Rate, Equilibrium & Energetics | 速率、平衡与能量学

📚 Rate, Equilibrium & Energetics | 速率、平衡与能量学

This combined revision guide covers the core dynamic concepts in Edexcel A-Level Chemistry: reaction kinetics, chemical equilibrium, and energy changes. These three areas form an interconnected framework for understanding why reactions occur and how fast they proceed.

本综合复习指南涵盖 Edexcel A-Level 化学的核心动态概念：反应动力学、化学平衡与能量变化。这三个领域构成了理解反应为何发生以及反应速率多快的相互关联框架。

1. Reaction Rate Fundamentals | 反应速率基础

Reaction rate is defined as the change in concentration of a reactant or product per unit time. The instantaneous rate is the gradient of a concentration-time graph at a specific moment.

反应速率定义为反应物或产物浓度随时间的变化量。瞬时速率是浓度-时间图上某特定时刻的切线斜率。

Rate = Δ[A] / Δt, where [A] is concentration in mol dm⁻³ and t is time in seconds.
Units for rate are typically mol dm⁻³ s⁻¹.
Monitoring techniques include colorimetry, gas volume measurement, pH probes, and conductimetry.

速率 = Δ[A] / Δt，其中 [A] 为浓度，单位 mol dm⁻³；t 为时间，单位秒。
速率单位通常为 mol dm⁻³ s⁻¹。
监测方法包括比色法、气体体积测量、pH 探头和电导法。

2. Collision Theory | 碰撞理论

For a reaction to occur, particles must collide with sufficient energy (exceeding the activation energy, Eₐ) and correct orientation. Only effective collisions lead to product formation.

反应发生的条件是粒子必须发生碰撞，且碰撞能量超过活化能（Eₐ）、取向正确。只有有效碰撞才能生成产物。

Effective Collision = Sufficient Energy + Correct Orientation

有效碰撞 = 足够能量 + 正确取向

The Boltzmann distribution curve illustrates the spread of molecular energies at a given temperature. The area under the curve equals the total number of particles, and the shaded region beyond Eₐ represents the fraction capable of reacting.

玻尔兹曼分布曲线展示了给定温度下分子能量的分布情况。曲线下面积等于粒子总数，Eₐ 右侧的阴影区域代表能够发生反应的粒子比例。

3. Factors Affecting Rate: Concentration & Pressure | 影响速率的因素：浓度与压力

Increasing concentration of reactants (or pressure for gases) increases the number of particles per unit volume, leading to more frequent collisions per second. This raises the rate of reaction.

增加反应物浓度（对气体而言增加压力）会提高单位体积内的粒子数目，导致每秒碰撞频率增加，从而加快反应速率。

Factor	Effect on Collision Frequency	Effect on Rate
Higher concentration	Increases	Increases
Higher pressure (gas)	Increases	Increases

因素	对碰撞频率的影响	对速率的影响
浓度升高	增大	加快
压力升高（气体）	增大	加快

A common misconception is that increasing concentration changes the activation energy. It does not — only the frequency of collisions increases, not the energy distribution.

常见误区是认为增大浓度会改变活化能。事实并非如此——增加的只是碰撞频率，能量分布并未改变。

4. Temperature and the Boltzmann Distribution | 温度与玻尔兹曼分布

Raising the temperature increases the average kinetic energy of particles. The Boltzmann curve flattens and shifts to the right, with a much larger proportion of molecules now having energy above Eₐ. This explains why a 10 K rise can roughly double the reaction rate.

升高温度会增大粒子的平均动能。玻尔兹曼曲线变得平坦并向右移动，能量超过 Eₐ 的分子比例显著增大。这解释了为何温度升高 10 K 能使反应速率大约翻倍。

Rate Increase ∝ Fraction of Molecules with E ≥ Eₐ

速率增加 ∝ 能量 ≥ Eₐ 的分子比例

Note: the area under the curve remains constant because the total number of particles does not change. Only the distribution shape changes.

注意：曲线下面积保持不变，因为总粒子数不变。变化的只是分布形状。

5. Catalysts and Activation Energy | 催化剂与活化能

A catalyst provides an alternative reaction pathway with a lower activation energy. It is not consumed in the reaction and does not alter the position of equilibrium.

