📚 How Fast? The Rate of Chemical Change | 多快？化学反应速率
Understanding how fast chemical reactions occur is essential in both laboratory and industrial settings. From the rusting of iron to the explosive combustion of fuels, the rate of a chemical change dictates how quickly products are formed and reactants are consumed. In IB Chemistry Reactivity 2.2, we explore the definition, measurement, and theoretical basis of reaction rates, including collision theory, activation energy, and the influence of factors such as concentration, temperature, surface area, and catalysts. We also delve into rate equations and how experimental data leads to the determination of reaction orders and mechanisms.
理解化学反应发生的快慢对于实验室研究与工业生产都至关重要。从铁的锈蚀到燃料的爆炸燃烧，化学反应速率决定了产物生成和反应物消耗的速度。在 IB 化学 Reactivity 2.2 中，我们将探讨反应速率的定义、测定方法及其理论基础，包括碰撞理论、活化能，以及浓度、温度、表面积和催化剂等因素的影响。还会深入学习速率方程，以及如何通过实验数据确定反应级数和反应机理。
1. Defining Reaction Rate | 定义反应速率
dD, the average rate over a time interval Δt can be written using one of the expressions:
Rate = -1/a (Δ[A]/Δt) = -1/b (Δ[B]/Δt) = +1/c (Δ[C]/Δt) = +1/d (Δ[D]/Δt)
The negative signs for reactants ensure that the calculated rate is a positive quantity. Units of rate are typically mol dm⁻³ s⁻¹, although mol dm⁻³ min⁻¹ or other time units may be used depending on the speed of the reaction.
化学反应速率衡量了反应物消耗或产物生成的快慢。在数学上，它表示为某一物质的浓度随时间的变化率。对于一般反应 aA + bB → cC + dD，在时间间隔 Δt 内的平均速率可以写成：
Rate = -1/a (Δ[A]/Δt) = -1/b (Δ[B]/Δt) = +1/c (Δ[C]/Δt) = +1/d (Δ[D]/Δt)
反应物前的负号是为了让计算出的速率保持正值。速率的常用单位是 mol dm⁻³ s⁻¹，根据反应快慢也可使用 mol dm⁻³ min⁻¹ 等其他时间单位。
It is also possible to determine the instantaneous rate at a specific moment by drawing a tangent to the concentration–time curve. The slope of the tangent gives the rate at that point. As the reaction progresses, the instantaneous rate generally decreases because reactant concentrations fall.
我们还可以通过在浓度–时间曲线上画切线来求出某一时刻的瞬时速率。切线的斜率即为该时刻的速率。随着反应进行，由于反应物浓度下降，瞬时速率通常会逐渐减小。
2. Experimental Measurement of Rates | 速率的实验测定
Several experimental techniques can be used to follow the progress of a reaction and calculate its rate. The choice depends on the physical or chemical property that changes as the reaction proceeds. Common methods include: measuring the decrease in mass when a gas is evolved (e.g. marble chips with acid in an open flask on a balance), collecting the volume of gas produced in a gas syringe or over water, monitoring colour change using a colorimeter or spectrophotometer, tracking pH changes for reactions that produce or consume H⁺ ions, and measuring electrical conductivity if the number or type of ions changes.
我们可以通过多种实验方法跟踪反应进程并计算速率，选择哪种方法取决于反应过程中变化的物理或化学性质。常见的方法有：在敞口容器中通过天平测量因气体逸出而导致的质量减少（如大理石与酸反应），用气体注射器或排水集气法收集气体体积，使用比色计或分光光度计监测颜色变化，对于产生或消耗 H⁺ 的反应追踪 pH 值的变化，以及当离子数目或种类改变时测量电导率。
can be followed by recording the volume of hydrogen gas evolved against time or by measuring the loss in mass as H₂ escapes. A graph of volume or mass versus time is plotted, and the slope at any point gives the rate.
例如，在反应 Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g) 中，速率可以通过记录氢气体积随时间的变化，或通过测量因 H₂ 逸出导致的质量损失来跟踪。绘制体积或质量对时间的曲线，曲线上任意一点的斜率即表示该时刻的速率。
3. Collision Theory Fundamentals | 碰撞理论基础
Collision theory states that for a reaction to occur, reactant particles must collide. However, not all collisions result in a chemical change. Two key requirements must be met: the colliding particles must possess a minimum amount of kinetic energy, known as the activation energy (Eₐ), and they must collide with the correct orientation so that the reactive parts of the molecules come into contact. Collisions that satisfy both conditions are called effective collisions.
