Entropy, Enthalpy Changes and Free Energy | 熵、焓变与自由能

📚 Entropy, Enthalpy Changes and Free Energy | 熵、焓变与自由能

In A-Level Chemistry, understanding why reactions occur requires more than just examining energy released or absorbed as heat. The concepts of entropy and free energy provide a deeper explanation for the direction of spontaneous change and the position of equilibrium. This article explores entropy, its role alongside enthalpy, and how the Gibbs free energy combines these two driving forces to predict chemical feasibility.

在A-Level化学中，理解反应为何发生，不能只研究以热的形式释放或吸收的能量。熵和自由能的概念为自发变化的方向和平衡位置提供了更深刻的解释。本文探讨熵的概念、熵与焓的作用，以及吉布斯自由能如何将这两种驱动力结合起来，预测化学反应的可行性。

1. What is Entropy? | 什么是熵？

Entropy, symbol S, is a measure of the disorder or randomness of a system. The more ways particles and their energy can be arranged, the higher the entropy. Solids have low entropy because particles are locked in fixed positions; liquids have higher entropy; gases have very high entropy due to free, chaotic motion. Entropy is measured in J K⁻¹ mol⁻¹.

熵（符号 S）是系统无序度或随机性的量度。粒子及其能量可以排列的方式越多，熵越高。固体由于粒子固定在确定位置，熵较低；液体熵较高；气体因自由、混乱的运动，熵很高。熵的单位是 J K⁻¹ mol⁻¹。

2. Entropy Changes in Physical Processes | 物理过程中的熵变

Melting, boiling and dissolving all involve increases in entropy because particles become more dispersed. For example, H₂O(s) → H₂O(l) has a positive ΔS, as the liquid water molecules have greater freedom. The reverse processes—freezing, condensation—lead to a decrease in entropy (negative ΔS). When a solute dissolves, the entropy usually increases due to the mixing of particles, though sometimes solvent ordering can lead to small decreases.

熔化、沸腾和溶解都会导致熵增加，因为粒子变得更加分散。例如，H₂O(s) → H₂O(l) 的 ΔS 为正值，因为液态水分子拥有更大的自由度。相反的过程——凝固、冷凝——则导致熵减小（ΔS 负值）。溶质溶解时，通常由于粒子混合熵增加，尽管有时溶剂的整齐排列可能导致小幅减小。

3. Standard Entropy | 标准熵

The standard molar entropy (S°) of a substance is the entropy of one mole under standard conditions (100 kPa, usually 298 K). Unlike enthalpy, absolute entropy values can be determined: a perfectly ordered crystal at 0 K has zero entropy (Third Law of Thermodynamics). Standard entropies of elements and compounds are listed in data tables. Gases generally have much larger S° values than solids.

物质的标准摩尔熵（S°）是一摩尔物质在标准条件下（100 kPa，通常298 K）的熵。与焓不同，熵的绝对值是可以测定的：完美有序的晶体在0 K时熵为零（热力学第三定律）。元素和化合物的标准熵值列于数据表中。气体的 S° 值通常远大于固体。

4. Calculating Entropy Change of a System | 计算系统的熵变

The entropy change of a chemical system, ΔS°system, is calculated from standard entropies: ΔS°system = Σ S°(products) – Σ S°(reactants). For example, for the reaction 2H₂(g) + O₂(g) → 2H₂O(l), the entropy of the system decreases sharply because three moles of gases turn into two moles of liquid.

化学系统的熵变 ΔS°system 由标准熵计算：ΔS°system = Σ S°(产物) – Σ S°(反应物)。例如，反应 2H₂(g) + O₂(g) → 2H₂O(l) 的系统熵大幅减小，因为三摩尔气体转化为两摩尔液体。

5. Entropy Change of the Surroundings | 环境的熵变

The entropy change of the surroundings depends on the enthalpy change of the reaction. Exothermic reactions transfer heat to the surroundings, increasing their entropy. The relationship is ΔS°surroundings = –ΔH°/T, where T is the absolute temperature in Kelvin. A negative ΔH° (exothermic) gives a positive ΔSsurr, while an endothermic reaction (positive ΔH°) decreases the entropy of the surroundings.

环境的熵变取决于反应的焓变。放热反应将热传递给环境，增加其熵。关系式为 ΔS°环境 = –ΔH°/T，其中 T 是开尔文温度。ΔH° 为负（放热）时，ΔS环境为正；而吸热反应（ΔH° 为正）则会降低环境的熵。

6. Total Entropy Change and Spontaneity | 总熵变与自发性

According to the Second Law of Thermodynamics, a process is spontaneous if the total entropy change of the universe (system + surroundings) is positive. ΔS°total = ΔS°system + ΔS°surroundings. If ΔS°total > 0, the reaction is thermodynamically feasible. A negative total entropy change means the reaction cannot occur on its own.

根据热力学第二定律，如果宇宙（系统+环境）的总熵变为正，即过程自发。ΔS°总 = ΔS°系统 + ΔS°环境。如果 ΔS°总 > 0，反应在热力学上是可行的。总熵变为负，意味着反应不能自发进行。

7. Introducing Gibbs Free Energy | 引入吉布斯自由能

To avoid having to calculate the surroundings’ entropy change separately, the Gibbs free energy (G) was introduced. ΔG combines both system entropy and enthalpy into a single criterion for spontaneity at constant temperature and pressure. The free energy change is defined as ΔG° = ΔH° – TΔS°system.

