Name: finding rate law from initial rates
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 53 s
Channel: JoVE

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IPC.7.F

Determining Order of Reaction

对于化学反应，速率定律 表示了反应速率 与反应物浓度之间的关系。反应物浓度的指数 影响反应速率，称为反应级数。反应级数是 利用初始速率法通过实验确定的，其中 化学反应在不同的反应物浓度下重复多次 以测量初始反应速率。反应物浓度的增加，使反应速率成线性比例增加，这是一级反应 的特征。如果反应物浓度加倍，初始速率增加四倍，则观察到的是二级反应。但是，如果反应物浓度的变化 不影响初始速率值，则会观察到的是零级反应。当所得的初始速率的数据 在初始反应物浓度的变化与相应速率之间 呈现不可分辨的关系时，计算速率定律 的比率。在此，反应物的任何两个浓度值 及其相应的反应速率 用于确定反应级数。但是有多种反应物的反应又如何呢？首先，使用初始速率法 分别确定每种反应物的 反应级数。接下来，将各反应级数 表示为各反应物浓度的指数，以给出速率定律。最后，速率定律中各个指数的总和 决定了总反应级数。反应级数描述了反应速率 依赖于反应物浓度，而 相对反应速度的直接度量 则由速率常数表示。速率常数 k 是将反应速率 与反应物浓度乘积相关联的比例系数。速率常数的单位取决于总反应级数，可以通过重新排列速率定律 求解速率常数来确定。对于零级反应，k 的单位是 M•s-1。一级反应的 k 的单位是 s-1，二级反应的 k 的单位 是 M-1•s-1。较大的速率常数表示反应快。相反，较小的速率常数 表示反应缓慢。值为零表示没有 任何化学反应。

确定反应顺序

速率定律描述了化学反应速率与其反应物的浓度之间的关系。 在速率定律中，通过观察反应物浓度变化时的反应速度变化，实验确定了变化率常数 k 和反应顺序。 确定速率定律的一个常见实验方法是初始速率方法。 这种方法包括测量使用不同初始反应物浓度进行的多项实验试验的反应率。 通过比较这些试验的测量速率，可以确定反应命令，以及随后的速率常数，这些常量一起被用于制定速率定律。 
 例如，一种反应的速率，涉及臭氧中的一氧化氮 [NO (g) + O3 (g) ⟶ NO2 (g) + O2 (g)] 可以根据 实验室初始速率方法的实验数据来确定。 
 <table style="margin-left: auto; margin-right: auto;">
 <tbody>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">  试用     </td>
 <td style="color: black; border: 1px solid black; text-align: center;"> [NO] (mol/L)</td>
 <td style="color: black; border: 1px solid black; text-align: center;">[O3] (mol/L)</td>
 <td style="color: black; border: 1px solid black; text-align: center;">  Δ[NO2]/Δt (mol/L·s)  </td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">1</td>
 <td style="color: black; border: 1px solid black; text-align: center;">     1.00 × 10−6      </td>
 <td style="color: black; border: 1px solid black; text-align: center;">   3.00 × 10−6    </td>
 <td style="color: black; border: 1px solid black; text-align: center;">    6.60 × 10−5     </td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">2</td>
 <td style="color: black; border: 1px solid black; text-align: center;">1.00 × 10−6</td>
 <td style="color: black; border: 1px solid black; text-align: center;">6.00 × 10−6</td>
 <td style="color: black; border: 1px solid black; text-align: center;">1.32 × 10−4</td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">3</td>
 <td style="color: black; border: 1px solid black; text-align: center;">1.00 × 10−6</td>
 <td style="color: black; border: 1px solid black; text-align: center;">9.00 × 10−6</td>
 <td style="color: black; border: 1px solid black; text-align: center;">1.98 × 10−4</td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">4</td>
 <td style="color: black; border: 1px solid black; text-align: center;">2.00 × 10−6</td>
 <td style="color: black; border: 1px solid black; text-align: center;">9.00 × 10−6</td>
 <td style="color: black; border: 1px solid black; text-align: center;">3.96 × 10−4</td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">5</td>
 <td style="color: black; border: 1px solid black; text-align: center;">3.00 × 10−6</td>
 <td style="color: black; border: 1px solid black; text-align: center;">9.00 × 10−6</td>
 <td style="color: black; border: 1px solid black; text-align: center;">5.94 × 10−4</td>
 </tr>
 </tbody>
 </table>
 根据速率数据，形成了一个通用的速率定律；速率 = k[NO]m[O3]n。 反应顺序m 和 n的值以及速率常数k 由实验数据通过三部分过程确定： 
 在步骤 1 中，m的值由 [NO] 变化的数据确定，而 [O3] 是恒定的。 在第 3 、第 4 和第 5 项审判中，[NO] 各不相同，而 [O3] 保持不变。 如果在第 3 轮至第 4 轮中 [NO] 翻一番，则率值翻一番；在第 3 轮至第 5 轮中[NO] 翻三番时，率值也翻三番。 因此，率值也直接成正比[NO]，速率定律中的 m 等于 1。 
 
