📚 Rate of Reaction | 反应速率
The rate of a chemical reaction measures how quickly reactants are converted into products, that is, how the concentration of a species changes with time. In A-Level Chemistry, understanding reaction rates involves defining the rate precisely, constructing rate equations, determining orders of reaction from experimental data, exploring the meaning and units of the rate constant, and using that information to propose reaction mechanisms. It also requires linking the rate to temperature through the Arrhenius equation, interpreting Maxwell-Boltzmann distributions, and explaining the action of catalysts. This article covers all the key Cambridge International A-Level concepts, including the initial rates method, continuous monitoring, half-life, temperature dependence and catalysis, together with worked calculations and common exam pitfalls.
化学反应速率衡量反应物转化为产物的快慢，也就是某种物质的浓度随时间变化的速度。在 A-Level 化学中，理解反应速率涉及准确定义速率、构建速率方程、由实验数据确定反应级数、理解速率常数的含义与单位，并据此推测反应机理。同时还需要通过阿伦尼乌斯方程把速率与温度联系起来，解读麦克斯韦-玻尔兹曼分布，并解释催化剂的作用。本文涵盖剑桥国际 A-Level 的全部核心概念，包括初始速率法、连续监测法、半衰期、温度依赖性和催化作用，并配有计算示例与常见考试易错点。
1. Defining Rate of Reaction | 反应速率的定义
itten as rate = −Δ[A]/Δt, because [A] is decreasing and the minus sign makes the rate positive. For a product P, rate = Δ[P]/Δt. The usual units are mol dm⁻³ s⁻¹, although mol dm⁻³ min⁻¹ also appears when a reaction is slow. The quantity Δ[A]/Δt gives an average rate over a time interval, whereas the gradient of a tangent drawn to a concentration-time curve gives the instantaneous rate at that particular moment.
化学反应速率定义为单位时间内反应物或产物浓度的变化量。对于反应物 A，速率常写成 rate = −Δ[A]/Δt，因为 [A] 在减小，负号使速率为正值。对于产物 P，rate = Δ[P]/Δt。常用单位为 mol dm⁻³ s⁻¹，若反应较慢也会出现 mol dm⁻³ min⁻¹。Δ[A]/Δt 表示某时间段内的平均速率，而在浓度-时间曲线上作切线所得的斜率表示该时刻的瞬时速率。
the rate must be defined in a way that takes the stoichiometry into account, so that the same numerical value is obtained whichever species is monitored. This gives the relationship shown below.
对于一般反应 aA + bB → cC + dD，速率的定义必须考虑化学计量数，这样无论监测哪一种物质，得到的速率数值都相同。由此得到下面的关系式。
rate = −(1/a) d[A]/dt = −(1/b) d[B]/dt = (1/c) d[C]/dt = (1/d) d[D]/dt
Notice that the rate of change of concentration of a species divided by its stoichiometric coefficient is the same for every species in the equation. This convention is essential when a question supplies data for one substance but asks you to calculate the rate with respect to another.
注意，每种物质浓度变化率除以其化学计量数后，对反应式中所有物质都是相等的。当题目只提供某一种物质的数据，却要求计算另一种物质对应的速率时，这一约定至关重要。
2. Rate Equations and Orders of Reaction | 速率方程与反应级数
The rate equation links the rate of reaction to the concentrations of species raised to powers. For a reaction involving A and B, the rate equation can be expressed as shown below, where m and n are the orders with respect to A and B respectively, and m + n is the overall order of reaction.
速率方程将反应速率与若干物质浓度的幂联系起来。对于涉及 A 和 B 的反应，速率方程可表示如下，其中 m 和 n 分别是相对于 A 和 B 的级数，m + n 为总反应级数。
rate = k [A]ᵐ [B]ⁿ
The orders of reaction m and n must be determined experimentally; they are not, in general, related to the stoichiometric coefficients a and b. A reaction can be zero order with respect to a substance, meaning its concentration has no effect on the rate, which happens when that substance is in large excess or when it is not involved in the rate-determining step. Typical orders are 0, 1 and 2, and the overall order is the sum of the individual orders.
