Rates of Reaction for Cambridge A-Level Chemistry | 剑桥A-Level化学：反应速率

📚 Rates of Reaction for Cambridge A-Level Chemistry | 剑桥A-Level化学：反应速率

In Cambridge A-Level Chemistry, chemical kinetics links practical rate measurements with the collision theory, the Maxwell-Boltzmann distribution and rate equations. You need to define reaction rate, describe experimental methods, explain the factors affecting rate, and use rate equations to deduce reaction mechanisms.

在剑桥A-Level化学中，化学动力学将实际速率测量与碰撞理论、麦克斯韦-玻尔兹曼分布和速率方程联系起来。你需要定义反应速率、描述实验方法、解释影响速率的因素，并运用速率方程推断反应机理。

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1. Defining Reaction Rate | 反应速率的定义

Reaction rate is the change in concentration of a reactant or product per unit time. For a simple reaction A → products, the average rate can be written as the decrease in [A] divided by the time interval, with a negative sign so that rate has a positive value.

反应速率是单位时间内反应物或产物浓度的变化。对于简单反应 A → 产物，平均速率可以表示为 [A] 的减少量除以时间间隔，并加上负号使速率为正值。

average rate = −Δ[A] / Δt = Δ[product] / Δt

Rate is usually expressed in mol dm⁻³ s⁻¹. If a concentration-time graph is plotted, the instantaneous rate at any time is the gradient of the tangent to the curve at that time.

速率通常以 mol dm⁻³ s⁻¹ 表示。若绘制浓度-时间图，某一时刻的瞬时速率就是该时刻曲线的切线斜率。

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2. Measuring Reaction Rates | 测定反应速率

Common experimental methods follow one measurable quantity that changes as the reaction proceeds. The choice depends on the reaction and the physical property that can be monitored continuously or at intervals.

常见的实验方法会跟踪反应进行时发生变化的某一可测量量。选择哪种方法取决于反应本身以及可以连续或间隔监测的物理性质。

Method | 方法	Quantity measured | 测量量	Example | 例子
Gas collection | 气体收集	Volume of gas evolved | 放出气体的体积	CaCO₃ + 2HCl → CaCl₂ + CO₂ + H₂O
Mass loss | 质量减少	Decrease in mass of open flask | 敞口烧瓶质量减少	Same reaction on a balance | 天平上的同一反应
Colorimetry | 比色法	Absorbance or colour intensity | 吸光度或颜色强度	Iodine clock or dye bleaching | 碘钟或染料褪色
Conductivity | 电导率	Change in ion concentration | 离子浓度变化	Hydrolysis of (CH₃)₃CCl producing H⁺ and Cl⁻ | 叔丁基氯水解生成 H⁺ 和 Cl⁻
Quenching and titration | 取样终止后滴定	Concentration at fixed times | 固定时刻的浓度	Acid-catalysed ester hydrolysis | 酸催化酯水解

For clock reactions, the time to a fixed visual endpoint is measured, and the initial rate is taken as proportional to 1/t. This avoids the need for continuous monitoring.

对于时钟反应，测量到达固定可视终点所需的时间，初始速率与 1/t 成正比。这避免了连续监测的需要。

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3. Collision Theory and Activation Energy | 碰撞理论与活化能

Collision theory states that for a reaction to occur, reactant particles must collide, they must collide with the correct orientation, and they must possess kinetic energy greater than or equal to the activation energy Eₐ. Activation energy is the minimum energy needed to break bonds and start the reaction.

碰撞理论指出，反应发生必须满足三个条件：反应物粒子必须发生碰撞、碰撞方向必须正确、并且动能必须大于或等于活化能 Eₐ。活化能是断裂化学键并启动反应所需的最低能量。

Not all collisions lead to reaction. Successful collisions are those that meet all three criteria. This explains why some fast-moving particles still fail to react if their orientation is wrong.

并非所有碰撞都会引发反应。有效碰撞是同时满足上述三个条件的碰撞。这解释了为什么一些运动很快的粒子如果取向不正确仍不能反应。

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4. Maxwell-Boltzmann Distribution | 麦克斯韦-玻尔兹曼分布

The Maxwell-Boltzmann distribution shows the spread of kinetic energies among molecules at a fixed temperature. The curve starts at the origin, rises to a maximum at the most probable energy, and then tails off. The total area under the curve equals the total number of molecules, and the shaded area to the right of Eₐ represents the molecules with enough energy to react.

麦克斯韦-玻尔兹曼分布展示了一定温度下分子动能的分布。曲线从原点开始，上升到最概然能量处出现最大值，然后逐渐下降。曲线下总面积等于分子总数，Eₐ 右侧的阴影面积代表具有足够能量发生反应的分子。

At a higher temperature, the distribution curve becomes flatter, the peak moves to the right, and the tail extends further. The number of molecules with energy E ≥ Eₐ increases significantly, so the reaction rate increases much more than expected from the small increase in average energy.

在较高温度下，分布曲线变得更平坦，峰值右移，尾部延伸更远。能量 E ≥ Eₐ 的分子数显著增加，因此反应速率的增加远大于平均能量小幅增加所带来的预期。

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5. Effect of Concentration and Pressure | 浓度与压强的影响

Increasing the concentration of a solution increases the number of particles per unit volume. This raises the collision frequency, so successful collisions occur more often and the rate increases. The exact mathematical relationship is given by the experimental rate equation.

增大溶液的浓度会增加单位体积内的粒子数。这会提高碰撞频率，使有效碰撞更频繁地发生，因此速率增大。精确的数学关系由实验速率方程给出。

For gases, increasing pressure at constant temperature reduces the volume and therefore increases the concentration, or partial pressure, of gas molecules. Collision frequency rises, and the reaction rate increases. For gas-phase rate equations, partial pressure can be used in place of concentration.

