Gibbs Free Energy | 吉布斯自由能考点精讲

📚 Gibbs Free Energy | 吉布斯自由能考点精讲

Gibbs free energy is a fundamental thermodynamic quantity that allows chemists to determine whether a reaction is feasible under constant temperature and pressure. In CCEA A-Level Chemistry, mastery of the Gibbs free energy concept is essential for explaining spontaneity, interpreting equilibrium constants, linking thermodynamics to electrochemistry, and performing quantitative problem solving. This guide covers every key examination point, from the core equation ΔG = ΔH – TΔS to its use in predicting reaction direction and calculating cell potentials.

吉布斯自由能是一个基本的热力学量，它使化学家能够确定反应在恒温恒压下是否可行。在 CCEA A-Level 化学中，掌握吉布斯自由能的概念对于解释反应自发性、解析平衡常数、将热力学与电化学联系起来以及进行定量问题求解至关重要。本指南涵盖了从核心方程 ΔG = ΔH – TΔS 到用于预测反应方向和计算电池电势的每一个关键考点。

1. Introduction to Gibbs Free Energy | 吉布斯自由能简介

Gibbs free energy, symbol G, is defined as the maximum amount of non‑expansion work that can be extracted from a closed system at constant temperature and pressure. In chemical reactions, the change in Gibbs free energy, ΔG, indicates whether a reaction can proceed without external intervention. A negative ΔG signals a thermodynamically feasible process; a positive ΔG means the reaction is not feasible under the given conditions. It is named after Josiah Willard Gibbs, who unified enthalpy and entropy into a single criterion for spontaneity.

吉布斯自由能，符号 G，定义为在恒温恒压下可以从封闭系统中提取的最大非体积功。在化学反应中，吉布斯自由能的变化 ΔG 表示反应是否可以在没有外部干预的情况下进行。负的 ΔG 表示热力学上可行的过程；正的 ΔG 意味着在该条件下反应不可行。它以 Josiah Willard Gibbs 的名字命名，他将焓和熵统一为判断自发性的单一标准。

In the CCEA specification, you will meet Gibbs free energy in both chemical energetics and electrochemistry topics. You are expected to define ΔG, state the relationship ΔG = ΔH – TΔS, and apply it to predict whether a reaction is spontaneous at a particular temperature. You must also relate ΔG to the equilibrium constant K and to the emf of electrochemical cells. Understanding Gibbs free energy therefore connects several large areas of the A‑Level Chemistry syllabus.

在 CCEA 考试大纲中，您将在化学能学和电化学部分接触到吉布斯自由能。您需要能够定义 ΔG，阐述关系式 ΔG = ΔH – TΔS，并应用它预测某个反应在特定温度下是否自发。您还必须将 ΔG 与平衡常数 K 以及电化学电池的电动势联系起来。因此，理解吉布斯自由能将 A-Level 化学课程中的几个大块内容连为一体。

2. The Gibbs Free Energy Equation: ΔG = ΔH – TΔS | 吉布斯自由能方程

The central equation is ΔG = ΔH – TΔS, where ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, T is the absolute temperature in kelvin, and ΔS is the change in entropy. This equation unites the two ‘driving forces’ of a chemical reaction: the tendency to minimise energy (exothermic, negative ΔH) and the tendency to maximise disorder (increase in entropy, positive ΔS). At a given temperature, the balance between these two factors determines ΔG.

核心方程为 ΔG = ΔH – TΔS，其中 ΔG 是吉布斯自由能的变化，ΔH 是焓变，T 是以开尔文为单位的绝对温度，ΔS 是熵变。这个方程将化学反应的两种“驱动力”统一起来：能量最低倾向（放热，负 ΔH）和混乱度最大倾向（熵增，正 ΔS）。在给定温度下，两者的平衡决定了 ΔG。

You must remember to use temperature in kelvin. If a question provides temperature in degrees Celsius, convert by adding 273. Standard conditions in thermodynamics are 298 K (25 °C) and 100 kPa pressure. ΔH is usually given in kJ mol⁻¹, while ΔS is often given in J K⁻¹ mol⁻¹. To avoid calculation errors, convert all quantities to consistent units — typically either convert ΔH to J mol⁻¹ or convert ΔS to kJ K⁻¹ mol⁻¹ before multiplying by T.