反应级数 m 和 n 必须通过实验测定，通常与化学计量数 a 和 b 没有直接关系。某一物质可以表现为零级，即其浓度对速率没有影响，这通常出现在该物质大量过量、或它不参与决速步的情况下。常见的级数为 0、1、2 级，总反应级数等于各分级数之和。
An important point for the exam is the difference between the order with respect to a reactant and its stoichiometric coefficient in the balanced equation. Only for a single-step (elementary) reaction do the two coincide, and even then the rate equation is written for the slow step only.
考试中的一个重要区分点是：某反应物的级数与其在配平方程式中的化学计量数并不相同。只有在单步（基元）反应中两者才一致，而且即便如此，速率方程也只是针对慢步骤书写的。
3. The Rate Constant k and Its Units | 速率常数 k 及其单位
The rate constant k is the proportionality constant in the rate equation. Its value is fixed at a given temperature and changes only when the temperature changes; it is independent of concentration. The magnitude of k increases as temperature rises, which is the fundamental reason why reactions speed up when heated. The units of k depend on the overall order of reaction, and deriving them correctly is a common exam requirement.
速率常数 k 是速率方程中的比例常数。在给定温度下 k 为定值，只在温度改变时变化，与浓度无关。温度升高时 k 增大，这正是加热能加快反应速率的根本原因。k 的单位取决于总反应级数，正确推导单位是常见的考试要求。
| Overall order | Rate equation form | Units of k |
| 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][B]² or k[A]³ | mol⁻² dm⁶ s⁻¹ |
m⁻³ s⁻¹ for rate, and cancel. For example, for a second-order reaction, k = rate / [A][B], so the units are (mol dm⁻³ s⁻¹) ÷ (mol dm⁻³)² = mol⁻¹ dm³ s⁻¹.
推导单位的快捷方法是把速率方程整理为 k = rate /（浓度项），用 mol dm⁻³ 代入浓度、用 mol dm⁻³ s⁻¹ 代入速率，再约分。例如二级反应中 k = rate / [A][B]，单位为 (mol dm⁻³ s⁻¹) ÷ (mol dm⁻³)² = mol⁻¹ dm³ s⁻¹。
4. Determining Orders: The Initial Rates Method | 测定级数：初始速率法
The initial rates method, also called the clock method when a sharp visual end-point is used, measures the rate at the very start of the reaction, before any concentrations have changed appreciably. This avoids complications from the reverse reaction and from products that might interfere. A series of experiments is carried out in which the concentration of one reactant is varied while all others are kept constant, and the effect on the initial rate is recorded.
初始速率法（若借助明显的视觉终点则称为计时法）测定的是反应刚开始、浓度尚未明显变化时的速率。这样可以避免逆反应以及产物干扰带来的复杂影响。实验时让某一种反应物的浓度改变、其余保持不变，记录其对初始速率的影响。
Consider the following data for a reaction between A and B.
考虑下列 A 与 B 反应的数据。
| Experiment | [A] / mol dm⁻³ | [B] / mol dm⁻³ | Initial rate / mol dm⁻³ s⁻¹ |
| 1 | 0.10 | 0.10 | 1.0 × 10⁻³ |
| 2 | 0.20 | 0.10 | 2.0 × 10⁻³ |
| 3 | 0.10 | 0.20 | 4.0 × 10⁻³ |
ng [B] quadruples the rate, so the reaction is second order with respect to B. The overall order is 3 and the rate equation is rate = k[A][B]².
比较实验 1 与 2，[A] 加倍使速率加倍，故对 A 为一级；比较实验 1 与 3，[B] 加倍使速率变为四倍，故对 B 为二级。总级数为 3，速率方程为 rate = k[A][B]²。
k that k comes out the same from every experiment, since a constant value confirms the rate equation is correct.