 在步骤 2 中，n的值由 [O3] 变化且 [NO] 不变的数据决定。 在试验 1、2 和 3 中，[NO]是恒定的，[O3] 是不同的。 反应速度与 [O3] 的变化成正比。 当 [O3] 在第 1 轮至第 2 轮中翻了一番时，利率会翻了一番；当 [O3] 在第 1 轮至第 3 轮中翻了一番时，率值也会增加三倍。 因此，该比率与 [O3] 直接成比例，n 等于 1。 因此，速率定律为： 速率 = k [NO]1 [O3]1 = k [NO][O3]
 在步骤 3 中，k 的值由一组浓度 (例如，试验 1 中的数据) 及其相应的比率决定。
 <img alt="Eq1" src="/files/ftp_upload/11376/11376_Equation 1.png" style="text-align: center; height: 145px;" />
 如果初始施量方法中的数据不直接暗示初始浓度和初始施量之间的关系，则可以使用速率定律比率计算反应顺序和施量常数。 
 例如，反应 2 NO (g) + Cl2 (g) ⟶ 2 NOCl (g) 的常规速率定律表示为： 速率= k [NO]m [Cl2]n。
 初始速率方法的数据如下： 
 <table style="margin-left: auto; margin-right: auto;">
 <tbody>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">  试用    </td>
 <td style="color: black; border: 1px solid black; text-align: center;">  [NO] (mol/L)  </td>
 <td style="color: black; border: 1px solid black; text-align: center;">  [Cl2] (mol/L)  </td>
 <td style="color: black; border: 1px solid black; text-align: center;">  初始率 (mol/L·s)     </td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">1</td>
 <td style="color: black; border: 1px solid black; text-align: center;">0.10</td>
 <td style="color: black; border: 1px solid black; text-align: center;">0.10</td>
 <td style="color: black; border: 1px solid black; text-align: center;">0.00300</td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">2</td>
 <td style="color: black; border: 1px solid black; text-align: center;">0.10</td>
 <td style="color: black; border: 1px solid black; text-align: center;">0.15</td>
 <td style="color: black; border: 1px solid black; text-align: center;">0.00450</td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">3</td>
 <td style="color: black; border: 1px solid black; text-align: center;">0.15</td>
 <td style="color: black; border: 1px solid black; text-align: center;">0.10</td>
 <td style="color: black; border: 1px solid black; text-align: center;">0.00675</td>
 </tr>
 </tbody>
 </table>
 m 和n的值可以使用代数法从实验数据中确定，然后 k 确定的值。 
 在步骤 1 中， m 的值由 [NO] 变化且 [Cl2] 恒定的数据决定。 速率定律的比率用两个不同试验 (例如试验 3 和试验 1) 的数据来表示。 
 <img alt="Eq2" src="/files/ftp_upload/11376/11376_Equation 2.png" style="text-align: center; height: 260px;" />
 在步骤 2 中，n的值由[Cl2]变化的数据确定， [NO] 是恒定的。 
 <img alt="Eq4" src="/files/ftp_upload/11376/11376_Equation 4.png" style="text-align: center; height: 120px;" />
 使用m 和n的计算值，速率定律表示为速率 = k [NO]2 [Cl2]。
 在步骤 3 中，速率常数k的数值由适当的单位确定。 反应速率单位为 mol/L·s 以速率定律中所有其他参数的单位替换 k 的单位。 在本例中，浓度单位为 mol3/L3。 k的单位应该是 L2/mol2·s，这样速率就以 mol/L·s 为单位 k的值是在速率定律表达式解算后确定的，方法是简单地替换任何试验试验试验 (例如试验 1) 中的值。 
 <img alt="Eq5" src="/files/ftp_upload/11376/11376_Equation 5.png" style="text-align: center; height: 70px;" /> 
 
