📚 A-Level Chemistry: Core Concepts of Reaction Kinetics | A-Level 化学:反应动力学核心概念
Reaction kinetics is the study of how fast chemical reactions occur and what factors control that speed. It provides a quantitative framework for understanding reaction mechanisms, rate laws, and the energy requirements of chemical change.
反应动力学是研究化学反应发生速率以及哪些因素控制这一速率的学科。它为理解反应机理、速率定律以及化学变化所需的能量提供了定量框架。
1. Defining Reaction Rate | 什么是反应速率?
The rate of a reaction is the change in concentration of a reactant or product per unit time. The average rate over an interval is calculated as Δ[substance]/Δt, but chemists often need the instantaneous rate, which is the gradient of a concentration–time graph at a particular moment.
反应速率是反应物或产物浓度随时间的变化量。一段时间内的平均速率通过 Δ[物质]/Δt 计算,但化学家通常需要瞬时速率,即浓度-时间曲线上某一点的切线斜率。
For a general reaction A → B, the rate can be expressed as:
对于一般反应 A → B,速率可以表示为:
rate = −d[A]/dt = d[B]/dt
Because reactant concentrations decrease, the negative sign makes the rate positive. Rates are always positive quantities and are measured in mol dm⁻³ s⁻¹.
由于反应物浓度减小,负号使速率为正值。速率始终是正量,单位为 mol dm⁻³ s⁻¹。
2. Measuring Reaction Rates | 测定反应速率
Experimental methods for following a reaction must be fast enough to capture the concentration change at the chosen time scale. Common techniques include measuring gas volume, monitoring colour change using a colorimeter, and removing samples for titration.
跟踪反应的实验方法必须足够快,以便在选定时间尺度上捕捉浓度变化。常用技术包括测量气体体积、用比色计监测颜色变化,以及取样进行滴定。
- Gas volume: A gas syringe measures the volume of gaseous product evolved at regular intervals.
- Colorimetry: The intensity of a coloured species is directly proportional to its concentration (Beer–Lambert law).
- Titration: Quenched samples are titrated to determine the concentration of a reactant or product.
- 气体体积法:用气筒以固定时间间隔测量生成气体的体积。
- 比色法:有色物质的颜色强度与其浓度成正比(比尔-朗伯定律)。
- 滴定法:对淬灭样品进行滴定,以确定反应物或产物的浓度。
3. The Rate Equation | 速率方程
The rate equation relates the rate of a reaction to the concentration of species raised to powers called orders. For a reaction aA + bB → products, the rate equation is generally:
速率方程将反应速率与各物种浓度的幂(称为级数)联系起来。对于反应 aA + bB → 产物,速率方程通常为:
rate = k[A]m[B]n
Here, k is the rate constant, and m and n are the orders of reaction with respect to A and B. The values of m and n must be determined experimentally; they are not derived from the stoichiometric coefficients.
其中 k 是速率常数,m 和 n 分别是关于 A 和 B 的反应级数。m 和 n 的值必须通过实验确定,不能由化学计量系数推导。
The overall order is m + n. If the concentration of a reactant is doubled and the rate doubles, the order with respect to that reactant is 1. If the rate quadruples, the order is 2; if the rate does not change, the order is 0.
总级数为 m + n。若某反应物浓度加倍后速率也加倍,则该反应物的级数为1;若速率变为四倍,则级数为2;若速率不变,则级数为0。
4. Zero-Order Reactions | 零级反应
In a zero-order reaction, the rate is independent of the concentration of the reactant. The rate equation is rate = k, and a concentration–time graph gives a straight line with a negative slope.
在零级反应中,速率与反应物浓度无关。速率方程为 rate = k,浓度-时间图是一条斜率为负的直线。
[A]= [A]0 − kt
The half-life of a zero-order reaction decreases as the initial concentration decreases because the amount consumed per unit time is fixed.
零级反应的半衰期随初始浓度降低而减小,因为单位时间内消耗的量为固定值。
5. First-Order Reactions | 一级反应
For a first-order reaction, rate = k[A]. The concentration–time curve is exponential, and the half-life is constant, independent of the initial concentration.
对于一级反应,rate = k[A]。浓度-时间曲线呈指数形式,半衰期恒定,与初始浓度无关。
The integrated rate law and half-life are:
积分速率定律和半衰期为:
ln[A]t = ln[A]0 − kt
t1/2 = ln 2 / k
A plot of ln[A] versus time is linear, with slope −k. This is a reliable way to test whether a reaction is first order.
ln[A] 对时间作图呈直线,斜率为 −k。这是检验一级反应的可靠方法。
6. Second-Order Reactions | 二级反应
When the overall order is 2, the reaction may be second order in one reactant (rate = k[A]²) or first order in each of two reactants (rate = k[A][B]). For a single reactant, the integrated rate law is:
当总级数为2时,反应可能对一种反应物呈二级(rate = k[A]²),或对两种反应物各呈一级(rate = k[A][B])。对于单一反应物,积分速率定律为:
1/[A]t = 1/[A]0 + kt
For this case, a plot of 1/[A] versus time gives a straight line. The half-life for a second-order reaction increases with decreasing concentration.
