Rate of Reaction | 反应速率

📚 Rate of Reaction | 反应速率

Reaction rate is at the heart of chemical kinetics. It determines how quickly reactants turn into products, influencing everything from industrial synthesis to biological processes. Understanding rate allows chemists to control and optimise reactions, predict yields, and propose plausible mechanisms. This article covers the key concepts required for Cambridge A‑Level Chemistry, including rate equations, experimental methods, collision theory, activation energy, and the role of catalysts.

反应速率是化学动力学的核心。它决定了反应物转变为产物的快慢，影响着从工业合成到生物过程的方方面面。理解反应速率使化学家能够控制和优化反应、预测产率并提出合理的机理。本文涵盖剑桥A‑Level化学所需的关键概念，包括速率方程、实验方法、碰撞理论、活化能以及催化剂的作用。

1. Introduction to Reaction Rate | 反应速率简介

Chemical kinetics is the study of the rates of chemical reactions and the factors that affect them. The rate of a reaction measures how the concentration of a reactant or product changes with time. It provides valuable insight into the pathway (mechanism) of a reaction. For A‑Level Chemistry, a sound grasp of rate is essential for topics such as equilibrium, industrial processes, and organic synthesis.

化学动力学研究化学反应速率及其影响因素。反应速率衡量反应物或产物的浓度随时间变化的快慢，它为了解反应途径（机理）提供了宝贵信息。对于A‑Level化学，扎实掌握反应速率对于平衡、工业过程和有机合成等主题至关重要。

2. Defining Rate of Reaction | 反应速率的定义

The rate of a chemical reaction is defined as the change in concentration of a reactant or product per unit time. Its units are typically mol dm⁻³ s⁻¹. For a reaction aA → bB, the rate can be expressed with respect to any species, but the stoichiometric coefficients must be accounted for:

化学反应速率定义为反应物或产物浓度在单位时间内的变化。其单位通常为 mol dm⁻³ s⁻¹。对于反应 aA → bB，速率可针对任何物种表示，但必须考虑化学计量系数：

Rate = −(1/a) Δ[A]/Δt = (1/b) Δ[B]/Δt

The negative sign ensures the rate is positive when referring to the disappearance of a reactant. Experimentally, we often determine the initial rate (t=0) from the gradient of a concentration–time curve.

负号确保提及反应物消耗时速率值为正。实验中，我们通常通过浓度–时间曲线在 t=0 处的斜率来确定初始速率。

3. Rate Equations and Order of Reaction | 速率方程与反应级数

The rate equation (or rate law) links the rate of reaction to the concentrations of the reactants raised to some powers. For a reaction between A and B, the rate equation takes the form:

速率方程（速率定律）将反应速率与反应物浓度的若干次幂联系起来。对于 A 和 B 之间的反应，速率方程形式为：

r = k [A]ᵐ [B]ⁿ

Here, k is the rate constant, and m and n are the orders with respect to A and B. The overall order is m + n. Orders are not necessarily equal to the stoichiometric coefficients; they must be determined experimentally. They can be zero, fractional, or integers.

其中 k 为速率常数，m 和 n 分别是相对于 A 和 B 的级数。总反应级数为 m + n。级数不一定等于化学计量系数，必须通过实验测定。它们可以是零、分数或整数。

The order of a reaction tells us how the rate is affected by changing the concentration of a particular reactant:

反应级数告诉我们改变某一反应物浓度时速率如何受到影响：

Zero order: rate is independent of [A], r = k

零级：速率与 [A] 无关，r = k
First order: rate doubles if [A] doubles, r ∝ [A]

一级：若 [A] 加倍则速率加倍，r ∝ [A]
Second order: rate quadruples if [A] doubles, r ∝ [A]²

二级：若 [A] 加倍则速率增至原来的四倍，r ∝ [A]²

4. The Rate Constant, k | 速率常数 k

The rate constant k is a proportionality constant in the rate equation. Its value is determined at a given temperature and is independent of concentration but strongly dependent on temperature. The units of k vary with the overall order of the reaction:

速率常数 k 是速率方程中的比例常数。其值在给定温度下确定，与浓度无关，但强烈依赖温度。k 的单位随反应总级数而变化：

Overall order	Units of k	总级数	k 的单位
0	mol dm⁻³ s⁻¹	0	mol dm⁻³ s⁻¹
1	s⁻¹	1	s⁻¹
2	dm³ mol⁻¹ s⁻¹	2	dm³ mol⁻¹ s⁻¹
3	dm⁶ mol⁻² s⁻¹	3	dm⁶ mol⁻² s⁻¹

Note that for a given reaction, knowing the units of k can immediately reveal the overall order if k is provided from experimental data.

注意：对于给定反应，如果从实验数据中获得 k，其单位可立即揭示总反应级数。

5. Initial Rates Method | 初始速率法

The initial rates method is a widely used technique to determine the order of reaction with respect to each reactant. The experiment involves measuring the initial rate of reaction (over the first few seconds) while deliberately varying the concentration of one reactant and keeping others in large excess or constant.