 反应顺序和率值恒定单位 
 在某些反应中，速率定律中的反应顺序恰好与化学方程中的反应系数相同。 这只是巧合，但情况往往并非如此。 速率定律对于某些反应物可能表现出分数阶，并且当一种反应物的浓度升高导致反应速率降低时，有时会观察到负反应阶数。速率定律只能通过实验确定，而不能通过反应化学计量法可靠地预测。 
 率值常数的单位将根据反应的整体顺序而有所不同。 零阶反应的率值常数单位是 mol/L·s (或 M/s) ，而对于一阶反应的单位是 1/s 二阶反应的率值常数单位是 L/mol·s (或 1/M·s) ，第三阶反应的单位是L2/mol2·s尽管浓度和时间的特定单位表示为 (mol/L) 和 (s) ，但任何其他有效单位都可用于表示浓度和时间的性质。 
 本文改编自 <a href="https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws#57033"> Openstax, 化学 2e, 第12.3节：速率定律。 </a>

速率定律描述了化学反应速率与其反应物浓度之间的关系。在速率定律中，速率常数 k 和……

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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, after that, the rate constant. These values are used to write the rate law.

For the reaction of nitric oxide with ozone, NO(g) + O3(g) → NO2(g) + O2(g), the data show how this works in the lab. When [NO] is held constant and [O3] changes, the rate changes in the same way. When [O3] doubles, the rate doubles. When [O3] triples, the rate triples. This shows that the reaction is first order in O3. A similar comparison using trials where [O3] stays constant shows that the rate is also directly proportional to [NO], so the reaction is first order in NO as well. The rate law is therefore rate = k[NO][O3].

In other reactions, the orders are found with an algebraic ratio of rate laws. For the reaction 2 NO(g) + Cl2(g) → 2 NOCl(g), the rate law is written as rate = k[NO]m[Cl2]n. Using the trial data, one step gives m = 2 and another gives n = 1. The rate law becomes rate = k[NO]2[Cl2]. The value of k is then found by using one trial and solving for the constant.

The units of the rate constant depend on the overall order of the reaction. Rate is measured in mol/L·s, and the units for k must match the rate law. For this example, the concentration terms give mol3/L3, so k must have units of L2/mol2·s. In general, a zero-order reaction has k in mol/L·s, a first-order reaction has k in 1/s, a second-order reaction has k in L/mol·s, and a third-order reaction has k in L2/mol2·s.

Reaction order does not always match the coefficients in the balanced equation. That match can happen, but it is only a coincidence. Rate laws can also include fractional orders, and some reactants can have negative orders if a higher concentration lowers the reaction rate. Because of this, rate laws are determined by experiment, not by stoichiometry. Although the examples here use mol/L and s, other valid concentration and time units can also be used.

Finding Rate Law from Initial Rates

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key terms and concepts

Use initial-rate data to find reaction order and the rate constant. Explore examples with NO, ozone, and NOCl, plus how rate constant units change.

Finding Rate Law from Initial Rates | JoVE K12

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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。

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IPC.7.B

Classifying Matter by State

Chemistry is the study of matter and the changes it undergoes. Matter is anything that has mass and occupies space. Matter is all around us; the air, ...

Classifying Matter by Composition

Matter: Pure Substances and Mixtures
According to its composition, the matter can be classified into two broad categories &mdash; pure substances and ...

Phase Transitions

Whether solid, liquid, or gas, a substance&#39;s state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the ...

phase-transitions-vaporization-and-condensation

Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize ...

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy ...

phase-transitions-sublimation-and-deposition

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and ...

Melting Points

Melting Points in Organic Chemistry
The melting point of a compound is the temperature at which the solid phase transitions into the liquid phase at a ...

Boiling Points

Source: Lara Al Hariri at the University of Massachusetts Amherst, MA, USA

	Preparation of the LaboratoryExpand
	Here, we show the laboratory preparation ...

Explain how physical and chemical properties of substances are related to their usage in everyday life such as in sunscreen, cookware, industrial applications, and fuels.

IPC.7.C

Emission Spectra

When solids, liquids, or condensed gases are heated sufficiently, they radiate some of the excess energy as light. Photons produced in this manner have a ...

Metal Flame Emission

Metal Flame Emission
Flame testing is an analytical technique where a sample is placed in a flame, and the characteristic flame color is used to identify ...

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution ...

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that ...

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are ...

Explain how electrons can transition from a high energy level to a low energy state, emitting photons at different frequencies for different energy transitions.

IPC.7.D

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a ...

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that ...

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of ...

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy ...

Balmer Series

The Bohr Model
Niels Bohr proposed a model for the hydrogen atom in 1913 that described discrete energy states are associated with a fixed electron orbit ...

Beer's Law

Absorbance and Fluorescence
When light hits a substance, it is either absorbed, transmitted, or reflected. Typically, a substance interacts with a range ...

The Wave Nature of Light

The nature of light has been a subject of inquiry since antiquity. In the seventeenth century, Isaac Newton performed experiments with lenses and prisms ...

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:

Finding Rate Law from Initial Rates

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