📚 A-Level Chemistry: Reaction Rates, Rate Equations and Activation Energy | A-Level 化学：反应速率、速率方程与活化能
Reaction rates, rate equations and activation energy form one of the highest-scoring areas of A-Level Chemistry. This guide brings together the collision model, the rate equation with its orders and rate constant, the Arrhenius equation, the Maxwell-Boltzmann distribution and the rate-determining step, and it keeps the wording close to what exam papers actually ask for in both explanation and calculation questions.
反应速率、速率方程与活化能是 A-Level 化学中拿分空间最大的板块之一。本文把碰撞模型、含级数与速率常数的速率方程、阿伦尼乌斯方程、麦克斯韦-玻尔兹曼分布以及决速步整合在一起，文字表述与计算要求都尽量贴近考卷的真实问法。
1. Reaction Rate and Collision Theory | 反应速率与碰撞理论
The rate of reaction is defined as the change in concentration of a reactant or a product per unit time. When we follow a reactant being used up, a negative sign is placed in front of the change so that the rate always comes out positive; when we follow a product, the positive change is used directly.
反应速率定义为反应物或生成物的浓度在单位时间内的变化。跟踪被消耗的反应物时，要在变化量前加负号，使速率始终为正值；跟踪生成物时，直接取正值即可。
Rate = Δ[product] / Δt = −Δ[reactant] / Δt
Rates are normally quoted in mol dm⁻³ s⁻¹, although units such as cm³ s⁻¹ or mol dm⁻³ min⁻¹ appear when gas volume or a clock reaction is being followed. A rate measured over a long time interval is an average rate; the gradient of the tangent drawn to a concentration-time curve gives the instantaneous rate at that particular moment.
速率的常用单位是 mol dm⁻³ s⁻¹，不过在测量气体体积或使用计时反应时，也会出现 cm³ s⁻¹ 或 mol dm⁻³ min⁻¹ 这类单位。在较长时间间隔内测得的速率是平均速率；浓度-时间曲线上某一点切线的斜率，对应该时刻的瞬时速率。
Collision theory explains why a reaction happens at all. Particles must collide, the collision must involve energy equal to or greater than the activation energy, and the particles must be correctly oriented. Most collisions fail one of these tests, which is why only a small fraction of collisions lead to reaction.
碰撞理论解释了反应为什么会发生。粒子必须发生碰撞，碰撞的能量必须大于或等于活化能，并且粒子的取向必须正确。大多数碰撞不能满足其中某一个条件，因此只有极小比例的碰撞真正导致反应发生。
2. Factors That Change the Rate | 影响反应速率的因素
Any factor that increases the frequency of successful collisions, or increases the proportion of collisions with energy at or above the activation energy, will increase the rate. Concentration, pressure, temperature, surface area and catalysts are the five factors that appear most often in exam questions.
凡是能提高有效碰撞频率，或提高能量达到或超过活化能的碰撞比例的因素，都会提高反应速率。浓度、压强、温度、表面积和催化剂是考卷中最常出现的五个因素。
| Factor 因素 | Effect and reason 影响与原因 |
| Concentration 浓度 | More particles per unit volume, so collisions are more frequent. 单位体积内粒子更多，碰撞更频繁。 |
| Pressure 压强 | For gases only: the same number of particles is squeezed into a smaller volume, so collision frequency rises. 仅适用于气体：相同数目的粒子被压缩到更小体积中，碰撞频率上升。 |
| Temperature 温度 | Particles move faster, so collisions are more frequent and, far more importantly, a much larger fraction of them exceed the activation energy. 粒子运动更快，碰撞更频繁，更关键的是超过活化能的粒子比例大幅增加。 |
| Surface area 表面积 | For solids, a powder exposes more surface for contact with the other reactant or with the catalyst. 对固体而言，粉末状暴露出更多表面，与另一反应物或催化剂接触更充分。 |
| Catalyst 催化剂 | Provides an alternative route with a lower activation energy. 提供一条活化能更低的替代反应路径。 |
A common exam trap is to describe temperature only in terms of collision frequency. In practice the dominant effect is the increased proportion of particles with energy greater than the activation energy, and marks are usually reserved for that statement.
一个常见的失分点是只把温度的影响描述为碰撞更频繁。实际上主导作用是能量超过活化能的粒子比例大幅提高，分数通常也正给在这一句上。
3. The Rate Equation and Orders of Reaction | 速率方程与反应级数
ucts, the rate equation is normally written in the form below, where m is the order with respect to A, n is the order with respect to B, and m + n is the overall order.
