📚 Edexcel A-Level Combined Science 145: Energetics, Rates and Equilibrium | Edexcel A-Level 综合科学 145：能量学、速率与平衡
This revision guide covers the Combined Science 145 topic cluster for Edexcel A-Level Chemistry: enthalpy changes, calorimetry, Hess’s law, reaction rates, collision theory, Maxwell-Boltzmann distributions, catalysts, dynamic equilibrium and equilibrium constants. Use the paired English-Chinese explanations to master key definitions and calculations before your exam.
本复习指南涵盖 Edexcel A-Level 化学综合科学 145 主题群：焓变、量热法、盖斯定律、反应速率、碰撞理论、麦克斯韦-玻尔兹曼分布、催化剂、动态平衡和平衡常数。使用中英对照解释，在考试前掌握关键定义与计算。
1. Enthalpy Changes and Reaction Profiles | 焓变与反应历程
Enthalpy change (ΔH) is the heat energy transferred at constant pressure. Exothermic reactions release energy to the surroundings, so ΔH is negative, while endothermic reactions absorb energy, so ΔH is positive.
焓变（ΔH）是在恒压下传递的热量。放热反应向周围环境释放能量，因此 ΔH 为负值；吸热反应从周围吸收能量，因此 ΔH 为正值。
Reaction profile diagrams show the relative enthalpy of reactants and products. For an exothermic reaction, the products sit lower than the reactants; for an endothermic reaction, the products sit higher. The activation energy (Eₐ) is always shown as the energy barrier from reactants to the transition state.
反应历程图显示了反应物和生成物的相对焓。放热反应的生成物位置低于反应物；吸热反应的生成物位置高于反应物。活化能（Eₐ）始终表示为从反应物到过渡态的能垒。
- ΔH negative → exothermic; ΔH positive → endothermic | ΔH 为负 → 放热；ΔH 为正 → 吸热
- Standard conditions: 100 kPa, 298 K, 1 mol dm⁻³ solutions | 标准条件：100 kPa、298 K、1 mol dm⁻³ 溶液
2. Calorimetry and Measuring ΔH | 量热法与 ΔH 的测量
Calorimetry is used to determine enthalpy changes for reactions in solution or combustion. The heat transferred is calculated using q = m c ΔT, where m is the mass of water or solution, c is the specific heat capacity, and ΔT is the temperature change.
量热法用于测定溶液反应或燃烧反应的焓变。传递的热量使用 q = m c ΔT 计算，其中 m 为水或溶液的质量，c 为比热容，ΔT 为温度变化。
q = m c ΔT
To convert heat energy into molar enthalpy change, divide q by the number of moles of the limiting reactant. Then attach a negative sign if the temperature rises, because the reaction is exothermic.
将热量除以限制反应物的物质的量，即可将热能转换为摩尔焓变。若温度升高，则在数值前加上负号，因为反应是放热的。
- ΔH = −q / n or ΔH = +q / n depending on direction of heat transfer | ΔH = −q / n 或 ΔH = +q / n，取决于热量传递方向
- Typical errors: heat loss to surroundings, incomplete combustion, assuming solution density equals water | 常见误差：向环境散热、燃烧不完全、假设溶液密度与水相同
3. Hess’s Law and Enthalpy Cycles | 盖斯定律与焓循环
Hess’s law states that the total enthalpy change for a reaction is independent of the route taken, provided the initial and final conditions are the same. This allows unknown ΔH values to be found from known enthalpy changes of formation or combustion.
盖斯定律指出，只要初始和最终条件相同，反应的总焓变与所采取的路径无关。因此可以利用已知的生成焓变或燃烧焓变来求解未知的 ΔH。
In a formation cycle, the reaction enthalpy is calculated as the sum of ΔHf of products minus the sum of ΔHf of reactants. In a combustion cycle, the reverse applies because reactants and products both burn to the same oxides.
