📚 Spontaneity | 自发性
In chemistry, spontaneity describes whether a process or reaction can occur without continuous external intervention. It does not imply that the change happens rapidly; rather, it is thermodynamically favoured. A spontaneous reaction may be extremely slow, yet still have a natural tendency to proceed. Understanding spontaneity requires linking enthalpy, entropy and temperature via Gibbs free energy.
在化学中，自发性描述某一过程或反应是否能在无持续外部干预的情况下发生。它并不意味着变化会快速进行，而是指热力学上有利。一个自发反应可能极其缓慢，但仍具有自然进行的倾向。理解自发性需要将焓、熵和温度通过吉布斯自由能联系起来。
1. The Concept of Spontaneous Change | 自发变化的概念
A spontaneous process is one that proceeds on its own under specified conditions. Examples include ice melting at 25 °C, iron rusting in moist air, and the expansion of a gas into a vacuum. In contrast, water freezing at 25 °C is non‑spontaneous; energy must be removed to force freezing.
自发过程是在指定条件下能够自行进行的过程。例如冰在25 °C融化、铁在潮湿空气中生锈、气体向真空膨胀。相反，水在25 °C结冰是非自发的，必须移走能量才能迫使它结冰。
Spontaneity does not equal speed. The conversion of diamond to graphite is spontaneous at room temperature, yet the rate is immeasurably small. Kinetics (activation energy) governs how fast a reaction occurs, while thermodynamics tells us the direction of change.
自发性不等于快速性。金刚石在室温下转变为石墨是自发的，但速率小到无法测量。动力学（活化能）决定反应进行的快慢，而热力学则指出变化的方向。
2. Entropy as a Measure of Disorder | 熵——无序度的量度
Entropy (S) is a thermodynamic quantity that measures the dispersal of energy and matter. A system with greater disorder, or more ways of arranging particles and energy, has higher entropy. The natural direction of change is toward more probable arrangements, i.e. those with larger total entropy.
熵（S）是量度能量和物质分散程度的热力学函数。系统越无序，或者说粒子和能量的排列方式越多，熵就越大。变化的自然方向是趋向更有可能的排布方式，也就是总熵更大的状态。
Entropy increases when a solid melts (solid to liquid), a liquid vaporises, or a solute dissolves. The number of thermally accessible microstates increases dramatically. For example, ice has a highly ordered hydrogen‑bonded lattice, whereas liquid water allows molecules many more orientations and positions.
固体熔化（固→液）、液体气化或溶质溶解时熵增加。热可及的微观状态数急剧增多。例如，冰具有高度有序的氢键晶格，而液态水使分子拥有多得多的取向和位置。
3. The Second Law of Thermodynamics | 热力学第二定律
The second law states that for any spontaneous process, the total entropy of the universe (system plus surroundings) increases. Mathematically, ΔSuniv = ΔSsys + ΔSsurr > 0 for a spontaneous change. If ΔSuniv < 0, the process is non‑spontaneous in the forward direction.
第二定律指出，任何自发过程发生后，宇宙的总熵（系统加环境）必定增加。数学上，对自发变化有 ΔSuniv = ΔSsys + ΔSsurr > 0。若 ΔSuniv < 0，则该正向过程为非自发。
The entropy change of the surroundings depends on the heat transferred at constant pressure, usually ΔSsurr = –ΔHsys/T. Thus an exothermic reaction (ΔH negative) increases the entropy of the surroundings, often driving spontaneity even when the system’s own entropy decreases.
环境的熵变取决于恒压下传递的热量，通常 ΔSsurr = –ΔHsys/T。因此放热反应（ΔH为负）使环境的熵增大，即便系统自身的熵减小，也常常驱动反应自发进行。
4. Energy Spreading and Microstates | 能量分散与微观状态
Entropy is related to the number of microstates (W) by Boltzmann's formula: S = k ln W, where k is Boltzmann's constant. When energy spreads over more particles or larger volume, the number of accessible microstates increases, raising entropy.