您必须记住使用开尔文温度。如果题目给出的温度是摄氏度，请加上 273 转换为开尔文。热力学中的标准条件是 298 K（25 °C）和 100 kPa 压力。ΔH 通常以 kJ mol⁻¹ 给出，而 ΔS 通常以 J K⁻¹ mol⁻¹ 给出。为避免计算错误，请将所有量转换为一致的单位——通常在乘以 T 之前，要么将 ΔH 转换成 J mol⁻¹，要么将 ΔS 转换成 kJ K⁻¹ mol⁻¹。

Example calculation: For a reaction, ΔH = -110 kJ mol⁻¹ and ΔS = -200 J K⁻¹ mol⁻¹. Convert ΔS to -0.200 kJ K⁻¹ mol⁻¹. At T = 298 K, ΔG = -110 – (298 × -0.200) = -110 + 59.6 = -50.4 kJ mol⁻¹. The negative value indicates feasibility at room temperature.
计算示例： 对于某个反应，ΔH = -110 kJ mol⁻¹，ΔS = -200 J K⁻¹ mol⁻¹。将 ΔS 转换为 -0.200 kJ K⁻¹ mol⁻¹。在 T = 298 K 时，ΔG = -110 – (298 × -0.200) = -110 + 59.6 = -50.4 kJ mol⁻¹。负值表明在室温下反应可行。

3. Feasibility, Spontaneity and the Sign of ΔG | 可行性、自发性与ΔG的符号

A reaction is said to be thermodynamically feasible if ΔG is negative. When ΔG = 0, the system is at equilibrium — the forward and reverse reactions occur at equal rates, and there is no net change in composition. A positive ΔG indicates that the forward reaction is not feasible under the specified conditions; however, the reverse reaction would have a negative ΔG.

如果 ΔG 为负，则反应称为热力学上可行。当 ΔG = 0 时，系统处于平衡状态——正向和逆向反应以相同的速率进行，组成没有净变化。正的 ΔG 表示在指定条件下正向反应不可行；然而，逆反应将具有负的 ΔG。

It is critical to distinguish between thermodynamic feasibility and kinetic inertness. A reaction with a negative ΔG might still proceed immeasurably slowly because of a high activation energy barrier. For instance, the combustion of diamond has a negative ΔG at room temperature, but diamonds do not burn in air because the activation energy is too high. This distinction is frequently tested in CCEA papers.

区分热力学可行性和动力学惰性至关重要。即使 ΔG 为负，如果活化能势垒很高，反应可能仍然进行得极为缓慢。例如，金刚石的燃烧在室温下具有负的 ΔG，但金刚石不会在空气中燃烧，因为活化能太高。这个区分在 CCEA 试卷中经常被考察。

Also remember that a negative ΔG tells us the reaction can occur, but says nothing about how fast. Catalysts lower activation energy but do not change ΔG or the equilibrium position.

还要记住，负的 ΔG 告诉我们反应能够发生，但并没有说明反应有多快。催化剂降低活化能，但不改变 ΔG 或平衡位置。

4. Temperature Dependence of Spontaneity | 温度对自发性的影响

Because T appears explicitly in the equation, the spontaneity of a reaction can change with temperature. The signs of ΔH and ΔS determine how ΔG varies with T. The four possible combinations are summarised below.

由于 T 明确出现在方程中，反应的自发性可能会随温度变化。ΔH 和 ΔS 的符号决定了 ΔG 如何随 T 变化。四种可能的组合总结如下。

ΔH sign	ΔS sign	ΔG at low T	ΔG at high T	Feasibility
Negative (exothermic)	Positive	Negative	Negative	Always feasible
Positive (endothermic)	Negative	Positive	Positive	Never feasible
Negative	Negative	Negative	Positive (when T > ΔH/ΔS)	Feasible only at low T
Positive	Positive	Positive	Negative (when T > ΔH/ΔS)	Feasible only at high T

When ΔH and ΔS have opposite signs, feasibility is independent of temperature. When they have the same sign, there is a transition temperature at which ΔG = 0. This temperature can be calculated by setting ΔG = 0 and solving T = ΔH / ΔS. Be careful with units: ΔH in J mol⁻¹ and ΔS in J K⁻¹ mol⁻¹ gives T in kelvin.

当 ΔH 和 ΔS 符号相反时，可行性与温度无关。当它们符号相同时，存在一个转变温度，此时 ΔG = 0。该温度可以通过设 ΔG = 0 并求解 T = ΔH / ΔS 来计算。注意单位：ΔH 以 J mol⁻¹ 和 ΔS 以 J K⁻¹ mol⁻¹ 给出时，计算得到的 T 为开尔文。

5. Relationship Between ΔG and the Equilibrium Constant | ΔG与平衡常数的关系

Under standard conditions, the standard Gibbs free energy change is linked to the equilibrium constant K by the equation ΔG° = -RT ln K. R is the gas constant, 8.314 J K⁻¹ mol⁻¹, and T is the temperature in kelvin. This equation allows chemists to calculate K from thermodynamic data, or conversely to determine ΔG° from an experimentally measured K.