在生成循环中，反应焓等于生成物 ΔHf 之和减去反应物 ΔHf 之和。在燃烧循环中则相反，因为反应物和生成物都燃烧生成相同的氧化物。
ΔHr = Σ ΔHf(products) − Σ ΔHf(reactants)
Always draw the cycle with arrows pointing in the direction of the definition. Reversing an arrow changes the sign of ΔH.
绘制循环时，箭头始终指向定义的方向。反转箭头会改变 ΔH 的正负号。
4. Bond Enthalpy Calculations | 键焓计算
Bond enthalpy is the energy required to break one mole of a covalent bond in the gaseous state. Mean bond enthalpies are averaged over many compounds, so calculations give an approximate ΔH.
键焓是在气态下断裂一摩尔共价键所需的能量。平均键焓是许多化合物中的平均值，因此计算得到的 ΔH 为近似值。
ΔH ≈ Σ E(bonds broken) − Σ E(bonds formed)
Bond breaking is always endothermic and bond making is always exothermic. If the energy released by forming bonds is greater than the energy absorbed breaking bonds, the overall reaction is exothermic.
断键总是吸热，成键总是放热。如果成键释放的能量大于断键吸收的能量，则总反应为放热反应。
| Bond | 键 | Mean bond enthalpy / kJ mol⁻¹ | 平均键焓 / kJ mol⁻¹ |
| C−H | 碳氢键 | 413 |
| O=O | 氧氧双键 | 498 |
| H−O | 氢氧键 | 463 |
5. Collision Theory and Rates of Reaction | 碰撞理论与反应速率
For a reaction to occur, particles must collide with energy greater than or equal to the activation energy, and in the correct orientation. The rate of reaction depends on the frequency of successful collisions.
要发生反应，粒子必须发生碰撞，且碰撞能量大于或等于活化能，并以正确方向碰撞。反应速率取决于有效碰撞的频率。
Increasing concentration or pressure increases the number of particles per unit volume, so successful collisions happen more often. Increasing temperature increases both collision frequency and the proportion of particles with energy above Eₐ.
增大浓度或压强会增加单位体积内的粒子数，因此有效碰撞更频繁。升高温度既增加碰撞频率，也提高能量超过 Eₐ 的粒子比例。
- Rate = change in concentration ÷ time | 速率 = 浓度变化量 ÷ 时间
- Units: mol dm⁻³ s⁻¹ | 单位：mol dm⁻³ s⁻¹
6. Maxwell-Boltzmann Distribution and Temperature | 麦克斯韦-玻尔兹曼分布与温度
The Maxwell-Boltzmann distribution shows the range of kinetic energies of gas particles at a given temperature. The area under the curve represents the total number of particles.
麦克斯韦-玻尔兹曼分布显示了给定温度下气体粒子动能的范围。曲线下的面积代表粒子总数。
The activation energy is drawn as a vertical line to the right of the peak. Only particles to the right of this line have enough energy to react.
活化能绘制为峰右侧的一条垂直线。只有位于该线右侧的粒子才有足够能量发生反应。
Raising the temperature flattens the curve and shifts the peak to the right, but keeps the total area constant. The number of particles with energy above Eₐ increases sharply, which explains why rate increases rapidly with temperature.
升高温度使曲线变平缓，峰值右移，但总面积保持不变。能量超过 Eₐ 的粒子数急剧增加，这解释了为什么速率随温度迅速增大。
7. Catalysts and Activation Energy | 催化剂与活化能
A catalyst increases the rate of a reaction by providing an alternative reaction pathway with a lower activation energy. The catalyst is chemically unchanged at the end of the reaction.
催化剂通过提供具有较低活化能的替代反应途径来提高反应速率。催化剂在反应结束时化学性质不变。
On a Maxwell-Boltzmann diagram, the Eₐ line moves to the left when a catalyst is added. A much larger area of the curve now lies to the right of Eₐ, so many more particles have sufficient energy to react.