随后可用任一组实验数据求速率常数：k = rate / ([A][B]²) = 1.0 × 10⁻³ / (0.10 × 0.10²) = 1.0 mol⁻² dm⁶ s⁻¹。务必检验由各组实验算出的 k 是否一致，因为 k 为定值恰好说明所设速率方程正确。
5. Continuous Monitoring and Concentration-Time Graphs | 连续监测与浓度-时间图
Continuous monitoring follows a physical property of the mixture throughout the reaction and converts it into concentration. Suitable techniques include measuring the volume of gas evolved with a gas syringe, measuring the loss in mass on a balance when a gas escapes, using a colorimeter when a coloured species is consumed or produced, following pH changes with a pH meter, and measuring electrical conductivity when the number of ions changes. In each case a calibration or a stoichiometric relationship converts the measured quantity into concentration.
连续监测法在整个反应过程中跟踪混合物的某种物理性质，并将其换算为浓度。可用的技术包括：用气体注射器测量放出的气体体积；用天平测量气体逸出导致的质量损失；当有颜色的物质被消耗或生成时使用色度计；用 pH 计跟踪 pH 变化；当离子数目发生变化时测量电导率。每种情况下都需要通过校准或化学计量关系把测量值换算成浓度。
The shape of the concentration-time graph immediately reveals the order with respect to that species. A straight line of constant negative gradient indicates zero order, because the rate does not change as the concentration falls. A curve whose gradient decreases steadily, giving a constant half-life, indicates first order. A steeper curve that flattens more rapidly indicates second order.
浓度-时间图的形状可以直接反映该物质的级数。斜率为恒定负值的直线表示零级，因为浓度下降时速率不变。斜率持续减小、半衰期恒定的曲线表示一级。下降更陡、更快趋于平缓的曲线表示二级。
For any of these graphs the rate at a chosen instant is obtained by drawing a tangent and calculating its gradient. Plotting these gradients against concentration gives a second graph whose shape confirms the order: a horizontal line for zero order, a straight line through the origin for first order, and a curve for second order. A useful alternative is to plot rate against [A]ⁿ and check which value of n gives a straight line.
对任何此类图形，某时刻的速率可通过作切线并求其斜率得到。再以这些斜率为纵轴、浓度为横轴作图，由第二张图的形状即可确认级数：零级为水平直线，一级为过原点的直线，二级为曲线。另一种有效方法是以速率对 [A]ⁿ 作图，检验哪一个 n 值能得到直线。
6. Half-Life and First-Order Reactions | 半衰期与一级反应
The half-life, t½, is the time taken for the concentration of a reactant to fall to half of its original value. For a first-order reaction the half-life is independent of the starting concentration, which makes it a convenient diagnostic test: if successive half-lives measured from a concentration-time graph are equal, the reaction is first order with respect to that reactant.
半衰期 t½ 是反应物浓度降至初始值一半所需的时间。对于一级反应，半衰期与起始浓度无关，这使它成为方便的判别依据：若从浓度-时间图上量出的连续半衰期相等，则该反应对此反应物为一级。
t½ = ln 2 / k = 0.693 / k
first-order reaction with a half-life of 25 s has k = 0.693 / 25 = 2.8 × 10⁻² s⁻¹. Note that half-life is a property of first-order kinetics only; for zero-order and second-order reactions the half-life changes as the reaction proceeds.
由于 ln 2 约等于 0.693，一级反应的速率常数可由半衰期方便地求出，反之亦然。例如半衰期为 25 s 的一级反应，k = 0.693 / 25 = 2.8 × 10⁻² s⁻¹。注意半期恒定只是一级动力学的特征；对零级和二级反应，半衰期会随反应进行而改变。
nts or drugs in the environment and the body. Questions often ask you to use the number of half-lives elapsed to find the fraction remaining, using fraction remaining = (½)ⁿ where n is the number of half-lives.