初始速率法是一种被广泛用于测定各反应物反应级数的技术。该实验通过有意改变一种反应物的浓度并让其他反应物大量过量或保持恒定，测量反应初始速率（前几秒）。

A common approach uses the iodine clock reaction, e.g. the peroxodisulfate–iodide reaction:

常用方法之一是碘钟反应，例如过二硫酸盐与碘化物的反应：

S₂O₈²⁻(aq) + 2I⁻(aq) → 2SO₄²⁻(aq) + I₂(aq)

By adding a small, known amount of thiosulfate and starch indicator, the time taken for the blue-black colour to appear can be recorded. The initial rate ∝ 1/t. By running several trials with different [I⁻] or [S₂O₈²⁻], the orders can be deduced from how the time changes.

加入少量已知量的硫代硫酸盐和淀粉指示剂，记录蓝黑色出现所需的时间。初始速率与 1/t 成正比。通过在不同 [I⁻] 或 [S₂O₈²⁻] 下进行多次试验，可根据时间的变化推断出级数。

6. Continuous Monitoring Methods | 连续监测法

Continuous monitoring involves following the progress of a reaction over time by measuring some physical property that changes as the reaction proceeds. Examples include:

连续监测法是指通过测量随反应进行而变化的某种物理性质来跟踪反应进程。例如：

Volume of gas evolved (e.g. Mg + 2HCl → MgCl₂ + H₂) – using a gas syringe or inverted burette.

气体释放体积（如 Mg + 2HCl → MgCl₂ + H₂）——使用气体注射器或倒置量管。
Change in mass – for reactions producing a gas, measuring mass loss on a balance.

质量变化——对于产生气体的反应，在天平上测量质量减少。
Colour change – using colorimetry to measure absorbance at a specific wavelength.

颜色变化——使用比色法在特定波长下测量吸光度。
Change in pH or electrical conductivity – suitable for reactions involving ionic species.

pH 或电导率变化——适用于涉及离子的反应。

From the collected data, a concentration–time graph can be plotted and the order can be inferred from the shape of the curve.

从收集的数据中可以绘制浓度–时间图，并通过曲线的形状推断反应级数。

7. Graphical Methods and Half‑Life | 图形法与半衰期

Concentration–time graphs provide a direct way to deduce reaction order. For a reactant, plotting [A] versus time yields characteristic shapes:

浓度–时间图为推断反应级数提供了直接途径。对于反应物，绘制 [A] 对时间的图会得到特征形状：

Zero order: straight line with negative slope; rate = k.

零级：斜率为负的直线；速率 = k。
First order: exponential decay; constant half‑life.

一级：指数衰减；半衰期恒定。
Second order: curve that falls more steeply initially and then levels off; half‑life increases as concentration decreases.

二级：初始下降更陡、随后趋于平缓的曲线；半衰期随浓度降低而增大。

The half‑life (t₁/₂) of a reaction is the time taken for the concentration of a reactant to fall to half its initial value. For first‑order reactions, t₁/₂ is independent of initial concentration:

反应的半衰期 (t₁/₂) 是指反应物浓度降至其初始值一半所需的时间。对于一级反应，t₁/₂ 与初始浓度无关：

t₁/₂ = ln 2 / k ≈ 0.693 / k

For zero‑order and second‑order reactions, t₁/₂ depends on initial concentration, which helps distinguish the order experimentally.

对于零级和二级反应，t₁/₂ 依赖于初始浓度，这有助于通过实验区分级数。

8. Collision Theory | 碰撞理论

Collision theory explains reaction rates on a molecular level. For a reaction to occur, particles must collide with sufficient energy (≥ activation energy) and with the correct orientation. The rate of reaction is proportional to the frequency of successful collisions.

碰撞理论从分子层面解释反应速率。反应要发生，微粒必须以足够的能量（≥ 活化能）和正确的取向发生碰撞。反应速率与有效碰撞的频率成正比。

Concentration (or pressure for gases) affects rate by increasing the number of particles per unit volume, leading to more frequent collisions. For heterogeneous reactions, increasing the surface area of a solid reactant exposes more particles to collisions, increasing the rate. Temperature raises the kinetic energy of particles, so more collisions exceed the activation energy barrier.

浓度（或气体的压力）通过增加单位体积内的微粒数来影响速率，导致碰撞更频繁。对于非均相反应，增大固体反应物的表面积使更多微粒暴露于碰撞，从而提高速率。温度升高会增大微粒的动能，因此更多碰撞超过活化能屏障。

9. Activation Energy and Energy Profiles | 活化能与能量曲线

Activation energy (Eₐ) is the minimum energy that colliding particles must possess for a reaction to take place. On an energy profile diagram, Eₐ is the energy difference between the reactants and the transition state. The transition state is an unstable, high‑energy arrangement of atoms where bonds are partially broken and formed.

活化能 (Eₐ) 是碰撞微粒必须具有的、反应得以发生的最低能量。在能量曲线图中，Eₐ 是反应物与过渡态之间的能量差。过渡态是不稳定的高能原子排布，此时化学键处于部分断裂和部分形成的状态。

A reaction with a large Eₐ will have a small fraction of particles with sufficient energy, hence a slow rate at a given temperature. Lowering Eₐ dramatically increases the proportion of successful collisions, which is exactly what catalysts achieve.