熵通过玻尔兹曼公式与微观状态数（W）相联系：S = k ln W，其中 k 为玻尔兹曼常数。当能量分散到更多粒子或更大体积时，可及微观状态数增多，熵随之增大。
Consider mixing two ideal gases. Before mixing, each gas occupies a separate container; after mixing, molecules spread throughout the entire volume. The number of positional microstates grows, making mixing spontaneous at constant temperature and pressure.
考虑两种理想气体的混合。混合前，每种气体处于独立容器中；混合后，分子散布于整个体积。位置微观状态数增大，使混合在恒温恒压下得以自发进行。
5. Gibbs Free Energy Equation | 吉布斯自由能方程
To avoid calculating ΔSuniv directly, Josiah Willard Gibbs defined a state function G, now called Gibbs free energy. At constant temperature and pressure, the criterion for spontaneity becomes ΔG < 0. The defining equation is:
为了避免直接计算 ΔSuniv，约西亚·威拉德·吉布斯定义了一个状态函数 G，即吉布斯自由能。在恒温恒压下，自发性的判据变为 ΔG < 0。该定义为：
ΔG = ΔH – TΔS
这里 ΔG 是反应的吉布斯自由能变，ΔH 为焓变，T 为绝对温度（单位 K），ΔS 为熵变。如果 ΔG 为负，正向反应自发；ΔG 为正，反应非自发，但逆向自发；ΔG = 0 时体系处于化学平衡。
1 mol dm⁻³ for solutions, specified temperature, usually 298 K). The relation ΔG° = Σ ΔG°f(products) – Σ ΔG°f(reactants) allows calculation from tabulated formation data.
标准吉布斯自由能变 ΔG° 指反应物和产物均处于标准态（1 bar，溶液 1 mol dm⁻³，指定温度，常为 298 K）时的变化。利用 ΔG° = Σ ΔG°f(产物) – Σ ΔG°f(反应物)，可从表格中的生成自由能数据计算。
6. Standard Free Energy Change Calculation | 标准自由能变的计算
ΔG° can also be obtained from standard enthalpy and entropy changes: ΔG° = ΔH° – NO₃⁻(aq), has ΔH° = +25.7 kJ mol⁻¹ and ΔS° = +108.7 J K⁻¹ mol⁻¹ at 298 K. Then ΔG° = 25.7 – (298 × 0.1087) ≈ – cess is spontaneous even though it is endothermic, because the entropy increase dominates.
ΔG° 也可以从标准焓变和标准熵变求得：ΔG° = ΔH° – TΔS°。例如，硝酸铵的溶解 NH₄NO₃(s) → NH₄⁺(aq) + NO₃⁻(aq)，在 298 K 时 ΔH° = +25.7 kJ mol⁻¹，ΔS° = +108.7 J K⁻¹ mol⁻¹。于是 ΔG° = 25.7 – (298 × 0.1087) ≈ –6.7 kJ mol⁻¹，表明尽管过程吸热，但由于熵增占主导，过程仍是自发的。
Units must be consistent: convert entropy to kJ K⁻¹ mol⁻¹, or enthalpy to J mol⁻¹. IB examination questions frequently ask students to calculate ΔG° and then deduce whether a reaction is spontaneous under standard conditions.
