📚 Gibbs Free Energy | 吉布斯自由能
The Gibbs free energy, G, is a thermodynamic potential that determines the spontaneity of a reaction at constant temperature and pressure. Named after Josiah Willard Gibbs, it combines both enthalpy and entropy to predict whether a process is feasible without external intervention. For A-Level Chemistry, mastering Gibbs free energy is essential because it links energetics, disorder, and equilibrium in a single quantitative framework.
吉布斯自由能 G 是一个在恒温恒压下判断反应自发性的热力学函数。它以约西亚·威拉德·吉布斯命名，将焓与熵结合起来预测一个过程是否无需外界干预即可自发进行。对 A-Level 化学而言，掌握吉布斯自由能至关重要，因为它将能量学、无序度和平衡统一在一个定量的框架之中。
1. What is Gibbs Free Energy? | 什么是吉布斯自由能？
Gibbs free energy, G, is defined by the relationship G = H – TS, where H is enthalpy, T is the absolute temperature in kelvin, and S is entropy. Since absolute values of G are rarely used, chemists focus on the change in Gibbs free energy, ΔG, for a process.
吉布斯自由能 G 由关系式 G = H – TS 定义，其中 H 为焓，T 为以开尔文表示的绝对温度，S 为熵。由于很少使用 G 的绝对值，化学家通常关注一个过程的吉布斯自由能变 ΔG。
For a reaction occurring at constant temperature and pressure, the change is given by the Gibbs equation: ΔG = ΔH – TΔS. This equation lies at the heart of predicting reaction feasibility.
对于发生在恒温恒压下的反应，其变化由吉布斯方程给出：ΔG = ΔH – TΔS。该方程是预测反应可行性的核心。
A process is thermodynamically spontaneous if ΔG < 0. If ΔG > 0, the forward reaction is non-spontaneous, though the reverse may be spontaneous. When ΔG = 0, the system is at equilibrium with no net change in macroscopic properties.
若 ΔG < 0，该过程是热力学上自发的。若 ΔG > 0，正向反应非自发，但其逆过程可能自发。当 ΔG = 0 时，系统处于平衡状态，宏观性质不发生净变化。
2. The Gibbs Equation: ΔG = ΔH – TΔS | 吉布斯方程：ΔG = ΔH – TΔS
The Gibbs equation shows that spontaneity is determined by two competing factors: the enthalpy change (ΔH) and the entropy change (ΔS) weighted by the absolute temperature T. An exothermic reaction (ΔH < 0) and an increase in entropy (ΔS > 0) both act to make ΔG negative.
吉布斯方程表明，自发性由两个相互竞争的因素决定：焓变 ΔH 和由绝对温度 T 加权的熵变 ΔS。放热反应 (ΔH < 0) 和熵增 (ΔS > 0) 都会使 ΔG 为负。
Care must be taken with units: ΔH is usually in kJ mol⁻¹, while ΔS is most often quoted in J K⁻¹ mol⁻¹. Before combining them, convert ΔS to kJ K⁻¹ mol⁻¹ by dividing by 1000, or express ΔH in J mol⁻¹.
必须注意单位：ΔH 通常用 kJ mol⁻¹ 表示，而 ΔS 常用 J K⁻¹ mol⁻¹ 给出。在合并计算之前，应将 ΔS 除以 1000 转换为 kJ K⁻¹ mol⁻¹，或者将 ΔH 转换成 J mol⁻¹。
Example: For a reaction at 298 K, ΔH = -92.4 kJ mol⁻¹ and ΔS = -198.7 J K⁻¹ mol⁻¹.
ΔG = -92.4 – (298 × (-0.1987)) = -92.4 + 59.2 = -33.2 kJ mol⁻¹
事例：在 298 K 时一反应的 ΔH = -92.4 kJ mol⁻¹，ΔS = -198.7 J K⁻¹ mol⁻¹。
ΔG = -92.4 – (298 × (-0.1987)) = -92.4 + 59.2 = -33.2 kJ mol⁻¹
Since ΔG < 0, the reaction is spontaneous under these conditions.
由于 ΔG < 0，该反应在此条件下是自发的。
3. Sign Conventions and Spontaneity | 符号规定与自发性
The sign of ΔG tells us the direction of spontaneous change:
ΔG 的符号告诉我们自发变化的方向：
- ΔG < 0: The forward reaction is spontaneous (exergonic).
- ΔG < 0：正向反应自发（放能过程）。
- ΔG > 0: The forward reaction is non-spontaneous; work must be done on the system (endergonic). The reverse reaction is spontaneous.
- ΔG > 0：正向反应非自发，需对系统做功（吸能过程）；逆反应自发。
- ΔG = 0: The system is at equilibrium. No net change occurs, and the free energy is at a minimum.
- ΔG = 0：系统处于平衡状态，无净变化，自由能达到极小值。
It is important to distinguish between ΔG (the actual free energy change under any conditions) and ΔG° (the standard free energy change). ΔG = 0 signals equilibrium for the actual reaction mixture, not necessarily when all species are at standard concentrations.
必须区分 ΔG（任意条件下的实际自由能变）与 ΔG°（标准自由能变）。当实际反应混合物达到 ΔG = 0 时表示平衡，这并不意味着所有物种都处于标准浓度。
4. Effect of Temperature on Reaction Feasibility | 温度对反应可行性的影响
The temperature T multiplies ΔS in the Gibbs equation, meaning that the entropy term becomes more influential at high temperatures. Depending on the signs of ΔH and ΔS, the feasibility can change with temperature.