催化剂提供了活化能更低的新反应路径。它在反应中不被消耗，也不改变平衡位置。

Homogeneous catalysts are in the same phase as reactants (e.g., enzymes in solution, H₂SO₄ in esterification).
Heterogeneous catalysts are in a different phase (e.g., Fe in the Haber process, V₂O₅ in the Contact process).
Catalysts work by adsorption of reactants onto active sites, weakening bonds and lowering Eₐ.

均相催化剂与反应物处于同一相态（例如溶液中的酶、酯化反应中的 H₂SO₄）。
多相催化剂与反应物处于不同相态（例如哈伯法中的 Fe、接触法中的 V₂O₅）。
催化剂通过将反应物吸附到活性位点、削弱化学键来降低 Eₐ。

Catalyst lowers Eₐ without changing ΔH

催化剂降低 Eₐ，但不改变 ΔH

6. Dynamic Equilibrium | 动态平衡

Dynamic equilibrium occurs in a closed system when the forward and reverse reaction rates are equal. Concentrations of all species remain constant, but reactions are still occurring at the molecular level.

动态平衡是在封闭体系中正逆反应速率相等时达到的状态。所有物质的浓度保持不变，但分子层面上的反应仍在持续进行。

Must be a closed system for equilibrium to be established.
Rates are equal, not zero.
Macroscopic properties (colour, pressure, concentration) are constant.

必须是封闭体系才能建立平衡。
正逆速率相等，但不是零。
宏观性质（颜色、压力、浓度）保持恒定。

7. Le Chatelier’s Principle | 勒夏特列原理

Le Chatelier’s principle states that if a system at equilibrium is subjected to a change in conditions, the equilibrium position will shift to counteract that change.

勒夏特列原理指出：如果平衡体系的条件发生改变，平衡位置将向抵消该改变的方向移动。

N₂(g) + 3H₂(g) ⇌ 2NH₃(g) ΔH = −92 kJ mol⁻¹

Change	Position Shift
Increase pressure	Toward fewer moles (products, 2 vs 4)
Increase temperature	Toward endothermic direction (backward)
Remove NH₃	Toward products (forward)

条件改变	平衡移动方向
增大压力	向气体摩尔数减少的方向（产物，2 vs 4）
升高温度	向吸热方向（逆反应）
移走 NH₃	向产物方向（正反应）

An inert gas added at constant volume will not affect equilibrium position because partial pressures remain unchanged. However, adding inert gas at constant pressure will lower partial pressures and can shift equilibrium in the direction of more gas moles.

恒容下加入惰性气体不会影响平衡位置，因为各组分分压不变。但恒压下加入惰性气体会降低分压，使平衡向气体摩尔数增大的方向移动。

8. The Equilibrium Constant Kc | 平衡常数 Kc

For a reaction aA + bB ⇌ cC + dD, the equilibrium constant expression is:

对于反应 aA + bB ⇌ cC + dD，平衡常数表达式为：

Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ

Kc is constant at a fixed temperature.
Pure solids and liquids are excluded from the equilibrium expression.
Large Kc (≫ 1) favours products; small Kc (≪ 1) favours reactants.

在固定温度下 Kc 为常数。
纯固体和纯液体不写入平衡表达式。
Kc 很大（≫ 1）时利于产物；Kc 很小（≪ 1）时利于反应物。

Units of Kc depend on the stoichiometry. For the Haber process, Kc = [NH₃]² / ([N₂][H₂]³), yielding units of dm⁶ mol⁻².

Kc 的单位取决于化学计量数。对于哈伯法，Kc = [NH₃]² / ([N₂][H₂]³)，单位为 dm⁶ mol⁻²。

9. Energetics: Enthalpy Changes | 能量学：焓变

Standard enthalpy change of reaction (ΔH°ᵣ) is the heat change when reaction quantities of reactants react under standard conditions (298 K, 1 atm, 1 mol dm⁻³).

标准反应焓变（ΔH°ᵣ）是指在标准条件下（298 K、1 atm、1 mol dm⁻³）按反应计量数完全反应时的热量变化。

ΔH = Σ(Products) − Σ(Reactants)

ΔH = Σ(生成物键能之和) − Σ(反应物键能之和)

Exothermic reactions: ΔH is negative; heat is released to surroundings.
Endothermic reactions: ΔH is positive; heat is absorbed from surroundings.
Bond breaking is endothermic; bond forming is exothermic.

