例，逐一进行说明。
如果反应为零级反应，则反应物浓度对反应速率没有影响。因此，反应速率等于速率常数 k。反应速率随浓度变化的图像是一条水平直线。
在一级反应关系中，反应物浓度与反应速率呈线性关系。因此，反应速率等于速率常数乘以反应物浓度。以反应速率对浓度作图，将得到一条直线，其斜率为 k。
如果反应为二级反应，则反应速率与浓度之间存在二次函数关系。因此，反应速率等于速率常数乘以浓度的平方。反应速率随浓度变化的图像呈抛物线形，其中k为斜率。
速率常数 k 是一个与温度相关的值，用于关联反应的活化能与反应速率。您将在下一个实验中探究这一关系。
反应速率通常以摩尔每升每秒表示。无论反应级数如何，速率的单位都相同。因此，速率常数的单位则取决于反应级数。例如，如果A为一级反应，B为零级反应，则速率方程中包含一个摩尔每升的量纲，因此速率常数的单位必须为每秒的倒数（秒⁻¹）。
那么我们如何确定反应级数呢？反应级数必须通过一系列实验来确定。如果有两种反应物，一种方法是保持其中一种反应物的浓度不变，改变另一种反应物的浓度，并记录生成一定量产物所需的时间。然后对第二种反应物重复相同的过程。通过绘制反应速率与反应物浓度变化的关系图，观察其图形是否符合零级、一级或二级反应的特征，即可估算出每个反应物的反应级数。将实验数据与相应的速率方程进行匹配，还可以计算出速率常数 k。
在本实验中，您将通过改变两种反应物的浓度并记录反应进行至溶液变为不透明所需的时间，来确定这两种反应物的反应级数。

浓度依赖性

化学动力学与反应速率定律
化学动力学是指化学反应的速率或反应速度。反应速率取决于反应的机理、复杂程度以及反应物的数量。反应物浓度对反应速率也有显著影响。
通过实验，速率定律对这种关系进行量化。每种反应物以其与反应速率的关系为基础，通过一个称为反应级数的因子影响反应速率。该因子的取值范围为0到2。
对于反应 aA + bB + ... → cC，其速率方程为 r = k[A]m[B]n
在此方程中，r 表示反应速率，k 表示反应速率常数，[A] 和 [B] 分别表示反应物 A 和 B 的浓度，m 和 n 分别表示反应物 A 和 B 的反应级数。反应速率 r 定义为产物浓度随时间的变化率，其单位为摩尔每升每秒（mol/(L·s)）。
<h4>反应级数</h4>
反应级数描述了反应物浓度对反应速率的幂依赖关系。总反应级数是各反应物反应级数的总和。需要牢记的是，反应级数与配平化学方程式中的化学计量系数无关。换句话说，不能利用化学计量关系来确定化学反应的反应级数。反应级数必须通过实验测定。
为了确定反应级数，保持第二种反应物的浓度恒定，同时改变第一种反应物的浓度。反应发生所需的时间以秒为单位进行测量；然而，该时间并不对应于反应进行到底所需的时间 完成。 相反，这是指反应所需的时间 开始随后比较不同反应物浓度下的反应时间，以确定反应级数。通过执行相同的一系列反应来确定第二种反应物的级数，此时保持第一种反应物的浓度恒定，而改变第二种反应物的浓度。
通过比较反应时间，可以确定反应级数。例如，如果反应时间在反应物浓度变化时保持不变，则该反应物为零级反应。这意味着反应速率等于反应速率常数 k，其单位必须为 M/s。如果反应时间随浓度变化呈线性变化（即浓度加倍时，反应时间变化倍数为 2），则该反应物为一级反应。这意味着反应速率等于反应速率常数与反应物浓度的乘积。此时，k 的单位为 1/s。最后，如果反应物浓度加倍时，反应时间变化倍数为 4，则该反应物为二级反应。这意味着反应速率等于速率常数乘以反应物浓度的平方，呈现二次关系。此时，k 的单位必须为 1/M⋅s。
反应的总级数是各个反应级数的总和。例如，如果反应对 A 为一级，则 m = 1；如果反应对 B 为零级，则 n = 0。由于 m + n = 1，因此该反应的总级数为一级。
<h4>反应速率常数</h4>
速率常数 k 针对特定反应及其反应温度具有专一性。该速率常数通过一系列实验确定。利用测得的反应速率和反应物的初始浓度，可通过速率方程求解速率常数。速率常数受温度影响，其关系由阿伦尼乌斯方程定义。该方程描述了 k 与活化能 Ea、温度 T 以及理想气体常数 R 之间的关系。其中常数 A 为比例常数，不应与反应物 A 混淆。
<img src="/CDNSource/lm/labs/50/50_Concepts_2.jpg" alt="阿伦尼乌斯方程；反应速率对温度的依赖性；化学动力学公式。" data-altupdatedat="1761830439000" />
<h4>参考文献</h4>
<ol>
	<li style="font-size:17px">Kotz, J.C., Treichel Jr, P.M., Townsend, J.R. (2012). 化学与化学反应性。贝尔蒙特，加利福尼亚州：Brooks/Cole, Cengage Learning。</li>
	<li style="font-size:17px">Silderberg, M.S. (2009). 化学：物质与变化的分子本质。波士顿，马萨诸塞州：McGraw Hill。</li>
</ol>

化学动力学与反应速率定律
化学动力学是指化学反应的速率或速度。该速率取决于反应机理，……

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reaction order and rate constants

Chemical kinetics describes the speed of a chemical reaction. The rate depends on the reaction mechanism, the complexity of the reaction, and the number of reactants involved. Reactant concentration also affects how fast a reaction happens. The rate law is the experimental relationship that connects these factors to reaction rate.