对于气体，在恒温下增大压强会减小体积，从而提高气体分子的浓度或分压。碰撞频率上升，反应速率增大。对于气相速率方程，可以用分压代替浓度。

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6. Effect of Temperature | 温度的影响

Raising the temperature increases the average kinetic energy of particles and slightly increases collision frequency. However, the dominant effect is that many more particles now have energy greater than Eₐ, so the number of successful collisions increases dramatically. A useful rule is that many reaction rates roughly double for a 10 °C rise near room temperature.

升高温度会增加粒子的平均动能，并略微增加碰撞频率。但主导效应是更多粒子现在具有大于 Eₐ 的能量，因此有效碰撞次数急剧增加。一个实用规则是，在室温附近许多反应速率每升高 10 °C 约增加一倍。

The rate constant k depends on temperature through the Arrhenius equation:

速率常数 k 通过阿伦尼乌斯方程随温度变化：

k = A e^−Eₐ/RT

Here A is the frequency factor, Eₐ is the activation energy, R is the gas constant, and T is the absolute temperature in Kelvin. A larger T or smaller Eₐ gives a larger k and a faster rate.

其中 A 为频率因子，Eₐ 为活化能，R 为气体常数，T 为开尔文温度。T 越大或 Eₐ 越小，k 越大，速率越快。

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7. Surface Area and Catalysts | 表面积与催化剂

For solid reactants, breaking a solid into smaller pieces increases its surface area. More particles are exposed at the surface and available for collisions, so the collision frequency increases and the reaction rate rises.

对于固体反应物，将固体破碎成更小的颗粒会增加其表面积。更多粒子暴露在表面并可用于碰撞，因此碰撞频率增加，反应速率增大。

Catalysts increase the rate of reaction without being used up. They provide an alternative reaction pathway with a lower activation energy. A lower Eₐ means that at a fixed temperature a much larger fraction of molecules has enough energy to react. Homogeneous catalysts are in the same phase as the reactants, while heterogeneous catalysts are in a different phase.

催化剂能提高反应速率而本身不被消耗。它们提供活化能较低的替代反应路径。Eₐ 降低意味着在固定温度下，具有足够能量发生反应的分子比例大大增加。均相催化剂与反应物处于同一相，而非均相催化剂则处于不同相。

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

For a general reaction aA + bB → products, the experimental rate equation takes the form:

对于一般反应 aA + bB → 产物，实验速率方程的形式为：

rate = k[A]^m[B]^n

The powers m and n are the orders with respect to A and B. They may be 0, 1, 2, or occasionally fractional. The overall order is m + n. Orders must be determined experimentally and are not simply the stoichiometric coefficients a and b.

指数 m 和 n 分别是反应对 A 和 B 的级数。它们可以是 0、1、2，偶尔也可能是分数。总级数为 m + n。反应级数必须通过实验确定，不能简单等同于化学计量数 a 和 b。

The units of the rate constant k depend on the overall order, because the rate always has units mol dm⁻³ s⁻¹.

速率常数 k 的单位取决于总级数，因为速率的单位始终是 mol dm⁻³ s⁻¹。

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

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9. Determining Orders: Initial Rates and Half-life | 确定反应级数：初始速率法与半衰期

In the initial rates method, the initial rate is measured for several experiments in which only one reactant concentration is changed while all others are kept constant. If doubling [A] doubles the rate, the order is first. If doubling [A] has no effect, the order is zero. If doubling [A] quadruples the rate, the order is second.

在初始速率法中，进行多组实验，只改变一种反应物的浓度而保持其他条件不变，并测量初始速率。如果 [A] 加倍时速率加倍，则为一级；如果 [A] 加倍但速率不变，则为零级；如果 [A] 加倍时速率变为四倍，则为二级。

The half-life of a first-order reaction is constant and independent of the initial concentration:

一级反应的半衰期是常数，与初始浓度无关：

t_½ = ln 2 / k

For a zero-order reaction, the half-life decreases as the initial concentration decreases. For a second-order reaction, the half-life increases as the initial concentration decreases. Measuring several half-lives from a concentration-time graph can therefore help identify first-order behaviour.

对于零级反应，初始浓度越低，半衰期越短。对于二级反应，初始浓度越低，半衰期越长。因此，从浓度-时间图上测量多个半衰期有助于识别一级反应。

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10. Reaction Mechanisms and Rate-Determining Step | 反应机理与决速步骤

Many reactions occur through a sequence of elementary steps called the reaction mechanism. The slowest step is the rate-determining step, and it controls the overall reaction rate. Species that appear in the rate equation are involved in or before the rate-determining step, and their orders equal their molecularity in that step. Intermediates produced and consumed within the mechanism do not appear in the overall rate equation.

许多反应通过一系列基元步骤进行，称为反应机理。最慢的一步是决速步骤，它控制整个反应的速率。速率方程中出现的物质参与了决速步骤或在其之前参与反应，它们的级数等于该步骤中的分子数。在机理中生成并消耗的中间体不会出现在总速率方程中。

For example, the reaction NO₂ + CO → NO + CO₂ has the rate equation rate = k[NO₂]². A proposed mechanism is:

例如，反应 NO₂ + CO → NO + CO₂ 的速率方程为 rate = k[NO₂]²。提出的机理为：

Step 1: 2NO₂ → NO₃ + NO (slow)

Step 2: NO₃ + CO → NO₂ + CO₂ (fast)

The slow step involves two NO₂ molecules, so the rate depends on [NO₂]². CO appears only in the fast step after the rate-determining step, so it does not appear in the rate equation.

慢步骤涉及两个 NO₂ 分子，因此速率取决于 [NO₂]²。CO 只出现在决速步骤之后的快步骤中，因此不出现在速率方程

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