对于写作 aA + bB → 生成物的反应，速率方程通常写成下面的形式，其中 m 为对 A 的级数，n 为对 B 的级数，m + n 为总级数。
Rate = k[A]ᵐ[B]ⁿ
The orders must be found by experiment; they are not the same as the stoichiometric coefficients a and b except by coincidence. This is one of the most frequently tested ideas in the whole topic.
级数必须通过实验确定；除个别巧合外，它们并不等于化学计量系数 a 和 b。这是整个板块中被考查频率最高的观念之一。
- Zero order: changing the concentration has no effect on the rate, so Rate = k.
零级：改变浓度对速率没有影响，因此 Rate = k。 - directly proportional to the concentration, so Rate = k[A]. Doubling [A] doubles the rate.
一级：速率与浓度成正比，因此 Rate = k[A]。浓度加倍，速率加倍。 - nal to the square of the concentration, so Rate = k[A]². Doubling [A] quadruples the rate.
二级：速率与浓度的平方成正比，因此 Rate = k[A]²。浓度加倍，速率变为四倍。
[A][B] and the overall order is two. Concentrations are always inserted in mol dm⁻³ in these expressions, and the concentration of a solid is treated as constant, which is why solids never appear in a rate equation.
当两种反应物都是一级时，速率方程写成 Rate = k[A][B]，总级数为二。代入该式时浓度一律以 mol dm⁻³ 为单位；固体的浓度视为常数，因此固体从不出现在速率方程中。
4. Determining Orders by Experiment | 实验测定反应级数
The initial rates method is the standard approach. Several experiments are run in which the concentration of one reactant is changed while all the others are kept constant, and the initial rate of each run is measured. Comparing pairs of runs reveals the order with respect to each reactant.
初始速率法是最标准的做法。进行若干组实验，每组只改变一种反应物的浓度，其余保持不变，并测定各组的初始速率。两两比较即可得到对每种反应物的级数。
Continuous monitoring follows a physical property that changes in proportion to concentration as the reaction proceeds. Colour intensity measured with a colorimeter, gas volume collected in a syringe, electrical conductivity, mass loss from an open flask, and pH or titration of quenched samples are all valid techniques. Clock reactions such as the iodine clock simply time how long it takes for a fixed amount of product to form, which is inversely proportional to the rate.
连续监测法则是追踪某个随反应进行而与浓度成比例变化的物理量。用比色计测颜色深浅、用注射器收集气体体积、测电导率、测敞口瓶的质量损失，以及测 pH 或对淬灭样品滴定，都属于可行技术。碘钟之类的计时反应，只是测定生成固定量产物所需的时间，该时间与速率成反比。
Half-lives offer a rapid graphical test. If successive half-lives measured from a concentration-time graph are constant, the reaction is first order with respect to that reactant. A reaction whose half-life doubles each time the concentration halves shows zero order behaviour in the concentration-time plot.
半衰期提供了一种快速的图像判断法。若从浓度-时间曲线上读出的连续半衰期保持恒定，则该反应对该反应物为一级。若浓度每减半一次半衰期就加倍，则相应的浓度-时间图表现为零级特征。
5. The Rate Constant k and Its Units | 速率常数 k 及其单位
The rate constant k is independent of concentration; it changes only when the temperature changes, or when a catalyst is added. It is therefore the quantity that carries all the information about conditions, which is why the Arrhenius equation is written in terms of k and not in terms of the rate.
速率常数 k 与浓度无关；它只随温度改变，或在加入催化剂时改变。因此它承载了关于反应条件的全部信息，这也是阿伦尼乌斯方程用 k 而不是用速率来表达的原因。
The units of k follow from the overall order and must be worked out every time rather than memorised blindly. The general result is that k has units of mol¹⁻ⁿ dm³ⁿ⁻³ s⁻¹ where n is the overall order.
k 的单位由总级数决定，每次都应推导而不是死记。一般结论是：当总级数为 n 时，k 的单位为 mol¹⁻ⁿ dm³ⁿ⁻³ s⁻¹。
| Overall order 总级数 | Rate equation 速率方程 | Units of k 单位 |
| 0 | Rate = k | mol dm⁻³ s⁻¹ |
| 1 | Rate = k[A] | s⁻¹ |
| 2 | Rate = k[A]² or k[A][B] | mol⁻¹ dm³ s⁻¹ |
