Introduction to Reaction Kinetics | 反应动力学导论
Reaction kinetics is the branch of chemistry that studies the rates of chemical reactions and the factors that influence them. While thermodynamics tells us whether a reaction is energetically feasible (ΔG < 0), kinetics tells us how fast it will proceed. A reaction may be thermodynamically favourable yet proceed so slowly that it is effectively unobservable — the conversion of diamond to graphite at room temperature is a classic example.
反应动力学是化学的一个分支，研究化学反应的速率及其影响因素。热力学告诉我们反应在能量上是否可行（ΔG < 0），而动力学告诉我们反应有多快。一个反应可能在热力学上有利，但进行得如此缓慢以至于实际上无法观察到——金刚石在室温下转化为石墨就是一个经典例子。
For A-Level Chemistry students, mastering kinetics is essential: it appears across all major exam boards (AQA, Edexcel, OCR, and CIE), typically accounting for 8–12% of the total marks in Paper 2 or equivalent. This article covers the core concepts — the rate equation, order of reaction, the rate constant, and experimental determination methods — with worked examples and common pitfalls.
对于A-Level 化学学生来说，掌握动力学至关重要：它出现在所有主要考试局（AQA、Edexcel、OCR 和 CIE）中，通常占 Paper 2 总分的 8–12%。本文涵盖核心概念——速率方程、反应级数、速率常数以及实验测定方法——附有例题和常见错误分析。
1. Defining Reaction Rate | 定义反应速率
The rate of reaction is defined as the change in concentration of a reactant or product per unit time. For a general reaction:
反应速率定义为反应物或产物浓度每单位时间的变化。对于一般反应：
aA + bB → cC + dD
The rate can be expressed in terms of any species, with appropriate stoichiometric adjustments:
Rate = −(1/a) · d[A]/dt = −(1/b) · d[B]/dt = (1/c) · d[C]/dt = (1/d) · d[D]/dt
The negative sign for reactants reflects that their concentrations decrease over time. The stoichiometric coefficients (a, b, c, d) ensure the rate is consistent regardless of which species is monitored.
负号表示反应物浓度随时间减少。化学计量系数（a、b、c、d）确保无论监测哪种物质，速率都是一致的。
Units: The rate of reaction has units of mol dm⁻³ s⁻¹ (concentration per unit time). In practice, rates can also be measured in terms of gas volume produced per second, mass loss per minute, or colour change (using a colorimeter).
单位：反应速率的单位是 mol dm⁻³ s⁻¹（浓度/时间）。实际上，速率也可以通过每秒产生的气体体积、每分钟质量损失或颜色变化（使用比色计）来测量。
2. The Rate Equation | 速率方程
The rate equation (also called the rate law) is a mathematical expression that links the rate of reaction to the concentrations of reactants. For the general reaction aA + bB → products:
速率方程（也称为速率定律）是将反应速率与反应物浓度联系起来的数学表达式。对于一般反应 aA + bB → 产物：
Rate = k [A]ᵐ [B]ⁿ
Where:
- k = the rate constant (速率常数), which is temperature-dependent
- [A], [B] = concentrations of reactants (mol dm⁻³)
- m, n = orders of reaction with respect to A and B respectively
其中：
- k = 速率常数，与温度有关
- [A], [B] = 反应物浓度（mol dm⁻³）
- m, n = 分别对 A 和 B 的反应级数
⚠️ Critical Distinction | 关键区别： The orders m and n are NOT necessarily equal to the stoichiometric coefficients a and b! The rate equation must be determined experimentally — it cannot be deduced from the balanced chemical equation. This is one of the most common mistakes in A-Level kinetics questions.
级数 m 和 n 不一定等于化学计量系数 a 和 b！速率方程必须通过实验确定——不能从平衡化学方程式推导。这是 A-Level 动力学问题中最常见的错误之一。
The overall order of the reaction is the sum of the individual orders: m + n.
反应的总级数是各级数之和：m + n。
3. Orders of Reaction | 反应级数
The order of reaction with respect to a given reactant describes how the rate depends on its concentration. Orders are typically 0, 1, or 2 (though fractional orders exist in more advanced contexts).
反应级数描述速率如何取决于给定反应物的浓度。级数通常为 0、1 或 2（尽管在更高级的上下文中存在分数级数）。
3.1 Zero Order (m = 0) | 零级反应
Rate = k [A]⁰ = k
The rate is independent of the concentration of A. Doubling [A] has no effect on the rate.