在这种情况下,1/[A] 对时间作图呈直线。二级反应的半衰期随浓度降低而增大。
7. Collision Theory | 碰撞理论
For a reaction to occur, reactant particles must collide with sufficient energy and the correct orientation. Only a fraction of collisions are successful; these are called effective collisions.
反应要发生,反应物粒子必须发生碰撞,且具有足够的能量和正确的取向。只有一小部分碰撞是成功的,称为有效碰撞。
The minimum energy required to break bonds is the activation energy (Eₐ). The rate of reaction depends on the fraction of collisions that have at least this energy.
断裂化学键所需的最低能量称为活化能(Eₐ)。反应速率取决于至少具有该能量碰撞的比例。
Table 1 summarises the factors that affect reaction rate:
表1总结了影响反应速率的因素:
| Factor | Effect |
| Concentration / pressure | Increases collision frequency |
| Temperature | Increases collision energy and frequency |
| Catalyst | Provides an alternative route with lower Eₐ |
| Surface area | Increases number of exposed particles |
| 因素 | 影响 |
| 浓度/压强 | 增加碰撞频率 |
| 温度 | 增加碰撞能量和频率 |
| 催化剂 | 提供活化能更低的新路径 |
| 表面积 | 增加暴露粒子数 |
8. Boltzmann Distribution | 玻尔兹曼分布
The Maxwell–Boltzmann distribution shows the spread of energies among particles at a given temperature. The area under the curve represents the total number of particles, and the shaded region to the right of Eₐ indicates the number with energy ≥ Eₐ.
麦克斯韦-玻尔兹曼分布显示在给定温度下粒子能量的分布。曲线下面积代表总粒子数,Eₐ右侧的阴影区域表示能量 ≥ Eₐ 的粒子数量。
When temperature increases, the curve flattens and shifts to the right, so the fraction of particles exceeding Eₐ increases significantly. This explains why a small rise in temperature causes a large increase in rate.
当温度升高时,曲线变得平坦并右移,因此超过Eₐ的粒子比例显著增大。这解释了为什么温度小幅升高会导致速率大幅增加。
9. The Arrhenius Equation | 阿伦尼乌斯方程
The Arrhenius equation links the rate constant, temperature, and activation energy:
阿伦尼乌斯方程将速率常数、温度和活化能联系起来:
k = A e−Eₐ/(RT)
A is the pre-exponential (frequency) factor, and R is the gas constant. Taking natural logarithms gives:
A 是指前因子(频率因子),R 是气体常数。取自然对数得到:
ln k = ln A − Eₐ/(RT)
Thus, plotting ln k against 1/T gives a straight line with slope −Eₐ/R. This allows experimental determination of Eₐ.
因此,以 ln k 对 1/T 作图得直线,斜率为 −Eₐ/R。这使得实验测定 Eₐ 成为可能。
10. Catalysis | 催化作用
A catalyst speeds up a reaction by providing an alternative pathway with a lower activation energy. It takes part in the reaction but is regenerated unchanged at the end.
催化剂通过提供活化能较低的新路径来加快反应。它参与反应,但在反应结束时保持不变地再生。
Homogeneous catalysis occurs when the catalyst and reactants are in the same phase, such as acid catalysis in ester hydrolysis. Heterogeneous catalysis involves a different phase, typical of solid catalysts in gas-phase reactions.
均相催化指催化剂与反应物处于同一相,例如酯水解中的酸催化。多相催化涉及不同相,常见于气相反应中的固体催化剂。
Catalysts are important in industrial processes because they reduce energy costs and increase productivity without being consumed.
催化剂在工业过程中非常重要,因为它们在自身不被消耗的情况下降低能源成本并提高生产率。
11. Rate-Determining Step | 速率控制步骤
Reactions often occur in a series of elementary steps known as a reaction mechanism. The slowest step in this sequence is the rate-determining step (RDS) because it limits the overall rate.
反应通常以一系列基元步骤发生,称为反应机理。该序列中最慢的步骤是速率控制步骤(RDS),因为它限制了总速率。
The rate equation can be predicted from the RDS. For example, if the RDS is A + B → X, the predicted rate law is rate = k[A][B]. Comparing the predicted rate law with the experimental one helps confirm or reject a proposed mechanism.
速率方程可以从RDS预测。例如,如果RDS是A + B → X,则预测的速率定律为 rate = k[A][B]。将预测的速率定律与实验测得的结果比较,有助于确认或排除所提出的机理。
12. Molecularity | 反应分子数
Molecularity refers to the number of reactant particles involved in an elementary step. A unimolecular step involves one molecule, a bimolecular step involves two, and a termolecular step involves three (rare due to low probability).
反应分子数指基元步骤中参与的反应物粒子数。单分子步骤涉及一个分子,双分子步骤涉及两个,三分子步骤涉及三个(因概率极低而罕见)。
Reaction order is defined experimentally for the overall reaction, while molecularity applies to a single elementary step. They are equal only when the elementary step is the entire reaction.
反应级数是通过实验对总反应定义的,而反应分子数适用于单个基元步骤。只有当该基元步骤就是整个反应时,两者才相等。
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