碰撞理论指出，反应物粒子必须发生碰撞才能引发化学反应。但并非所有碰撞都会引起化学变化。必须同时满足两个关键要求：碰撞的粒子必须拥有最低限度的动能，即活化能 (Eₐ)；而且必须以正确的取向碰撞，使分子中能发生反应的部分相互接触。满足这两个条件的碰撞称为有效碰撞。
The rate of reaction is proportional to the number of effective collisions per unit time. Any factor that increases the frequency of collisions or the fraction of collisions that are effective will increase the reaction rate.
反应速率正比于单位时间内的有效碰撞次数。任何能提高碰撞频率或增大有效碰撞比例的因素，都会加快反应速率。
4. Activation Energy and Energy Profiles | 活化能与能量曲线
Activation energy (Eₐ) is the minimum energy that colliding particles must have in order for a reaction to take place. It can be thought of as an energy barrier that must be overcome. On a reaction coordinate diagram, the energy of the system rises to a maximum at the transition state (or activated complex) and then falls as products are formed. The difference in energy between the reactants and the transition state is the activation energy for the forward reaction. If the products are lower in energy than the reactants, the reaction is exothermic; if higher, it is endothermic.
活化能 (Eₐ) 是碰撞粒子发生反应所必须具备的最低能量，可将其看作必须克服的能垒。在反应坐标图中，体系能量先升高至过渡态（或活化络合物）达到最高点，然后随着产物生成而降低。反应物与过渡态之间的能量差即为正反应的活化能。如果产物能量比反应物低，则反应为放热反应；若产物能量更高，则为吸热反应。
Only particles with kinetic energy equal to or greater than Eₐ can surmount this barrier when they collide with the correct orientation. The larger the activation energy, the smaller the fraction of particles that possess sufficient energy at a given temperature, resulting in a slower reaction.
只有动能等于或大于 Eₐ 的粒子，在以正确取向碰撞时才能越过这个能垒。活化能越大，在给定温度下拥有足够能量的粒子比例就越小，反应也就越慢。
5. Concentration and Pressure Effects | 浓度与压强的影响
Increasing the concentration of reactants in a solution increases the number of particles per unit volume. This leads to a higher frequency of collisions between reactant particles, thereby increasing the rate of reaction. For gaseous reactions, raising the pressure (at constant temperature) effectively increases the concentration of gas molecules, producing a similar effect. According to collision theory, a higher concentration or pressure does not alter the activation energy, but it does raise the total number of collisions per second, including the number of effective collisions.
增大溶液中反应物的浓度，会提高单位体积内的粒子数目，从而增加反应物粒子之间的碰撞频率，加快反应速率。对于气体反应，在恒温下提高压强相当于增加气体分子的浓度，产生类似的效果。根据碰撞理论，更高的浓度或压强并不会改变活化能，但会提高每秒的总碰撞次数，其中也包括有效碰撞的次数。
6. Surface Area and Reaction Rate | 表面积与反应速率
For reactions involving solids, the rate depends on the surface area of the solid exposed to the other reactants. Breaking a solid into smaller pieces or grinding it into a powder greatly increases its total surface area. This allows more reactant particles to be exposed at the surface, increasing the frequency of collisions per unit time and thus accelerating the reaction. For instance, powdered calcium carbonate reacts much faster with hydrochloric acid than large marble chips of the same mass.
对于有固体参与的反应，速率取决于固体暴露给其他反应物的表面积大小。把固体破碎成小块或研磨成粉末能大幅增加其总表面积。这使得更多反应物粒子暴露在表面上，提高了单位时间内的碰撞频率，从而加快了反应。例如，粉末状的碳酸钙与盐酸反应，远比相同质量的大块大理石快得多。
7. Temperature and the Maxwell-Boltzmann Distribution | 温度与麦克斯韦-玻尔兹曼分布
Raising the temperature increases the average kinetic energy of the particles. This is described quantitatively by the Maxwell-Boltzmann distribution, which shows the distribution of kinetic energies among particles at a given temperature. The curve is asymmetric, with a small fraction of very slow particles, a large fraction around the most probable energy, and a tail to the right representing high-energy particles. Only those particles with energy greater than the activation energy Eₐ are able to react upon collision.
升高温度会增加粒子的平均动能。麦克斯韦-玻尔兹曼分布定量地描述了在某一温度下粒子动能的分布情况。该曲线是不对称的，一小部分粒子动能很低，大部分集中在最概然能量附近，而右侧的拖尾代表高能粒子。只有动能大于活化能 Eₐ 的粒子，在碰撞时才有可能发生反应。
When the temperature is increased, the distribution curve flattens and shifts to the right. The area under the curve to the right of Eₐ, which represents the fraction of particles with sufficient energy to react, increases dramatically. Moreover, the particles move faster, increasing the collision frequency. Both factors contribute to a higher rate of reaction. A useful rule of thumb is that for many reactions, a 10 °C rise in temperature roughly doubles the rate.