速率不依赖于 A 的浓度。将 [A] 加倍对速率没有影响。
Examples: Many surface-catalysed reactions, such as the decomposition of ammonia on a tungsten surface, exhibit zero-order behaviour when the catalyst surface is saturated.
例子：许多表面催化反应，如氨在钨表面的分解，当催化剂表面饱和时表现出零级行为。
3.2 First Order (m = 1) | 一级反应
Rate = k [A]¹ = k[A]
The rate is directly proportional to the concentration of A. Doubling [A] doubles the rate.
速率与 A 的浓度成正比。[A] 加倍，速率加倍。
This is the most common order in A-Level chemistry. Examples include most radioactive decay processes and many substitution reactions.
这是 A-Level 化学中最常见的级数。例子包括大多数放射性衰变过程和许多取代反应。
3.3 Second Order (m = 2) | 二级反应
Rate = k [A]²
The rate is proportional to the square of the concentration. Doubling [A] quadruples the rate.
速率与浓度的平方成正比。[A] 加倍，速率增加四倍。
Examples: Many Sₙ2 reactions, the decomposition of HI (2HI → H₂ + I₂), and reactions involving two molecules of the same species in the rate-determining step.
例子：许多 Sₙ2 反应、HI 的分解（2HI → H₂ + I₂），以及涉及两个相同物种分子在速率决定步骤中的反应。
4. The Rate Constant (k) | 速率常数
The rate constant k is the proportionality constant in the rate equation. Its value is characteristic of a specific reaction at a given temperature.
速率常数 k 是速率方程中的比例常数。其值是在给定温度下特定反应的特征。
4.1 Units of k | k 的单位
The units of k depend on the overall order of the reaction. This is frequently tested in exams:
k 的单位取决于反应的总级数。这在考试中经常考察：
| Overall Order | 总级数 | Rate Equation | 速率方程 | Units of k | k 的单位 |
|---|---|---|
| 0 | Rate = k | mol dm⁻³ s⁻¹ |
| 1 | Rate = k[A] | s⁻¹ |
| 2 | Rate = k[A][B] or k[A]² | mol⁻¹ dm³ s⁻¹ |
| 3 | Rate = k[A]²[B] etc. | mol⁻² dm⁶ s⁻¹ |
General rule: Units of k = mol¹⁻ⁿ dm³ⁿ⁻³ s⁻¹, where n is the overall order.
一般规则：k 的单位 = mol¹⁻ⁿ dm³ⁿ⁻³ s⁻¹，其中 n 是总级数。
4.2 Temperature Dependence — The Arrhenius Equation | 温度依赖性——阿伦尼乌斯方程
The rate constant k increases with temperature, described by the Arrhenius equation:
k = A e⁻ᴱᵃ/ᴿᵀ
Where: A = pre-exponential factor (指前因子), Eₐ = activation energy (J mol⁻¹), R = gas constant (8.314 J K⁻¹ mol⁻¹), T = temperature (K).
Key insight: A small increase in temperature produces a disproportionately large increase in k (and therefore rate) because of the exponential relationship. A 10°C rise typically doubles or triples the rate for many reactions at room temperature.
关键理解：由于指数关系，温度的微小升高会导致 k（以及速率）不成比例地大幅增加。对于室温下的许多反应，升高 10°C 通常会使速率加倍或三倍。
5. Determining Orders Experimentally | 实验测定反应级数
There are several experimental methods to determine the order of reaction. The two most common at A-Level are the initial rates method and the continuous monitoring method (using concentration–time graphs).
有几种实验方法可以确定反应级数。A-Level 中最常见的两种是初速率法和连续监测法（使用浓度-时间图）。
5.1 The Initial Rates Method | 初速率法
This involves measuring the initial rate of reaction (the gradient at t = 0) for several experiments where the starting concentration of one reactant is varied while all others are kept constant.
这涉及测量几个实验的初始反应速率（t = 0 时的梯度），其中一个反应物的初始浓度变化，而所有其他反应物保持不变。
Worked Example | 例题：
The reaction 2NO(g) + 2H₂(g) → N₂(g) + 2H₂O(g) was studied. The following initial rate data were collected:
| Experiment | [NO] / mol dm⁻³ | [H₂] / mol dm⁻³ | Initial rate / mol dm⁻³ s⁻¹ |
|---|---|---|---|
| 1 | 0.10 | 0.10 | 2.0 × 10⁻³ |
| 2 | 0.20 | 0.10 | 8.0 × 10⁻³ |
| 3 | 0.10 | 0.30 | 6.0 × 10⁻³ |
Step 1 — Find order with respect to NO: Compare experiments 1 and 2 where [H₂] is constant. [NO] doubles (0.10 → 0.20). Rate changes from 2.0×10⁻³ to 8.0×10⁻³ — a factor of 4. Since 2ᵐ = 4, m = 2. The reaction is second order with respect to NO.
