📚 Rates of Reaction | 反应速率
Chemical kinetics, the study of reaction rates, reveals how quickly reactants are converted into products. Understanding rates helps us control industrial processes, predict shelf lives of pharmaceuticals, and explain why some reactions, like rusting, take years while others, like explosions, are instantaneous. In A-Level Chemistry, mastering rates of reaction involves exploring collision theory, the factors that influence speed, rate equations, and the mathematical models that underpin them.
化学动力学研究反应速率，揭示反应物转化为产物的快慢。理解速率有助于我们控制工业流程、预测药物的保质期，并解释为什么某些反应（如铁锈）耗时数年而其他反应（如爆炸）瞬间完成。在A-Level化学中，掌握反应速率需要探索碰撞理论、影响反应速度的因素、速率方程及其背后的数学模型。
1. Introduction to Reaction Rate | 反应速率简介
ion of a reactant or product per unit time. For a reactant A, the rate can be expressed as – m⁻³ s⁻¹, but for faster reactions we may use mol dm⁻³ min⁻¹ or even mol dm⁻³ s⁻¹ for slow ones. The rate is always a positive quantity.
化学反应速率定义为反应物或产物浓度随时间的变化率。对于反应物A，速率可表示为 –Δ[A]/Δt，其中负号表示消耗；对于产物B，速率 = Δ[B]/Δt。常用单位是 mol dm⁻³ s⁻¹，对于较快反应可用 mol dm⁻³ min⁻¹，而对于慢反应仍使用 mol dm⁻³ s⁻¹。速率始终为正值。
2. Collision Theory and Activation Energy | 碰撞理论与活化能
For a reaction to occur, particles must collide with sufficient energy and the correct orientation. The minimum energy required for a successful collision is called the activation energy, Eₐ. Only those collisions where the colliding particles have energy equal to or greater than Eₐ can lead to a reaction. The Maxwell–Boltzmann distribution shows that at any temperature, only a small fraction of molecules possess such energy.
反应发生要求粒子必须碰撞并具有足够的能量和正确的取向。成功碰撞所需的最低能量称为活化能，Eₐ。只有碰撞粒子的能量等于或大于Eₐ时，反应才可能发生。麦克斯韦–玻尔兹曼分布表明，在任何温度下，只有一小部分分子拥有这样的能量。
perature has such a marked effect on reaction rates. Additionally, increasing concentration or pressure simply increases the frequency of collisions, which also explains their influence on rate.
升高温度使分布向右移动，显著增加了E ≥ Eₐ的粒子比例，这就是温度对反应速率影响显著的原因。此外，增大浓度或压力只是增加了碰撞频率，从而解释它们对速率的影响。
3. Factors Affecting Reaction Rates: Concentration and Pressure | 影响反应速率的因素：浓度与压力
For reactions in solution, increasing the concentration of reactants raises the number of particles per unit volume, leading to more frequent collisions. According to collision theory, the rate is directly proportional to the product of the concentrations raised to some power. For gaseous reactions, increasing the partial pressure has the same effect as increasing concentration.
对于溶液中的反应，增大反应物浓度会提高单位体积内的粒子数，碰撞更加频繁。根据碰撞理论，速率与各反应物浓度的某次幂的乘积成正比。对于气体反应，增加分压与增加浓度的效果相同。
Experimentally, doubling the concentration of a reactant may double the rate (first order) or quadruple it (second order), or sometimes leave the rate unchanged (zero order). These relationships are captured by the rate equation, which we will discuss later.
实验上，某反应物浓度加倍可能使速率加倍（一级）、增至四倍（二级），或有时速率不变（零级）。这些关系由速率方程描述，稍后讨论。
4. Effect of Temperature | 温度的影响
Temperature is arguably the most dramatic factor. A general rule of thumb is that a 10°C rise roughly doubles the rate of many reactions. This is not due to a large increase in collision frequency (which rises only slightly) but to the exponential increase in the number of molecules that exceed the activation energy barrier.
温度可能是影响最显著的因素。经验规则是温度每升高10°C，许多反应的速率大约加倍。这不是因为碰撞频率大幅增加（仅略有上升），而是因为超过活化能垒的分子数呈指数增长。
The shape of the Maxwell–Boltzmann energy distribution curve changes such that the area under the curve to the right of Eₐ becomes much larger. Since the rate depends on this area, the effect is profound. A catalyst, by contrast, provides a different pathway with a lower Eₐ, also increasing this area without raising the temperature.
麦克斯韦–玻尔兹曼能量分布曲线的形状发生变化，Eₐ右侧曲线下的面积显著增大。由于速率取决于该面积，效果十分显著。相比之下，催化剂提供一条低Eₐ的新路径，同样增大该面积但无需升温。
5. Surface Area and Catalysts | 表面积与催化剂
In heterogeneous reactions, where a solid reactant is involved, the surface area to volume ratio determines how many particles are exposed for collisions. Grinding a solid into a powder increases the rate because more reactant particles are accessible. This is particularly important in industrial processes, e.g., the catalytic converter uses a finely divided catalyst to speed up exhaust gas reactions.