放热反应：ΔH 为负值，热量释放到环境。
吸热反应：ΔH 为正值，热量从环境吸收。
断键吸热，成键放热。

ΔH°ᵣ = Σ(Bond enthalpies of bonds broken) − Σ(Bond enthalpies of bonds formed)

ΔH°ᵣ = Σ(断裂键的键能) − Σ(形成键的键能)

10. Entropy and Spontaneity | 熵与自发性

Entropy (S) measures the degree of disorder or randomness in a system. Gases have higher entropy than liquids, which have higher entropy than solids.

熵（S）衡量体系的无序程度或混乱度。气体的熵大于液体，液体的熵大于固体。

ΔS°ₛᵧₛₜₑₘ = ΣS°(products) − ΣS°(reactants)

ΔS°ₛᵧₛₜₑₘ = ΣS°(生成物) − ΣS°(反应物)

The Gibbs free energy change determines spontaneity:

吉布斯自由能变决定反应的自发性：

ΔG = ΔH − TΔS

ΔG < 0: reaction is spontaneous (feasible).
ΔG = 0: system is at equilibrium.
ΔG > 0: reaction is non-spontaneous.

ΔG < 0：反应自发进行。
ΔG = 0：体系处于平衡状态。
ΔG > 0：反应非自发。

An endothermic reaction can still be spontaneous if the entropy increase is large enough, such that TΔS exceeds ΔH at high temperatures.

吸热反应仍可自发进行，前提是熵增足够大，使得在高温下 TΔS 超过 ΔH。

11. Integrated Application: The Haber Process | 综合应用：哈伯法

The Haber process N₂ + 3H₂ ⇌ 2NH₃ exemplifies all principles discussed. Operating at 450 °C, 200 atm, with an iron catalyst, industrial conditions balance rate, yield and economics.

哈伯法 N₂ + 3H₂ ⇌ 2NH₃ 体现了上述所有原理。工业条件为 450 °C、200 atm，使用铁催化剂，在速率、产率和经济性之间取得平衡。

Condition	Rate Effect	Yield Effect	Compromise
450 °C	Fast enough	Lower than at low T	Moderate temperature
200 atm	Increases	Higher yield	High but not extreme
Fe catalyst	Increases	No effect	Essential for viability

条件	对速率	对产率	折中方案
450 °C	足够快	低于低温条件	中等温度
200 atm	加快	提高产率	高但不过高
Fe 催化剂	加快	无影响	工业可行性关键

The unreacted gases are recycled, and ammonia is removed by liquefaction, continuously shifting equilibrium toward products.

未反应的气体被循环利用，氨通过液化分离，持续将平衡推向产物方向。

12. Exam Strategy | 考试策略

Edexcel examiners frequently test these concepts through graph analysis, equilibrium calculations, and explaining industrial conditions. Marks are often lost by omitting the word ‘rate’ when asked about collision frequency changes.

Edexcel 考官经常通过图表分析、平衡计算和解释工业条件来考察这些概念。学生常因在回答碰撞频率变化时遗漏”速率”一词而失分。

Always specify ‘closed system’ when defining dynamic equilibrium.
Refer to ‘activation energy is lowered’ rather than ‘energy is raised’ when explaining catalysts.
For Kc calculations, construct an ICE table (Initial, Change, Equilibrium) systematically.
Clearly distinguish ΔH from Eₐ — ΔH is the overall energy change, Eₐ is the energy barrier.

定义动态平衡时务必说明”封闭体系”。
解释催化剂时应说”活化能被降低”而非”能量被提高”。
计算 Kc 时，系统性地建立 ICE 表格（初始、变化、平衡）。
明确区分 ΔH 与 Eₐ——ΔH 是总能量变化，Eₐ 是能垒。

Practice drawing Boltzmann curves at two temperatures and labelling Eₐ. This skill alone earns multiple marks in the kinetics section.

练习绘制两个温度下的玻尔兹曼曲线并标注 Eₐ。仅此一项技能就能在动力学部分获得多分。

Published by TutorHao | Chemistry Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Rate, Equilibrium & Energetics | 速率、平衡与能量学