在标准条件下，标准吉布斯自由能变与平衡常数 K 通过方程 ΔG° = -RT ln K 联系起来。R 是气体常数，8.314 J K⁻¹ mol⁻¹，T 是开尔文温度。该方程使化学家可以从热力学数据计算 K，或者反过来从实验测得的 K 确定 ΔG°。

The implications of this relationship are profound:

If ΔG° is negative, ln K is positive, so K > 1: equilibrium favours products.
If ΔG° is positive, ln K is negative, so K < 1: equilibrium favours reactants.
If ΔG° = 0, ln K = 0 and K = 1, meaning products and reactants are equally favoured.

该关系的含义深远：

如果 ΔG° 为负，ln K 为正，因此 K > 1：平衡有利于产物。
如果 ΔG° 为正，ln K 为负，因此 K < 1：平衡有利于反应物。
如果 ΔG° = 0，则 ln K = 0 且 K = 1，意味着产物和反应物同等地受青睐。

For gaseous reactions, K is expressed as K_p with partial pressures; for solution reactions, K is expressed as K_c with concentrations. The formula ΔG° = -RT ln K applies equally to both equilibrium constants, provided the standard state is consistent. When solving problems, be aware that CCEA often asks for K_c and K_p interchangeably, and you must use the correct ΔG° units.

对于气体反应，K 表示为 K_p，使用分压；对于溶液反应，K 表示为 K_c，使用浓度。公式 ΔG° = -RT ln K 同样适用于这两种平衡常数，只要标准状态一致。在解题时，请注意 CCEA 经常交替要求 K_c 和 K_p，您必须使用正确的 ΔG° 单位。

6. Gibbs Free Energy and Electrochemical Cells | 吉布斯自由能与电化学电池

In electrochemistry, the Gibbs free energy change for a cell reaction is related to the cell potential E by the equation ΔG = -nFE, where n is the number of moles of electrons transferred in the redox reaction, F is the Faraday constant (approximately 96 500 C mol⁻¹), and E is the emf of the cell in volts. Under standard conditions, it becomes ΔG° = -nFE°. This powerful link allows you to calculate one quantity from the other and to determine cell potentials from thermodynamic data.

在电化学中，电池反应的吉布斯自由能变与电池电势 E 的关系由方程 ΔG = -nFE 给出，其中 n 是氧化还原反应中转移的电子的摩尔数，F 是法拉第常数（约为 96 500 C mol⁻¹），E 是以伏特为单位的电池电动势。在标准条件下，变为 ΔG° = -nFE°。这一强大的联系使您可以从一个量计算另一个量，并从热力学数据确定电池电势。

A positive cell potential corresponds to a negative ΔG, indicating a spontaneous reaction. This is why a cell with a greater overall E° can supply electrical energy. You may be required to calculate ΔG° from standard electrode potentials, or to find E° given ΔG° and n. Always check the balanced half‑equations to determine n correctly; it must be the number of electrons lost and gained in the overall redox process.

正电池电势对应负的 ΔG，表明反应自发进行。这就是具有更大总 E° 值的电池可以提供电能的原因。您可能需要根据标准电极电势计算 ΔG°，或者给定 ΔG° 和 n 求 E°。请务必检查配平的半反应式以正确确定 n；它必须是在整个氧化还原过程中失去和获得的电子数。

7. Calculating ΔG from Standard Free Energies of Formation | 从标准生成自由能计算ΔG

Another route to ΔG° is via standard Gibbs free energies of formation, ΔG_f°. Analogous to Hess’s law for enthalpy, the standard free energy change for a reaction can be calculated using:

ΔG° = Σ ΔG_f°(products) – Σ ΔG_f°(reactants)

Data tables provide ΔG_f° values for compounds, usually in kJ mol⁻¹. This method is especially useful when ΔH and ΔS data are not directly available. It is also directly testable: you may need to calculate ΔG° for a reaction, then find K, or combine with an electrochemical cell calculation.

另一种计算 ΔG° 的途径是通过标准吉布斯生成自由能 ΔG_f°。与焓的盖斯定律类似，反应的标准自由能变可以用下式计算：

ΔG° = Σ ΔG_f°(产物) – Σ ΔG_f°(反应物)

数据表提供化合物的 ΔG_f° 值，通常以 kJ mol⁻¹ 为单位。当无法直接得到 ΔH 和 ΔS 数据时，此方法特别有用。它也是可以直接考察的内容：您可能需要计算反应的 ΔG°，然后求出 K，或与电化学电池计算相结合。

Note that the standard free energy of formation of any element in its standard state is zero, exactly like standard enthalpy of formation. Be careful to multiply the tabulated value by the stoichiometric coefficient in the balanced equation.