在涉及固体反应物的多相反应中，表面积与体积之比决定了可参与碰撞的粒子数量。将固体研磨成粉末可增大速率，因为更多的反应物粒子暴露出来。这在工业过程中尤为重要，例如催化转化器使用细碎催化剂加速废气反应。
A catalyst is a substance that increases the rate of reaction without being consumed. It works by providing an alternative reaction pathway with a lower activation energy. Both homogeneous and heterogeneous catalysts appear in A-Level syllabuses, with examples such as V₂O₅ in the Contact process and Fe in the Haber process.
催化剂是一种能提高反应速率而自身不被消耗的物质。它通过提供活化能更低的替代反应路径起作用。A-Level大纲中既有均相催化剂也有多相催化剂，例如接触法中的V₂O₅和哈伯法中的Fe。
6. Measuring Reaction Rates | 测量反应速率
Several experimental techniques are used to follow the progress of a reaction. Common methods include monitoring the volume of gas evolved (using a gas syringe or displacement of water), measuring the change in mass if a gas is released, titrimetric analysis (withdrawing samples at intervals and quenching), and spectrophotometry if one species absorbs light at a specific wavelength.
有多种实验技术可跟踪反应过程。常用方法包括监测气体释放的体积（使用气体注射器或排水法），若释放气体则测量质量变化，滴定分析（间隔取样并淬灭），以及如果某物种在特定波长有吸收则使用分光光度法。
For example, in the reaction between marble chips and dilute HCl, the mass of CO₂ lost can be recorded at regular time intervals. A graph of mass against time or volume against time yields a curve whose gradient at any point gives the instantaneous rate. The initial rate is often used to determine the form of the rate equation.
例如，在大理石碎片与稀盐酸的反应中，CO₂的质量损失可定期记录。质量–时间图或体积–时间图给出曲线，曲线上任一点的切线斜率即为瞬时速率。初始速率常用于确定速率方程的形式。
7. The Rate Equation and Order of Reaction | 速率方程与反应级数
ten proportional to [A]ᵐ[B]ⁿ, where m and n are the orders with respect to A and B. The overall order is m+n. The orders are not simply the stoichiometric coefficients; they must be determined experimentally.
rate = k [A]ᵐ [B]ⁿ
速率方程将反应速率与反应物浓度的某次幂联系起来。对于反应 aA + bB → 产物，速率通常正比于 [A]ᵐ[B]ⁿ，其中m和n分别是A和B的级数。总级数为m+n。级数并非就是化学计量系数，而必须由实验确定。
Possible orders are 0, 1, 2, and sometimes non‑integral. Zero order means the rate is independent of the concentration of that reactant. First order implies rate is directly proportional to its concentration; second order means rate is proportional to the square of the concentration or to the product of two concentrations.
可能的级数为0、1、2，有时为非整数。零级表示速率与该反应物浓度无关；一级表示速率与其浓度成正比；二级表示速率与浓度的平方或两个浓度的乘积成正比。
8. Determining Order from Experimental Data | 由实验数据确定级数
Two main methods are used: the initial rates method and graphical analysis of concentration–time data. In the initial rates method, several experiments are carried out with different starting concentrations. The initial rate for each is measured, and the effect of changing one reactant’s concentration while keeping others constant reveals its order.
主要有两种方法：初始速率法和浓度–时间图的图形分析。初始速率法进行若干不同起始浓度的实验，测量各自的初始速率，通过改变一种反应物浓度而保持其他不变来揭示其级数。
For graphical analysis, concentration‑time curves are plotted. For a zero‑ tant, the plot of [A] against time is a straight line with negative slope = k. For a first‑order reactant, a plot of ln[A] against time is linear, and the half‑ plot of 1/[A] against time is linear. The following table summarises these relationships:
图形分析则绘制浓度–时间曲线。对于零级反应物，[A]对时间作图是一条斜率为 –k 的直线。对于一级反应物，ln[A]对时间作图成线性，且半衰期恒定，与初始浓度无关。对于二级，1/[A]对时间作图为直线。下表总结了这些关系：
| Order | Linear Plot | Relationship | Half‑life |
| 0 | [A] vs t | [A] = [A]₀ – kt | t₁/₂ = [A]₀/(2k) |
| 1 | ln[A] vs t | ln[A] = ln[A]₀ – kt | t₁/₂ = ln2/k (constant) |
| 2 | 1/[A] vs t | 1/[A] = 1/[A]₀ + kt | t₁/₂ = 1/(k[A]₀) |
9. The Rate Constant k | 速率常数k
The rate constant, k, is the proportionality factor in the rate equation. Its magnitude reflects how fast a reaction proceeds at a given temperature; a larger k means a faster reaction. Crucially, k is independent of concentration but is affected by temperature and the presence of a catalyst. The units of k depend on the overall reaction order.