在麦克斯韦-玻尔兹曼图中，加入催化剂后 Eₐ 线向左移动。曲线中位于 Eₐ 右侧的面积大大增加，因此有更多粒子具有足够的能量进行反应。
- Heterogeneous catalyst: different phase from reactants | 多相催化剂：与反应物不同相
- Homogeneous catalyst: same phase as reactants | 均相催化剂：与反应物相同相
- Enzymes are biological catalysts | 酶是生物催化剂
8. Dynamic Equilibrium and Le Chatelier’s Principle | 动态平衡与勒夏特列原理
Dynamic equilibrium occurs in a closed system when the forward and reverse reactions proceed at equal rates. The concentrations of reactants and products remain constant, but both reactions continue.
动态平衡发生在封闭系统中，此时正反应与逆反应速率相等。反应物和生成物的浓度保持不变，但两个反应仍在继续进行。
Le Chatelier’s principle states that if a system at equilibrium is subjected to a change in concentration, pressure or temperature, the position of equilibrium shifts to oppose the change.
勒夏特列原理指出，若处于平衡状态的系统受到浓度、压强或温度的改变，平衡位置会移动以对抗该改变。
- Increase concentration of a reactant → shift to products | 增大反应物浓度 → 平衡向生成物方向移动
- Increase pressure → shift to side with fewer gas moles | 增大压强 → 平衡向气体摩尔数较少的一侧移动
- Increase temperature → shift in endothermic direction | 升高温度 → 平衡向吸热方向移动
9. Equilibrium Constants in Homogeneous Systems | 均相体系中的平衡常数
For a general homogeneous reaction aA + bB ⇌ cC + dD, the equilibrium constant Kc is expressed as the product concentrations raised to their stoichiometric powers divided by the reactant concentrations raised to theirs.
对于一般的均相反应 aA + bB ⇌ cC + dD，平衡常数 Kc 表示为生成物浓度以其化学计量数为幂的乘积，除以反应物浓度以其化学计量数为幂的乘积。
Kc = [C]ᶜ [D]ᵈ / [A]ᵃ [B]ᵇ
Kc is only affected by temperature. If Kc is large, the equilibrium lies far to the right; if Kc is small, the equilibrium lies far to the left.
Kc 仅受温度影响。若 Kc 较大，平衡位置偏向右侧；若 Kc 较小，平衡位置偏向左侧。
- Units of Kc depend on the stoichiometry of the reaction | Kc 的单位取决于反应的化学计量数
- Pure solids and liquids are not included in Kc expressions | 纯固体和纯液体不写入 Kc 表达式
10. Exam Technique for Combined Science 145 | 综合科学 145 的考试技巧
When answering enthalpy questions, show Hess cycles with labelled arrows and ensure each ΔH has the correct sign. For rate questions, always link observations to collision frequency and activation energy rather than just stating ‘particles collide more’.
回答焓变题目时，画出带标注箭头的盖斯循环，并确保每个 ΔH 的正负号正确。回答速率问题时，始终将现象与碰撞频率和活化能联系起来，而不仅仅是陈述“粒子碰撞更多”。
For equilibrium questions, identify whether the forward reaction is exothermic or endothermic from the given ΔH. Then apply Le Chatelier’s principle step by step: state the change, state the shift, and explain the effect on yield or concentration.
对于平衡题目，先根据给定的 ΔH 判断正反应是放热还是吸热。然后逐步应用勒夏特列原理：说明变化、说明平衡移动方向，并解释对产率或浓度的影响。
Practice calculating Kc using initial and equilibrium moles, then convert to concentrations by dividing by the total volume. Always check the units of Kc and round to the appropriate number of significant figures.
练习使用初始物质的量和平衡物质的量计算 Kc，然后除以总体积转换为浓度。务必检查 Kc 的单位，并按要求保留适当数量的有效数字。
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