为了避免单独计算环境的熵变，引入了吉布斯自由能（G）。ΔG 将系统熵和焓组合成一个在恒温恒压下判断自发性的单一判据。自由能变化定义为 ΔG° = ΔH° – TΔS°系统。

8. Deriving ΔG from Total Entropy | 由总熵推导 ΔG

Starting from ΔS°total = ΔS°system – ΔH°/T, multiply through by T: TΔS°total = TΔS°system – ΔH°. Because a reaction is feasible when ΔS°total > 0, the product TΔS°total must also be positive. Rearranging gives –ΔH° + TΔS°system > 0, or ΔH° – TΔS°system < 0. Thus, we define ΔG = ΔH – TΔS, and the condition for feasibility is ΔG < 0.

由 ΔS°总 = ΔS°系统 – ΔH°/T 出发，两边同乘以 T：TΔS°总 = TΔS°系统 – ΔH°。由于反应可行时 ΔS°总 > 0，乘积 TΔS°总也必定为正。整理可得 –ΔH° + TΔS°系统 > 0，即 ΔH° – TΔS°系统 < 0。因此，我们定义 ΔG = ΔH – TΔS，可行的条件为 ΔG < 0。

9. ΔG and Spontaneous Reactions | ΔG 与自发反应

For a reaction to be spontaneous, ΔG must be negative. There are four possible sign combinations. If ΔH < 0 and ΔS > 0, ΔG is always negative—reaction feasible at all temperatures. If ΔH > 0 and ΔS < 0, ΔG is always positive—reaction never feasible. If both are positive, ΔG is negative only at high temperatures. If both are negative, ΔG is negative only at low temperatures.

反应要自发，ΔG 必须为负。共有四种符号组合。若 ΔH < 0 且 ΔS > 0，ΔG 始终为负——反应在所有温度下均可行。若 ΔH > 0 且 ΔS < 0，ΔG 始终为正——反应永不可行。若两者均为正，仅在高温时 ΔG 为负。若两者均为负，仅在低温时 ΔG 为负。

10. Calculating Gibbs Free Energy Changes | 计算吉布斯自由能变

Standard free energy changes (ΔG°) can be calculated from standard free energies of formation (ΔGf°) using ΔG° = Σ ΔGf°(products) – Σ ΔGf°(reactants). Alternatively, use the Gibbs equation ΔG° = ΔH° – TΔS°. Remember to convert ΔS° from J K⁻¹ mol⁻¹ to kJ K⁻¹ mol⁻¹ when combining with ΔH° in kJ mol⁻¹. Temperature must be in Kelvin.

标准自由能变（ΔG°）可以由标准生成自由能（ΔGf°）计算：ΔG° = Σ ΔGf°(产物) – Σ ΔGf°(反应物)。也可以使用吉布斯方程 ΔG° = ΔH° – TΔS°。注意当 ΔH° 以 kJ mol⁻¹ 为单位时，要把 ΔS° 从 J K⁻¹ mol⁻¹ 转换为 kJ K⁻¹ mol⁻¹。温度必须使用开尔文。

11. Relationship Between ΔG° and Equilibrium Constant | ΔG° 与平衡常数的关系

For a system at equilibrium, ΔG = 0. The standard free energy change is related to the equilibrium constant K by the equation ΔG° = –RT ln K, where R = 8.31 J K⁻¹ mol⁻¹. If ΔG° is negative, ln K is positive and K > 1—the equilibrium favours products. A large positive ΔG° means a very small K, indicating the reaction hardly proceeds.

系统处于平衡时，ΔG = 0。标准自由能变与平衡常数 K 的关系为 ΔG° = –RT ln K，其中 R = 8.31 J K⁻¹ mol⁻¹。若 ΔG° 为负，则 ln K 为正且 K > 1——平衡倾向于产物。ΔG° 为较大的正值意味着 K 非常小，反应几乎不发生。

12. Temperature Dependence and Feasibility | 温度依赖性与可行性

Because ΔG° depends on T, a reaction that is not feasible at room temperature may become feasible at higher temperatures if ΔS°system > 0. This is often the case for endothermic reactions. Graphs of ΔG versus T are linear with slope –ΔS° and intercept ΔH°. The ‘crossover temperature’ where ΔG = 0 is given by T = ΔH°/ΔS° (with consistent units). This concept links directly to Ellingham diagrams for extraction of metals.

由于 ΔG° 依赖于 T，ΔS°系统 > 0 的吸热反应在室温下不可行，在较高温度下可能变得可行。ΔG 对 T 的图形是直线，斜率为 –ΔS°，截距为 ΔH°。ΔG = 0 的 “转变温度” 由 T = ΔH°/ΔS°（单位一致）给出。这一概念直接关联到提取金属的埃灵厄姆图。

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Entropy, Enthalpy Changes and Free Energy | 熵、焓变与自由能