具有较大 Eₐ 的反应中，拥有足够能量的微粒比例很小，因此在给定温度下速率缓慢。降低 Eₐ 能显著提高有效碰撞的比例，而这正是催化剂所实现的效果。

10. The Arrhenius Equation | 阿伦尼乌斯方程

The quantitative relationship between the rate constant, temperature, and activation energy is given by the Arrhenius equation:

速率常数、温度和活化能之间的定量关系由阿伦尼乌斯方程给出：

k = A e^(–Eₐ/RT)

where A is the pre‑exponential factor, R is the gas constant (8.31 J K⁻¹ mol⁻¹), and T is the absolute temperature in kelvin.

其中 A 是指前因子，R 是气体常数（8.31 J K⁻¹ mol⁻¹），T 为热力学温度（开尔文）。

Taking natural logarithms gives a linear form:

取自然对数可得线性形式：

ln k = −Eₐ/RT + ln A

A plot of ln k against 1/T yields a straight line with slope = −Eₐ/R. This enables the determination of activation energy from experimental data. The Arrhenius equation also explains why a small increase in temperature can cause a large increase in k and hence the reaction rate.

以 ln k 对 1/T 作图得到一条直线，其斜率 = −Eₐ/R。据此可从实验数据确定活化能。阿伦尼乌斯方程还解释了为何温度小幅升高即可导致 k 大幅增加，从而使反应速率急剧上升。

11. Catalysts and Reaction Rate | 催化剂与反应速率

A catalyst is a substance that increases the rate of a chemical reaction without being consumed in the overall process. It works by providing an alternative reaction pathway with a lower activation energy. This means a much larger fraction of particles have enough energy to overcome the barrier, resulting in a higher frequency of successful collisions.

催化剂是能加快化学反应速率但本身在总过程中不被消耗的物质。它通过提供一条活化能更低的替代反应途径来发挥作用。这意味着拥有足够能量克服能垒的微粒比例大大增加，从而有效碰撞频率更高。

Catalysts can be classified as homogeneous (in the same phase as the reactants) or heterogeneous (in a different phase). A classic example of heterogeneous catalysis is the Haber process using solid iron to synthesise ammonia. An example of homogeneous catalysis is the oxidation of iodide ions by peroxodisulfate, catalysed by Fe²⁺ ions. Enzymes are biological catalysts that are highly specific and operate under mild conditions.

催化剂可分为均相（与反应物同相）和非均相（与反应物不同相）。非均相催化的经典例子是哈伯法中使用固体铁合成氨。均相催化的例子是过二硫酸盐氧化碘离子，由 Fe²⁺ 催化。酶是生物催化剂，具有高度专一性并在温和条件下起作用。

12. Reaction Mechanisms and the Rate‑Determining Step | 反应机理与决速步

Many reactions proceed through a series of elementary steps, collectively called the reaction mechanism. The overall rate of the reaction is controlled by the slowest step in the sequence, known as the rate‑determining step (RDS). The rate equation therefore reflects the molecularity of this slow step, not the overall stoichiometry.

许多反应经过一系列基元步骤进行，统称为反应机理。反应的总速率由序列中最慢的步骤控制，称为决速步（RDS）。因此，速率方程反映了该慢步骤的分子数，而非总化学计量关系。

For example, the reaction 2NO(g) + O₂(g) → 2NO₂(g) has the experimental rate equation r = k [NO]² [O₂], suggesting that two NO molecules and one O₂ molecule are involved in the RDS. In the case of NO₂ + CO → NO + CO₂, the experimentally observed rate equation is r = k [NO₂]², which can be explained by a two‑step mechanism: (1) NO₂ + NO₂ → NO₃ + NO (slow), (2) NO₃ + CO → NO₂ + CO₂ (fast). Here, the RDS involves only NO₂, and CO appears in a subsequent fast step, so its concentration does not appear in the rate equation.

例如，反应 2NO(g) + O₂(g) → 2NO₂(g) 的实验速率方程为 r = k [NO]² [O₂]，提示决速步中包含两个 NO 分子和一个 O₂ 分子。对于 NO₂ + CO → NO + CO₂，实验测得的速率方程为 r = k [NO₂]²，这可以用两步机理解释：(1) NO₂ + NO₂ → NO₃ + NO（慢），(2) NO₃ + CO → NO₂ + CO₂（快）。此处决速步仅涉及 NO₂，CO 出现在随后的快步骤中，因此其浓度不出现在速率方程中。

Thus, the rate equation is a powerful tool for probing reaction mechanisms. A proposed mechanism must be consistent with the experimentally determined rate equation, and any intermediate species must be accounted for by fast steps that do not limit the rate.

因此，速率方程是探究反应机理的有力工具。所提出的机理必须与实验确定的速率方程一致，且任何中间物种都必须在非限速的快步骤中得到合理解释。

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Rate of Reaction | 反应速率