单位必须一致：将熵换算为 kJ K⁻¹ mol⁻¹，或将焓换算为 J mol⁻¹。IB 化学考试经常要求学生计算 ΔG° 并由此推断反应在标准条件下是否自发。
7. Temperature and Spontaneity | 温度与自发性
Because ΔG = ΔH – TΔS, temperature can switch the sign of ΔG. Four sign combinations illustrate the effect:
因为 ΔG = ΔH – TΔS，温度可以改变 ΔG 的符号。四种符号组合说明温度的影响：
| ΔH sign | ΔS sign | Spontaneous at |
| – (exothermic) | + (more disorder) | All temperatures (ΔG < 0 always) |
| – (exothermic) | – (less disorder) | Low temperatures (enthalpy driven) |
| + (endothermic) | + (more disorder) | High temperatures (entropy driven) |
| + (endothermic) | – (less disorder) | Never spontaneous (ΔG > 0 always) |
对 ΔH 为负、ΔS 为正的反应，所有温度下都自发。ΔH 为负、ΔS 为负时，低温有利于自发（焓驱动）。ΔH 为正、ΔS 为正时，高温有利于自发（熵驱动）。ΔH 和 ΔS 都为负’时（原文笔误，应为都为正），不可能自发，因为在任何温度下 ΔG 始终为正。实际工作中，可确定阈值温度 T = ΔH/ΔS，当 ΔH 和 ΔS 同号时，自发方向在 T 上下反转。
8. Free Energy and Equilibrium Constant | 自由能与平衡常数
Under non‑ ln Q applies, where Q is the reaction quotient. At equilibrium, ΔG = 0 and Q = K, giving:
在非标准条件下，ΔG = ΔG° + RT ln Q，其中 Q 为反应商。平衡时 ΔG = 0，Q = K，于是得到：
ΔG° = –RT ln K
这里 R 是理想气体常数（8.31 J K⁻¹ mol⁻¹），T 为热力学温度，K 为平衡常数。该方程将热力学与化学平衡联系起来。若 ΔG° 为负值，则 ln K 为正，K > 1，平衡位置偏向产物；若 ΔG° 为正值，K < 1，反应物居多。
de of ΔG° indicates how far the equilibrium lies from equal concentrations. A ΔG° of about – duct. Even a small negative ΔG° can make a reaction spontaneous under standard conditions.
ΔG° 的大小表明平衡偏离等浓度的程度。ΔG° 约为 –40 kJ mol⁻¹ 时 K ≈ 10⁷，几乎完全转化；ΔG° 为 +40 kJ mol⁻¹ 时 K ≈ 10⁻⁷，产物极少。即使是较小的负 ΔG°，也能使反应在标准条件下自发。
9. Coupled Reactions and Biological Systems | 耦合反应与生物体系
lysis of adenosine triphosphate (ATP) to adenosine diphosphate (ADP) and phosphate has ΔG°' ≈ –30.5 kJ mol⁻¹ under cellular conditions.
ΔG 为正的反应可以通过与一个强自发过程相耦合而被推动，只要净 ΔG 为负。活细胞广泛利用这一原理。在细胞条件下，三磷酸腺苷（ATP）水解为二磷酸腺苷（ADP）与磷酸根的 ΔG°' 约为 –30.5 kJ mol⁻¹。
For example, the synthesis of glutamine from glutamate and ammonia has ΔG°' ≈ +14 kJ mol⁻¹, i.e. non‑ aneous. The coupling is achieved through a shared intermediate, involving phosphorylation.
例如，由谷氨酸与氨合成谷氨酰胺的 ΔG°' 约为 +14 kJ mol⁻¹，是非自发的。当与 ATP 水解耦合时，总反应变为自发。这种耦合通过共享中间体（涉及磷酸化）实现。
10. Summary and Key Takeaways | 总结与关键要点
modynamic concept driven by the dispersal of energy. The Gibbs free energy change, ΔG = ΔH – reaction. Standard free energy change ΔG° links to the equilibrium constant through ΔG° = –RT ln K, connecting thermodynamics and chemical equilibrium.
自发性是由能量分散驱动的热力学概念。吉布斯自由能变 ΔG = ΔH – TΔS 提供了恒温恒压下便捷的判据：正向反应自发当且仅当 ΔG < 0。标准自由能变 ΔG° 通过 ΔG° = –RT ln K 与平衡常数相联系，将热力学与化学平衡结合起来。
- Entropy (S) measures the disorder or energy dispersal of a system.
- The second law: ΔSuniv > 0 for spontaneous change.
- Temperature can reverse spontaneity when ΔH and ΔS have the same sign.
- ΔG° determines the position of equilibrium: the more negative, the larger K.
- Coupled reactions allow thermodynamically unfavourable steps to proceed in biochemistry.
- 熵（S）量度系统的无序度或能量分散程度。
- 第二定律：自发变化要求 ΔSuniv > 0。
- 当 ΔH 与 ΔS 同号时，温度可以逆转自发性。
- ΔG° 决定平衡位置：越负则 K 越大。
- 耦合反应使热力学不利的步骤能在生物化学中发生。
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