速率常数k是速率方程中的比例因子。其大小反映了给定温度下反应进行的快慢，k越大反应越快。关键的是，k与浓度无关，但受温度和催化剂影响。k的单位取决于总反应级数：
- Overall order 0: units of k = mol dm⁻³ s⁻¹
- Overall order 1: k = s⁻¹
- Overall order 2: k = dm³ mol⁻¹ s⁻¹
- Overall order n: units are mol1–n dm3n–3 s⁻¹
- 总级数为0：k的单位 = mol dm⁻³ s⁻¹
- 总级数为1：k = s⁻¹
- 总级数为2：k = dm³ mol⁻¹ s⁻¹
- 总级数为n：单位为 mol⁽¹⁻ⁿ⁾ dm⁽³ⁿ⁻³⁾ s⁻¹
Therefore, if you are given the units of the rate constant, you can deduce the overall order of the reaction. This is a common style of exam question.
因此，若给出速率常数的单位，即可推断反应的总级数。这是常见的考试题型。
10. The Arrhenius Equation | 阿伦尼乌斯方程
The Arrhenius equation quantitatively describes how the rate constant varies with temperature:
k = A e–Eₐ/RT
where A is the pre‑exponential factor (related to collision frequency and orientation), Eₐ is the activation energy in J mol⁻¹, R is the gas constant (8.31 J K⁻¹ mol⁻¹), and T is the absolute temperature in kelvin. The exponential term emphasises that a small increase in T produces a large increase in k.
阿伦尼乌斯方程定量描述了速率常数随温度的变化：k = A e–Eₐ/RT，其中A为指前因子（与碰撞频率和取向相关），Eₐ是活化能（J mol⁻¹），R是气体常数（8.31 J K⁻¹ mol⁻¹），T为开尔文温度。指数项强调T的微小升高会导致k的大幅增加。
Taking natural logarithms gives the linear form:
ln k = ln A – Eₐ/(RT)
A plot of ln k against 1/T yields a straight line with gradient = – Eₐ, making the gradient less steep, while a higher temperature gives a smaller 1/T value.
取自然对数得到线性形式：ln k = ln A – Eₐ/(RT)。以ln k对1/T作图，得到斜率为 –Eₐ/R、截距为ln A的直线，从而可实验测定活化能。催化剂的作用是降低Eₐ，使斜率变小；而温度越高则1/T值越小。
11. Reaction Mechanisms and the Rate-Determining Step | 反应机理与速率决定步骤
Many reactions occur in a series of elementary steps. The slowest step in the mechanism is the rate‑determining step (RDS). The overall rate equation is determined by this slow step, not by the overall stoichiometry. The order with respect to each reactant in the rate equation reflects the molecularity of the RDS.
许多反应经历一系列基元步骤。机理中最慢的一步称为速率决定步骤（RDS）。总速率方程由此慢步骤决定，而非总计量系数。速率方程中各反应物的级数反映了RDS的分子数。
es two NO molecules and one H₂ molecule colliding in a termolecular step. Any subsequent fast steps will not affect the rate equation. Identifying the RDS allows chemists to propose plausible mechanisms.
例如，反应2NO + 2H₂ → N₂ + 2H₂O。若实验测定速率方程为rate = k [NO]²[H₂]，则RDS可能涉及两个NO分子和一个H₂分子的三分子碰撞步骤。后续的快步骤不影响速率方程。识别RDS使化学家能提出合理的机理。
A catalyst may change the mechanism by introducing a new RDS with a lower activation energy. Homogeneous catalysts often form an intermediate in a fast step that regenerates the catalyst later, and the rate equation can give clues about the catalytic cycle.
催化剂可能通过引入具有较低活化能的新RDS来改变机理。均相催化剂常在快步骤中形成中间体，随后再生成催化剂，速率方程可为催化循环提供线索。
12. Summary and Exam Tips | 总结与应试技巧
Rates of reaction integrate many core concepts of A-Level Chemistry: kinetics, thermodynamics, and mechanism. Remember that the order of reaction is determined by experiment, not by stoichiometric coefficients. Be comfortable converting between rate‑concentration graphs and concentration‑time graphs. Practice working out units of k and using the Arrhenius equation graphically.
反应速率整合了A-Level化学的许多核心概念：动力学、热力学和机理。切记反应级数由实验决定，而非化学计量系数。要能熟练地在速率–浓度图和浓度–时间图之间转换。练习推导k的单位并图像化运用阿伦尼乌斯方程。
In exams, you may be given a table of initial rates and asked to deduce orders, or provided with concentration‑time data to plot graphs. Always state clearly what you are measuring and show your reasoning. When explaining temperature effects, reference the Maxwell–Boltzmann distribution and the exponential increase in successful collisions, not just a rise in collision frequency. For catalysts, always state that they provide an alternative pathway with lower activation energy, and note that they are not consumed.
考试中，可能会给出初始速率表要求推断级数，或提供浓度–时间数据作图。务必清晰说明所测内容并展示推理过程。解释温度影响时应引用麦克斯韦–玻尔兹曼分布和成功碰撞的指数增加，而不仅仅是碰撞频率的上升。对于催化剂，始终说明其提供一条活化能较低的替代路径，并指出自身不被消耗。
Published by TutorHao | Chemistry Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图