注意，任何处于标准状态的单质，其标准生成自由能为零，与标准生成焓完全一样。要小心地将表中数值乘以配平方程中的化学计量系数。

8. Non‑Standard Conditions and the Reaction Quotient | 非标准条件与反应商

When reactants and products are not under standard conditions, the actual ΔG is given by the equation ΔG = ΔG° + RT ln Q, where Q is the reaction quotient. Q has the same form as the equilibrium constant K but uses the current concentrations or pressures, not the equilibrium values. This equation explains how a system can still proceed in the forward direction even when ΔG° is positive, provided Q is small enough.

当反应物和产物不处于标准条件时，实际的 ΔG 由方程 ΔG = ΔG° + RT ln Q 给出，其中 Q 是反应商。Q 的形式与平衡常数 K 相同，但使用当前浓度或压力，而不是平衡值。该方程解释了即使 ΔG° 为正，只要 Q 足够小，系统仍然能够正向进行。

If Q < K, then ln(Q/K) < 0, so ΔG < 0 and the forward reaction is spontaneous.
If Q > K, then ΔG > 0 and the reverse reaction is spontaneous.
At equilibrium, Q = K and ΔG = 0.

如果 Q < K，则 ln(Q/K) < 0，因此 ΔG < 0，正向反应自发进行。
如果 Q > K，则 ΔG > 0，逆反应自发进行。
在平衡时，Q = K 且 ΔG = 0。

This relation is qualitatively important for understanding how changes in concentration or pressure drive a reaction towards equilibrium. While CCEA may not always require extensive Q‑based calculations, the principle that ΔG depends on concentration is an integral part of the topic.

这种关系对于理解浓度或压力的变化如何驱动反应趋向平衡在定性上很重要。尽管 CCEA 不一定总是要求基于 Q 的大量计算，但 ΔG 取决于浓度这一原理是该主题不可分割的一部分。

9. Exam Tips and Common Pitfalls in CCEA Chemistry | CCEA化学应试技巧与常见误区

Here are key points to remember when tackling Gibbs free energy questions in CCEA A‑Level Chemistry:

以下是在应对 CCEA A‑Level 化学中的吉布斯自由能问题时应记住的关键点：

Always convert temperature to kelvin. A miscalculation of T is one of the most frequent errors.
Watch unit consistency: if ΔH is in kJ and ΔS in J, you must convert one before using ΔG = ΔH – TΔS.
Remember that a negative ΔG means feasible, but not necessarily fast. Do not mix thermodynamics with kinetics.
When using ΔG° = -RT ln K, first convert ΔG° to J mol⁻¹ if needed, because R = 8.314 J K⁻¹ mol⁻¹.
For electrochemical cells, the relation ΔG° = -nFE° must have E° in volts (J C⁻¹), giving ΔG° in J mol⁻¹. Multiply by n and F carefully; n must match the electrons in the balanced equation.
Practice calculating the temperature at which a reaction becomes feasible by setting ΔG = 0 and solving T = ΔH/ΔS. Ensure ΔH is in J and ΔS in J K⁻¹.

始终将温度转换为开尔文。T 的计算错误是最常见的错误之一。
注意单位一致性：如果 ΔH 以 kJ 为单位而 ΔS 以 J 为单位，在使用 ΔG = ΔH – TΔS 之前必须转换其中一个。
记住负的 ΔG 意味着可行，但不一定快速。切勿将热力学与动力学混淆。
当使用 ΔG° = -RT ln K 时，如果需要，先将 ΔG° 转换为 J mol⁻¹，因为 R = 8.314 J K⁻¹ mol⁻¹。
对于电化学电池，关系式 ΔG° = -nFE° 中的 E° 必须以伏特（J C⁻¹）为单位，从而得出 ΔG° 以 J mol⁻¹ 为单位。仔细乘以 n 和 F；n 必须与配平方程式中的电子数相匹配。
练习通过设 ΔG = 0 并求解 T = ΔH/ΔS 来计算反应变为可行的温度。确保 ΔH 以 J 为单位，ΔS 以 J K⁻¹ 为单位。

In addition, when interpreting data, be prepared to justify why a reaction that seems thermodynamically feasible does not occur under ordinary conditions — typically because of a high activation energy barrier or because the reaction is not at equilibrium. Linking these ideas demonstrates deep understanding and earns high marks on CCEA extended‑answer questions.

此外，在解释数据时，要准备好论证为什么一个看似热力学上可行的反应在普通条件下却并未发生——通常是由于活化能势垒高，或者反应未处于平衡状态。将这些观点联系起来可以展示深刻的理解，并在 CCEA 的长答题型中获得高分。

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Gibbs Free Energy | 吉布斯自由能考点精讲