第 1 步——求对 NO 的级数：比较实验 1 和 2，[H₂] 恒定。[NO] 加倍（0.10 → 0.20）。速率从 2.0×10⁻³ 变为 8.0×10⁻³——4 倍。由于 2ᵐ = 4，m = 2。反应对 NO 是二级的。
Step 2 — Find order with respect to H₂: Compare experiments 1 and 3 where [NO] is constant. [H₂] triples (0.10 → 0.30). Rate changes from 2.0×10⁻³ to 6.0×10⁻³ — a factor of 3. Since 3ⁿ = 3, n = 1. The reaction is first order with respect to H₂.
第 2 步——求对 H₂ 的级数：比较实验 1 和 3，[NO] 恒定。[H₂] 增加三倍（0.10 → 0.30）。速率从 2.0×10⁻³ 变为 6.0×10⁻³——3 倍。由于 3ⁿ = 3，n = 1。反应对 H₂ 是一级的。
Rate equation: Rate = k [NO]² [H₂]
Overall order: 2 + 1 = 3
Step 3 — Calculate k: Using experiment 1: 2.0×10⁻³ = k (0.10)² (0.10), so k = 2.0×10⁻³ / (0.01 × 0.10) = 2.0 mol⁻² dm⁶ s⁻¹.
5.2 Concentration–Time Graphs | 浓度-时间图
By monitoring the concentration of a reactant over time, the order can be determined from the shape of the graph:
通过监测反应物浓度随时间的变化，可以从图形形状确定级数：
Zero order: A straight line with constant negative gradient. [A] = [A]₀ − kt. The half-life decreases as concentration decreases (t₁/₂ ∝ [A]₀).
零级：具有恒定负梯度的直线。[A] = [A]₀ − kt。半衰期随浓度降低而减少（t₁/₂ ∝ [A]₀）。
First order: A curve showing exponential decay. ln[A] = ln[A]₀ − kt. A plot of ln[A] vs. t gives a straight line (gradient = −k). The half-life is constant — independent of initial concentration.
一级：显示指数衰减的曲线。ln[A] = ln[A]₀ − kt。ln[A] 对 t 作图得到一条直线（梯度 = −k）。半衰期是恒定的——与初始浓度无关。
Second order: 1/[A] = 1/[A]₀ + kt. A plot of 1/[A] vs. t gives a straight line (gradient = +k). The half-life increases as concentration decreases.
二级：1/[A] = 1/[A]₀ + kt。1/[A] 对 t 作图得到一条直线（梯度 = +k）。半衰期随浓度降低而增加。
6. The Rate-Determining Step | 速率决定步骤
Most chemical reactions occur not in a single step but through a series of elementary steps called the reaction mechanism. The rate-determining step (RDS) is the slowest step in this sequence — it acts as a bottleneck that governs the overall rate of the reaction.
大多数化学反应不是一步完成的，而是通过一系列称为反应机理的基元步骤进行的。速率决定步骤（RDS）是这个序列中最慢的步骤——它像一个瓶颈，控制着整个反应的速率。
🔑 The Golden Rule | 黄金法则： The species that appear in the rate equation are those that are involved in (or before) the rate-determining step. The orders in the rate equation correspond to the number of molecules of each species participating in the RDS.
出现在速率方程中的物质是那些参与（或在）速率决定步骤中的物质。速率方程中的级数对应于参与 RDS 的每种物质的分子数。
Example — Propanone iodination:
CH₃COCH₃ + I₂ → CH₃COCH₂I + HI
Experimentally: Rate = k [CH₃COCH₃] [H⁺]. Note that [I₂] does NOT appear in the rate equation, meaning iodine is not involved in the RDS.