In the rate law, each reactant contributes through a reaction order. The general form is r = k[A]^m[B]^n for aA + bB + ... → cC. Here, r is the reaction rate, k is the rate constant, and [A] and [B] are the reactant concentrations. The exponents m and n show the reaction order for each reactant.

The reaction rate is the change in product concentration over time. Its units are moles per liter per second. The overall reaction order is the sum of the individual orders. Reaction order is not the same as the numbers in the balanced chemical equation, so stoichiometric coefficients cannot be used to find it. Reaction orders must be measured experimentally.

To find a reaction order, one reactant concentration is changed while the other is held constant. The reaction time is measured in seconds, but this is the time for the reaction to start, not the time to completion. The times from different concentrations are compared to determine the order. The same process is repeated for the second reactant by switching which concentration is varied.

If the reaction time stays the same even when concentration changes, the reactant is zero-order. In that case, the rate equals k, and k has units of M/s. If the time changes linearly with concentration, the reactant is first order. Then the rate equals k times the reactant concentration, and k has units of 1/s. If doubling the concentration changes the time by a factor of 4, the reactant is second order. Then the rate equals k times the square of the concentration, and k has units of 1/M·s.

The overall order is the sum of the individual orders. For example, if A is first order and B is zero-order, the total order is first order because m + n = 1. The rate constant, k, is specific to the reaction and the temperature used. It is found from the experimental data by using the measured rate and initial concentrations in the rate equation.

The rate constant also depends on temperature through the Arrhenius equation. This equation relates k to activation energy, Ea, temperature, T, and the ideal gas constant, R. The constant A in the equation is a proportionality constant. It should not be confused with reactant A.

Reaction Order and Rate Constants

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factors-influencing-the-rate-of-chemical-reactions

Factors Influencing the Rate of Chemical Reactions

A variety of factors influence the rate of chemical reactions. For a chemical reaction to happen, atoms must collide with enough energy to overcome the ...

Concentration and Rate Law

The rate of a reaction is affected by the concentrations of reactants. Rate laws (differential rate laws) or rate equations are mathematical expressions ...

Measuring Reaction Rates

Polarimetry finds application in chemical kinetics to measure the concentration and reaction kinetics of optically active substances during a chemical ...

Temperature Dependence

Chemical Kinetics 
The reaction rate is the speed at which a chemical reaction occurs. The reaction rate is defined as the change in concentration of a ...

Reaction Rate

The rate of reaction is the change in the amount of a reactant or product per unit time. Reaction rates are therefore determined by measuring the time ...

Chemical Kinetics and the Reaction Rate Law
Chemical kinetics refers to the rate or speed of a chemical reaction. The rate depends on the mechanism, ...

Matter and Its Interactions: Develop a model based on evidence to illustrate that the release or absorption of energy from a chemical reaction system depends upon the changes in total bond energy. (P: 2, CC: 5, CI: PS1)

Solution Formation

There is no one solvent that can dissolve every type of solute. Some substances that readily dissolve in a certain solvent might be insoluble in a ...

Energetics of Solution Formation

The formation of a solution is an example of a spontaneous process, which is a process that occurs under specified conditions without energy from some ...

General Properties of Solutions

Many common substances around us exist as a solution, such as ocean water, air, and gasoline. All solutions are mixtures of substances that are composed ...

Solutions and Concentrations

Source: Laboratory of Dr. Michael Evans &#8212; Georgia Institute of Technology
A solution is a homogeneous mixture containing some components in small ...

Solubility

Solubility
Solubility describes how much of a solute can dissolve in a given volume of a specific solvent. Solubility is usually reported in terms of ...

Solution, Solubility, and Solubility Equilibrium
A solution is a homogeneous mixture&#160;composed of a solvent, the major component, and a solute, the ...

Solution Equilibrium and Saturation

Imagine adding a small amount of sugar to a glass of water, stirring until all the sugar has dissolved, and then adding a bit more. You can repeat this ...

Intermolecular Forces in Solutions

The formation of a solution is an example of a spontaneous process, a process that occurs under specified conditions without energy from some external ...

Matter and Its Interactions: Develop models to illustrate the changes in the composition of the nucleus of the atom and the energy released during the processes of fission, fusion, and radioactive decay. (P: 2, CC: 5, CI: PS1)

9C.3.1.1.3

Chemical and Solubility Equilibria

The free energy change associated with dissolving a solute in a liter of solvent is called the free energy of a solution, &#916;Gsolution. The overall ...

Matter and Its Interactions: Apply scientific principles and evidence to provide an explanation about the effects of changing the surface area, agitation, temperature, and concentration of the reacting particles on the rate at which the reaction occurs. (P: 6, CC: 1, CI: PS1)

9C.3.2.1.2

3 Developing possible explanations of phenomena or designing solutions to engineering problems
 3.2 Constructing explanations and designing solutions 
  3.2.1 Students will be able to apply scientific principles and empirical evidence (primary or secondary) to explain the causes of phenomena or identify weaknesses in explanations developed by the students or others.

Reaction Order and Rate Constants

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