半期的应用远不止实验室，例如放射性衰变（始终为一级反应），以及污染物或药物在环境与体内的残留时间。常见题目要求根据经过的半期个数求剩余分数，可用公式：剩余分数 = (½)ⁿ，其中 n 为半期个数。
7. Reaction Mechanisms and the Rate-Determining Step | 反应机理与决速步
A reaction mechanism is a sequence of elementary steps that together give the overall equation. The slowest step in the sequence is called the rate-determining step, and the rate equation reflects only the species that appear in that slow step. This is the single most powerful link between kinetics and mechanism, and it explains why the orders in the rate equation usually differ from the stoichiometric coefficients of the overall equation.
反应机理是一系列基元步骤，它们加和起来给出总反应方程式。其中最慢的一步称为决速步，速率方程只反映出现在该慢步骤中的物种。这是动力学与机理之间最有力的联系，也解释了为什么速率方程中的级数通常与总方程式的化学计量数不同。
, consistent with a slow bimolecular collision between H₂ and I₂. By contrast, if a rate equation such as rate = k[NO₂]² is given for a reaction involving NO₂ and CO, this indicates that the slow step involves two NO₂ molecules and that CO enters in a later, faster step.
例如，总反应 H₂(g) + I₂(g) → 2HI(g) 经实验测得对 H₂ 为一级、对 I₂ 为一级，即 rate = k[H₂][I₂]，这与 H₂ 与 I₂ 之间慢的双分子碰撞相符。相反，若某涉及 NO₂ 与 CO 的反应给出的速率方程为 rate = k[NO₂]²，则说明慢步骤涉及两个 NO₂ 分子，而 CO 是在随后较快的步骤中参与反应。
Two further points are worth remembering. First, an intermediate formed in one step and consumed in a later step never appears in the rate equation. Second, a catalyst does appear in the rate equation if it takes part in the rate-determining step, which is common in acid-catalysed reactions. When asked to propose a mechanism, always make sure the steps sum to the overall equation and that the slow step is consistent with the given rate equation.
还有两点值得牢记。第一，在某一步生成、又在后续步骤中被消耗的中间体不会出现在速率方程中。第二，若催化剂参与决速步，它就应当出现在速率方程中，这在酸催化反应中很常见。被要求提出机理时，务必检查各步骤加和是否等于总方程式，且慢步骤是否与给定速率方程一致。
8. Temperature Dependence and the Arrhenius Equation | 温度依赖性与阿伦尼乌斯方程
Increasing the temperature increases the rate of almost every reaction, mainly by increasing the rate constant k. As a rough rule of thumb, a rise of 10 K roughly doubles the rate of many reactions at room temperature, but the effect is not a simple proportionality and is best described by the Arrhenius equation.
升高温度几乎总能加快反应速率，主要通过增大速率常数 k 实现。一个粗略的经验规律是：室温附近温度升高 10 K，许多反应的速率约增加一倍，但这种影响并非简单正比关系，最准确的描述是阿伦尼乌斯方程。
k = A e−Ea/RT
ln k = ln A − Ea / (R T)
Here A is the pre-exponential factor, related to the frequency and orientation of collisions, 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 temperature in kelvin. Because the exponential term contains T in the denominator with a negative sign, k increases as T increases. A plot of ln k against 1/T gives a straight line of gradient −Ea/R and intercept ln A, which is the standard graphical method for determining activation energy.
式中 A 为指前因子，与碰撞频率和取向有关；Ea 为活化能，单位 J mol⁻¹；R 为气体常数 8.31 J K⁻¹ mol⁻¹；T 为热力学温度，单位 K。由于指数项中 T 位于分母且带负号，T 增大时 k 增大。以 ln k 对 1/T 作图得到一条直线，斜率为 −Ea/R、截距为 ln A，这是测定活化能的标准作图法。
Questions often require the activation energy from two temperatures. Using the two-point form of the Arrhenius equation avoids drawing a graph.