当温度升高时，分布曲线变平并向右移动。Eₐ 右侧曲线下的面积代表具有足够能量发生反应的粒子比例，该面积会显著增大。同时，粒子运动加快，碰撞频率也增加。这两个因素共同导致了反应速率的提升。一个有用的经验规则是，对许多反应而言，温度每升高 10 °C，反应速率大约加倍。
8. Catalysts and Their Mechanisms | 催化剂及其机理
A catalyst is a substance that increases the rate of a chemical reaction without itself being chemically consumed. It works by providing an alternative reaction pathway with a lower activation energy (Eₐ cat). Because the activation energy is reduced, a much larger fraction of particles possesses the necessary energy to undergo effective collisions at the same temperature. On an energy profile diagram, a catalysed pathway shows a lower energy peak compared with the uncatalysed reaction. Importantly, a catalyst does not alter the enthalpy change (ΔH) of the reaction, nor does it change the position of equilibrium.
催化剂是能增大化学反应速率而自身在化学上不被消耗的物质。其作用原理是提供一条活化能 (Eₐ cat) 较低的替代反应路径。由于活化能降低，在相同温度下，有足够能量进行有效碰撞的粒子比例大大增加。在能量曲线图中，催化路径的能量波峰比非催化路径更低。重要的是，催化剂不会改变反应的焓变 (ΔH)，也不会改变平衡位置。
There are two common types of catalysts: homogeneous catalysts, which are in the same phase as the reactants (e.g. an aqueous acid catalysing an ester hydrolysis), and heterogeneous catalysts, which are in a different phase (typically a solid catalyst with gaseous or liquid reactants). Heterogeneous catalysts usually work by adsorbing reactant molecules onto active sites on their surface, weakening bonds and facilitating reaction. Examples include iron in the Haber process and platinum in catalytic converters.
常见催化剂有两类：均相催化剂，与反应物处于同一相（例如水溶液中的酸催化酯水解反应）；以及非均相催化剂，处于不同相（通常是固体催化剂与气体或液体反应物）。非均相催化剂一般通过将反应物分子吸附到其表面的活性位点上，削弱化学键、促进反应来进行。例子包括哈伯法中的铁催化剂和催化转化器中的铂。
9. Rate Equations and Order of Reaction | 速率方程与反应级数
(or rate law). For a reaction aA + bB → products, the rate equation often takes the form:
Rate = k[A]m[B]n
Here k is the rate constant, which is temperature-dependent, and m and n are the orders of reaction with respect to A and B. The overall order of the reaction is m + n. The orders m and n are usually small integers (0, 1, 2) and must be determined experimentally; they are not necessarily the stoichiometric coefficients a and b.
反应速率与反应物浓度之间的关系可以用速率方程（速率定律）来概括。对于反应 aA + bB → 产物，速率方程通常具有以下形式：
Rate = k[A]m[B]n
其中 k 是速率常数（受温度影响），m 和 n 分别是对于 A 和 B 的反应级数。总反应级数为 m + n。级数 m 和 n 通常为小的整数（0, 1, 2），必须通过实验测定，它们不一定等于化学计量系数 a 和 b。
If m = 0, the rate is independent of the concentration of A – a zero‑ line with a negative slope equal to k. If m = 1, the rate is directly proportional to [A] – a first‑order reaction. A plot of ln[A] versus time yields a straight line with slope –k. If m = 2, the rate is proportional to [A]² – a second‑order reaction. A plot of 1/[A] versus time is linear with slope +k.
若 m = 0，速率与 A 的浓度无关——即零级反应；[A] 对时间作图得到一条斜率为 –k 的直线。若 m = 1，速率与 [A] 成正比——即一级反应；ln[A] 对时间作图得到一条斜率为 –k 的直线。若 m = 2，速率与 [A]² 成正比——即二级反应；1/[A] 对时间作图得到一条斜率为 +k 的直线。
10. Determining Rate Law Experimentally | 实验确定速率定律
e rate equation is the method of initial rates. A series of experiments are carried out in which the initial concentration of one reactant is changed while all others are kept constant. The initial rate is measured (usually by drawing a tangent to the concentration– he initial rate changes with the concentration of that reactant, the order with respect to it can be deduced. For instance, if doubling [A] doubles the initial rate, the reaction is first order in A; if the rate quadruples, it is second order; if the rate remains unchanged, it is zero order.
找出速率方程最常用的方法是初始速率法。进行一系列实验，每次只改变一种反应物的初始浓度，而保持其他反应物浓度不变，
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