📚 Gibbs Free Energy | 吉布斯自由能
Gibbs free energy is a thermodynamic potential that measures the maximum reversible work a system can perform at constant temperature and pressure. It is a central concept in chemical thermodynamics, used to predict the spontaneity of reactions and the position of equilibrium.
吉布斯自由能是一种热力学势，衡量系统在恒温恒压下所能做的最大可逆功。它是化学热力学的核心概念，用于预测反应的自发性和平衡位置。
1. What is Gibbs Free Energy? | 什么是吉布斯自由能？
te temperature in kelvin, and S is entropy. The change in Gibbs free energy for a process is given by ΔG = ΔH - TΔS at constant temperature.
吉布斯自由能，符号为 G，将焓和熵结合为一个值。其定义为 G = H - TS，其中 H 是焓，T 是开尔文绝对温度，S 是熵。对于恒温过程，吉布斯自由能的变化由 ΔG = ΔH - TΔS 给出。
on is non-spontaneous under those conditions, and if ΔG = 0, the system is at equilibrium.
ΔG 的符号决定反应是否自发：ΔG 为负表示正反应自发，ΔG 为正表示该条件下反应非自发，若 ΔG = 0，则系统处于平衡状态。
2. The Fundamental Equation: ΔG = ΔH - TΔS | 基本方程
The fundamental Gibbs equation is:
基本吉布斯方程为：
ΔG = ΔH - TΔS
ΔH is the enthalpy change (heat absorbed or released), ΔS is the entropy change (measure of disorder), and T is the kelvin temperature. This equation applies at constant temperature and pressure.
ΔH 是焓变（吸收或放出的热量），ΔS 是熵变（无序度的量度），T 是开尔文温度。该方程适用于恒温恒压条件。
Values must use consistent units: ΔH typically in kJ mol⁻¹, ΔS in J K⁻¹ mol⁻¹, so when calculating ΔG, convert ΔS to kJ K⁻¹ mol⁻¹ or ΔH to J mol⁻¹. In many exam problems, you calculate ΔG directly from given standard formation data or via this equation.
数值必须使用一致的单位：ΔH 通常为 kJ mol⁻¹，ΔS 为 J K⁻¹ mol⁻¹，因此在计算 ΔG 时，需将 ΔS 转换为 kJ K⁻¹ mol⁻¹ 或将 ΔH 转换为 J mol⁻¹。在许多考试题中，你需要根据给定的标准生成数据或通过该方程直接计算 ΔG。
3. Enthalpy and Entropy Contributions | 焓和熵的贡献
Enthalpy (ΔH) reflects the heat change: exothermic reactions (negative ΔH) tend to be favourable, while endothermic reactions (positive ΔH) are unfavourable. Entropy (ΔS) measures the dispersal of energy and matter: an increase in entropy (positive ΔS) favours spontaneity, while a decrease (negative ΔS) opposes it.
焓（ΔH）反映热量变化：放热反应（ΔH 为负）倾向有利，吸热反应（ΔH 为正）则不利。熵（ΔS）衡量能量和物质的分散程度：熵增加（ΔS 为正）有利于自发，熵减少（ΔS 为负）则不利于自发。
The TΔS term scales the entropy contribution by temperature: at high temperatures, the entropy term becomes more significant, potentially overriding an unfavourable enthalpy change.
TΔS 项通过温度来缩放熵的贡献：在高温下，熵项变得更加重要，可能压倒不利的焓变。
The following table summarises the combined effect on spontaneity:
下表总结了综合效应对自发性的影响：
| ΔH sign | ΔS sign | ΔG sign (depends on T) | Spontaneity |
|---|---|---|---|
| Negative (-) | Positive (+) | Always negative | Spontaneous at all T |
| Negative (-) | Negative (-) | Negative at low T; positive at high T | Spontaneous only below a certain T |
| Positive (+) | Positive (+) | Positive at low T; negative at high T | Spontaneous only above a certain T |
| Positive (+) | Negative (-) | Always positive | Non-spontaneous at all T |
4. Standard Gibbs Free Energy Change, ΔG° | 标准吉布斯自由能变
The standard Gibbs free energy change, ΔG°, refers to the ΔG when all reactants and products are in their standard states (1 bar pressure for gases, 1 mol dm⁻³ concentration for solutions, pure solids/liquids) at a specified temperature, usually 298 K.
标准吉布斯自由能变 ΔG° 是指所有反应物和产物均处于标准状态（气体压力为 1 bar，溶液浓度为 1 mol dm⁻³，纯固体/液体）时在指定温度（通常为 298 K）下的 ΔG。
ΔG° can be calculated from standard free energies of formation (ΔG°f) using the formula:
ΔG° 可由标准生成自由能（
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