题目常要求由两个温度的数据求活化能。使用阿伦尼乌斯方程的两点式可以不必作图。
ln(k₂/k₁) = (Ea/R) × (1/T₁ − 1/T₂)
Remember that Arrhenius plot calculations demand absolute temperature in kelvin, and that Ea must come out in J mol⁻¹ unless you divide by 1000 to give kJ mol⁻¹. A very common error is to forget to convert °C to K by adding 273.
切记阿伦尼乌斯作图与计算必须使用热力学温度 K，且算出的 Ea 单位是 J mol⁻¹，除非除以 1000 换算为 kJ mol⁻¹。最常见的错误是忘记把摄氏度加 273 换算成开尔文。
9. Collision Theory and the Boltzmann Distribution | 碰撞理论与玻尔兹曼分布
Collision theory states that for a reaction to occur, particles must collide with one another, with at least the activation energy, and with a favourable orientation. Most collisions do not lead to reaction because the particles do not have enough energy or are not aligned correctly. The activation energy is the minimum energy that colliding particles must possess for a successful reaction.
碰撞理论认为，反应要发生，粒子之间必须发生碰撞，且碰撞能量至少达到活化能，并具有合适的取向。大多数碰撞并不会引发反应，因为粒子能量不足或取向不合适。活化能是相互碰撞的粒子发生成功反应所需的最低能量。
The Maxwell-Boltzmann distribution describes how molecular energies are spread at a given temperature. When the temperature is raised, the distribution curve becomes flatter and its peak moves to the right, so a much greater proportion of molecules have energy greater than the activation energy. The area under the curve to the right of Ea increases substantially, which is why rates rise steeply with temperature.
麦克斯韦-玻尔兹曼分布描述了给定温度下分子能量的分布情况。温度升高时，分布曲线变得更为平缓，峰值向右移动，因此能量高于活化能的分子比例大幅增加。曲线在 Ea 右侧的面积显著增大，这就是速率随温度急剧上升的原因。
Two features of the curve are frequently examined. First, the curve starts at the origin, since no molecule has zero energy. Second, the total area under the curve is constant, because it represents the total number of molecules, so the curve can only flatten and shift right, never rise in area. Adding a catalyst does not change the distribution at all; it simply lowers the value of Ea, so a larger fraction of the same distribution lies beyond the new, lower threshold.
曲线的两个特征经常被考到。第一，曲线从原点出发，因为没有分子能量为零。第二，曲线下的总面积恒定，因为它代表分子总数，所以曲线只能变平缓并向右移动，不可能面积增大。加入催化剂并不会改变分布本身，只是降低了 Ea 的数值，使同一分布中有更大比例落在新的、更低的能量阈值右侧。
10. Catalysts and Their Effect on Rate | 催化剂及其对速率的影响
A catalyst is a substance that increases the rate of a reaction by providing an alternative reaction pathway with a lower activation energy, and it is not consumed in the overall reaction. Because it is regenerated, a small amount of catalyst can affect a large amount of reactant. A catalyst does not change the enthalpy change of the reaction, nor does it change the position of equilibrium; it simply enables the system to reach equilibrium faster, and it speeds up the forward and reverse reactions equally.
催化剂是一种通过提供活化能更低的替代反应路径来加快反应速率的物质，且在总反应中不被消耗。由于它会被再生，少量催化剂即可影响大量反应物。催化剂不改变反应的焓变，也不改变平衡位置，只是使体系更快达到平衡，并且同等加快正、逆反应速率。
A homogeneous catalyst is in the same phase as the reactants, as in the acid catalysis of an esterification by aqueous H⁺ ions. A heterogeneous catalyst is in a different phase, usually a solid in contact with gaseous or liquid reactants, as in iron in the Haber process or platinum and rhodium in catalytic converters. In heterogeneous catalysis the reactants adsorb onto the surface, react, and the products desorb, which explains why a large surface area improves performance.
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