📚 Gibbs Free Energy | 吉布斯自由能 考点精讲
Gibbs free energy (G) is a thermodynamic potential that combines enthalpy and entropy to determine the feasibility and spontaneity of a chemical reaction at constant temperature and pressure. In A-Level Edexcel Chemistry, mastering Gibbs free energy is essential for predicting reaction direction, calculating equilibrium constants, and linking energetics to electrochemical cells. This article provides a comprehensive revision guide covering all key concepts, equations, and common pitfalls.
吉布斯自由能（G）是一个结合焓和熵的热力学势函数，用于判断恒温恒压下化学反应的可行性和自发性。在 A-Level Edexcel 化学中，掌握吉布斯自由能对于预测反应方向、计算平衡常数以及将能量学与电化学联系起来至关重要。本文提供全面的复习指南，涵盖所有核心概念、方程和常见易错点。
1. Introduction to Gibbs Free Energy | 吉布斯自由能简介
l or physical process occurring at constant temperature and pressure, the change in Gibbs free energy is given by the fundamental relation ΔG = ΔH − TΔS. A negative ΔG indicates that the process is thermodynamically feasible without external intervention.
吉布斯自由能，符号 G，定义为 G = H − TS。由于 H（焓）和 S（熵）都是状态函数，因此 G 也是状态函数。对于任何在恒温恒压下发生的化学或物理过程，吉布斯自由能的变化由基本关系式 ΔG = ΔH − TΔS 给出。ΔG 为负值表示该过程在热力学上是可行的，无需外界干预即可发生。
The quantity ΔH represents the enthalpy change and reflects the heat absorbed or released by the system. ΔS is the entropy change, which measures the dispersal of energy and matter. T is the absolute temperature in kelvin. It is critical to pay attention to units: ΔH is typically expressed in kJ mol⁻¹, while ΔS is often given in J K⁻¹ mol⁻¹. Therefore, before substituting into the equation, one must either convert ΔH to J mol⁻¹ or ΔS to kJ K⁻¹ mol⁻¹ to obtain ΔG in consistent units.
ΔH 表示焓变，反映系统吸收或释放的热量。ΔS 是熵变，衡量能量和物质的分散程度。T 为开尔文温标下的绝对温度。必须注意单位：ΔH 通常以 kJ mol⁻¹ 表示，而 ΔS 常以 J K⁻¹ mol⁻¹ 给出。因此，代入方程前须将 ΔH 换算为 J mol⁻¹ 或将 ΔS 换算为 kJ K⁻¹ mol⁻¹，以便获得单位一致的 ΔG。
2. The Fundamental Equation and Calculations | 基本方程与计算
The cornerstone of all Gibbs free energy calculations is the equation:
ΔG = ΔH − TΔS
吉布斯自由能计算的核心是下列方程：
ΔG = ΔH − TΔS
energy change for a reaction can also be calculated from the standard Gibbs free energies of formation of reactants and products:
ΔG° = Σ ΔG°ₓ(products) − Σ ΔG°ₓ(reactants)
使用标准状态数据（上标 °）时，方程变为 ΔG° = ΔH° − TΔS°。反应的标准吉布斯自由能变化也可以通过反应物和产物的标准生成吉布斯自由能来计算：
ΔG° = Σ ΔG°ₓ(产物) − Σ ΔG°ₓ(反应物)
th ΔH° = −110 kJ mol⁻¹ and ΔS° = −200 J K⁻¹ mol⁻¹. First convert ΔH° to J mol⁻¹: −110 000 J mol⁻¹. Then ΔG° = −110 000 − (298 × −200) = −110 000 + 59 600 = −50 400 J mol⁻¹ = −50.4 kJ mol⁻¹. The negative value indicates the reaction is feasible under standard conditions.
在考试中，你可能会被给予 ΔH° 和 ΔS° 以及指定的温度，并被要求计算 ΔG°。例如，计算某反应在 298 K、ΔH° = −110 kJ mol⁻¹、ΔS° = −200 J K⁻¹ mol⁻¹ 时的 ΔG°。首先将 ΔH° 转换为 J mol⁻¹：−110 000 J mol⁻¹。然后 ΔG° = −110 000 − (298 × −200) = −110 000 + 59 600 = −50 400 J mol⁻¹ = −50.4 kJ mol⁻¹。负值表明该反应在标准条件下是可行的。
3. Feasibility and the Sign of ΔG | 可行性与 ΔG 的符号
The sign of ΔG determines whether a reaction can proceed spontaneously in the forward direction:
- ΔG < 0: The reaction is thermodynamically spontaneous (feasible) under the given conditions.
- ΔG = 0: The system is at equilibrium; there is no net change.
- ΔG > 0: The forward reaction is not feasible; the reverse reaction is spontaneous.
ΔG 的符号决定反应能否正向自发进行：
- ΔG < 0：反应在给定条件下是热力学自发的（可行）。
- ΔG = 0：系统处于平衡状态，无净变化。
- ΔG > 0：正向反应不可行，逆反应自发。
It is vital to distinguish between thermodynamic feasibility and kinetic rate. A negative ΔG does not guarantee a rapid reaction; many thermodynamically favoured reactions occur slowly because of a high activation energy. The combustion of graphite, for example, has ΔG° of about −394 kJ mol⁻¹ yet requires a spark to initiate.
必须区分热力学可行性和动力学速率。ΔG 为负并不保证反应迅速；许多热力学有利的反应因活化能较高而进行缓慢。例如，石墨的燃烧 ΔG° 约为 −394 kJ mol⁻¹，但仍需火花引发。
ΔG also depends on the conditions (temperature, pressure, concentration). A reaction that is not feasible under standard conditions can become feasible if conditions are changed. This is the basis for shifting the equilibrium position.
ΔG 还取决于条件（温度、压力、浓度）。在标准条件下不可行的反应，若改变条件可能变得可行。这正是改变平衡位置的基础。
4. Temperature Dependence and the ‘Crossover’ Temperature | 温度依赖性与转折温度
the effect of temperature depends on the signs of ΔH and ΔS. Four scenarios are possible:
由于 ΔG = ΔH − TΔS，温度的影响取决于 ΔH 和 ΔS 的符号。共有四种可能情形：
| ΔH sign | ΔS sign | ΔG at low T | ΔG at high T | Feasibility |
|---|---|---|---|---|
| − (exothermic) | + (more disorder) | − | − | Always feasible |
| + (endothermic) | − (less disorder) | + | + | Never feasible |
| − (exothermic) | − (less disorder) | − | + | Feasible at low T |
| + (endothermic) | + (more disorder) | + | − | Feasible at high T |
对应的中文版：
| ΔH 符号 | ΔS 符号 | 低温 ΔG | 高温 ΔG | 可行性 |
|---|---|---|---|---|
| −（放热） | +（混乱度增） | − | − | 总是可行 |
| +（吸热） | −（混乱度减） | + | + | 永不可行 |
| −（放热） | −（混乱度减） | − | + | 低温可行 |
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