温度 T 在吉布斯方程中与 ΔS 相乘，这意味着在高温下熵项的权重更大。根据 ΔH 和 ΔS 的符号，反应的可行性可随温度变化。
| ΔH sign | ΔS sign | ΔG behaviour | Spontaneity |
|---|---|---|---|
| – (exothermic) | + (entropy increases) | Always negative | Spontaneous at all temperatures |
| + (endothermic) | – (entropy decreases) | Always positive | Never spontaneous; reverse is spontaneous |
| – (exothermic) | – (entropy decreases) | Negative at low T, positive at high T | Spontaneous below T = ΔH/ΔS |
| + (endothermic) | + (entropy increases) | Positive at low T, negative at high T | Spontaneous above T = ΔH/ΔS |
When ΔH and ΔS have the same sign, there exists a transition temperature at which ΔG = 0. This temperature is given by:
T = ΔH / ΔS
Care must be taken to express both ΔH and ΔS in compatible units (e.g., J mol⁻¹ and J K⁻¹ mol⁻¹) before calculating T.
当 ΔH 和 ΔS 同号时，存在一个转变温度使 ΔG = 0。该温度由下式求得：
T = ΔH / ΔS
在计算 T 时需注意将 ΔH 和 ΔS 化为一致的单位（如 J mol⁻¹ 和 J K⁻¹ mol⁻¹）。
5. Standard Gibbs Free Energy Change (ΔG°) | 标准吉布斯自由能变 (ΔG°)
The standard Gibbs free energy change, ΔG°, refers to the free energy change when all reactants and products are in their standard states: 100 kPa for gases, 1 mol dm⁻³ for solutions, and the pure substance at 298 K for solids and liquids.
标准吉布斯自由能变 ΔG° 是指所有反应物和生成物均处于标准状态时的自由能变：气体为 100 kPa，溶液为 1 mol dm⁻³，固体和液体则在 298 K 下为纯物质。
ΔG° can be calculated from the standard free energies of formation (ΔG°f) of the substances involved, using a relation analogous to that for standard enthalpy changes:
ΔG° = Σ ΔG°f(products) – Σ ΔG°f(reactants)
ΔG° 可由所涉及物质的标准生成自由能 ΔG°f 计算得到，采用与标准焓变相类似的关系式：
ΔG° = Σ ΔG°f(生成物) – Σ ΔG°f(反应物)
Note that ΔG°f for any element in its standard state is defined as zero, just as for ΔH°f.
注意，与标准生成焓 ΔH°f 相同，标准状态下任何元素的 ΔG°f 定义为零。
6. Calculating ΔG° from Standard Free Energies of Formation | 由标准生成自由能计算 ΔG°
Consider the reaction: 2SO2(g) + O2(g) → 2SO3(g) at 298 K. The standard free energies of formation are:
- ΔG°f[SO2(g)] = -300.2 kJ mol⁻¹
- ΔG°f[SO3(g)] = -371.1 kJ mol⁻¹
- ΔG°f[O2(g)] = 0 (element)
Now apply the formula:
ΔG° = [2 × (-371.1)] – [2 × (-300.2) + 0] = -742.2 + 600.4 = -141.8 kJ mol⁻¹
考虑反应：2SO2(g) + O2(g) → 2SO3(g) 于 298 K。标准生成自由能如下：
- ΔG°f[SO2(g)] = -300.2 kJ mol⁻¹
- ΔG°f[SO3(g)] = -371.1 kJ mol⁻¹
- ΔG°f[O2(g)] = 0（元素）
代入公式：
ΔG° = [2 × (-371.1)] – [2 × (-300.2) + 0] = -742.2 + 600.4 = -141.8 kJ mol⁻¹
The negative value indicates that the formation of SO3 is thermodynamically favoured under standard conditions.
负值表明在标准条件下生成 SO3 在热力学上是有利的。
7. Relating ΔG° to the Equilibrium Constant (ΔG° = -RT ln K) | ΔG° 与平衡常数的关系 (ΔG° = -RT ln K)
One of the most powerful applications of ΔG° is its relationship with the equilibrium constant K:
ΔG° = -RT ln K
where R is the universal gas constant (8.314 J mol⁻¹ K⁻¹), T is temperature in kelvin, and ln K is the natural logarithm of the equilibrium constant.
ΔG° 最重要的应用之一就是它与平衡常数 K 的关系：
ΔG° = -RT ln K
式中 R 是通用气体常数 (8.314 J mol⁻¹ K⁻¹)，T 为开尔文温度，ln K 是平衡常数的自然对数。
When K > 1, ln K is positive, giving ΔG° < 0; the equilibrium favours products. When K < 1, ln K is negative, giving ΔG° > 0; reactants predominate. If K = 1, ΔG° = 0.
当 K > 1 时，ln K 为正，ΔG° < 0，平衡倾向于生成物。当 K < 1 时，ln K 为负，ΔG° > 0，反应物占优势。若 K = 1，则 ΔG° = 0。
Example: For a reaction with ΔG° = -30.0 kJ mol⁻¹ at 298 K, first convert ΔG° to J mol⁻¹: -30000 J mol⁻
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