例子——丙酮碘化：
实验结果表明：Rate = k [CH₃COCH₃] [H⁺]。注意 [I₂] 没有出现在速率方程中，这意味着碘不参与 RDS。
The accepted mechanism involves two steps:
- Slow (RDS): CH₃COCH₃ + H⁺ → CH₃C(OH)=CH₂ (enol formation, slow)
- Fast: CH₃C(OH)=CH₂ + I₂ → CH₃COCH₂I + HI (iodination, fast)
The RDS involves one molecule of propanone and one H⁺ ion — matching the rate equation (first order in each). Iodine only reacts after the slow step, so its concentration does not affect the rate.
RDS 涉及一个丙酮分子和一个 H⁺ 离子——与速率方程匹配（各为一级）。碘只在慢步骤之后反应，因此其浓度不影响速率。
7. Common Exam Pitfalls | 常见考试误区
❌ Pitfall 1: Assuming the stoichiometric coefficients equal the orders of reaction. They usually don’t. Always determine orders experimentally.
❌ 误区 1：假设化学计量系数等于反应级数。它们通常不相等。始终通过实验确定级数。
❌ Pitfall 2: Confusing “rate of reaction” (which changes as the reaction proceeds) with the “rate constant k” (which is constant at a fixed temperature).
❌ 误区 2：混淆”反应速率”（随反应进行而变化）和”速率常数 k”（在固定温度下恒定）。
❌ Pitfall 3: Forgetting that the units of k change with overall order. Always check your units — if they don’t match the expected pattern, you’ve likely made an error in determining the order.
❌ 误区 3：忘记 k 的单位随总级数而变化。始终检查单位——如果它们与预期模式不匹配，你可能在确定级数时犯了错误。
❌ Pitfall 4: In continuous monitoring, using a “clock reaction” and assuming the time to a visible endpoint is directly the rate. The initial rate is inversely proportional to the time taken (Rate ∝ 1/t), but only if the extent of reaction at the endpoint is constant.
❌ 误区 4：在连续监测中，使用”时钟反应”并假设到达可见终点的时间直接等于速率。初始速率与所用时间成反比（Rate ∝ 1/t），但仅当终点处的反应程度恒定时才成立。
❌ Pitfall 5: Not appreciating that a catalyst provides an alternative pathway with a lower Eₐ — it does not change the enthalpy change (ΔH) of the reaction.
❌ 误区 5：不理解催化剂提供了一条具有较低 Eₐ 的替代途径——它不改变反应的焓变（ΔH）。
8. Summary | 总结
| Concept | 概念 | Key Point | 要点 |
|---|---|
| Rate equation | 速率方程 | Rate = k[A]ᵐ[B]ⁿ — determined experimentally, not from stoichiometry | 通过实验确定，而非化学计量比 |
| Order of reaction | 反应级数 | 0, 1, or 2; shows how rate depends on concentration | 显示速率如何取决于浓度 |
| Rate constant k | 速率常数 k | Temperature-dependent; units vary with overall order | 依赖温度；单位随总级数变化 |
| Rate-determining step | 速率决定步骤 | Slowest step in mechanism; species in RDS appear in rate equation | 机理中最慢的步骤；RDS 中的物种出现在速率方程中 |
| Arrhenius equation | 阿伦尼乌斯方程 | k = Ae⁻ᴱᵃ/ᴿᵀ; explains exponential temperature dependence | 解释指数温度依赖性 |
| Half-life | 半衰期 | Constant for 1st order only; diagnostic tool for determining order | 仅一级反应恒定；用于确定级数的诊断工具 |
Practice Questions | 练习题
Q1. The reaction 2A + B → C + D was studied. The following data were obtained:
| Experiment | [A] / mol dm⁻³ | [B] / mol dm⁻³ | Initial rate / mol dm⁻³ s⁻¹ |
|---|---|---|---|
| 1 | 0.10 | 0.10 | 1.5 × 10⁻³ |
| 2 | 0.30 | 0.10 | 4.5 × 10⁻³ |
| 3 | 0.10 | 0.20 | 6.0 × 10⁻³ |
(a) Determine the order with respect to A and B.
(b) Write the rate equation.
(c) Calculate the value and units of the rate constant k.
Q2. Explain why the rate of a reaction increases when the temperature is raised, in terms of the Maxwell-Boltzmann distribution and the Arrhenius equation. (6 marks)
Q3. The mechanism for the reaction 2NO₂ + F₂ → 2NO₂F is proposed to be:
Step 1: NO₂ + F₂ → NO₂F + F (slow)
Step 2: NO₂ + F → NO₂F (fast)
Deduce the rate equation and explain your reasoning.
Answers available upon request — test yourself first!
答案可应要求提供——先测试自己！
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