Entropy and Gibbs Free Energy | 熵与吉布斯自由能

📚 Entropy and Gibbs Free Energy | 熵与吉布斯自由能

In A-level Chemistry, entropy and Gibbs free energy provide a thermodynamic framework for explaining whether a chemical reaction is likely to proceed under given conditions. Entropy measures the dispersal of energy and matter, while Gibbs free energy combines entropy and enthalpy changes to predict reaction feasibility at constant temperature and pressure.

在A-level化学中，熵和吉布斯自由能提供了热力学框架，用于解释化学反应在给定条件下是否可能进行。熵衡量能量与物质的分散程度，而吉布斯自由能结合熵变和焓变，在恒温恒压下预测反应可行性。

---

1. What Is Entropy? | 什么是熵？

Entropy, symbol S, is a thermodynamic quantity that measures the number of ways energy and particles can be arranged in a system. A system with greater disorder, more random motion, or more widely dispersed energy has higher entropy.

熵（符号 S）是热力学量，衡量体系中能量和粒子可排列方式的多少。体系越无序、粒子运动越随机、能量分散越广，熵就越高。

Gases generally have higher entropy than liquids, and liquids have higher entropy than solids, because the particles have greater freedom of movement and are less ordered in the gaseous state.

气体的熵通常高于液体，液体的熵高于固体，因为气体粒子运动自由度更大、排列更无序。

Standard entropy S° is measured in J K⁻¹ mol⁻¹ under standard conditions: 298 K, 100 kPa, and 1 mol dm⁻³ for aqueous ions.

标准熵 S° 的单位为 J K⁻¹ mol⁻¹，标准条件为 298 K、100 kPa，溶液离子浓度为 1 mol dm⁻³。

---

2. Standard Entropy and Its Trends | 标准熵及其变化趋势

Standard entropy values are always positive for substances, unlike standard enthalpy of formation, which is defined as zero for elements in their standard states. In fact, a perfect crystal at 0 K would have zero entropy, but at standard conditions all substances possess some entropy.

物质的标准熵值总是正值，这与标准生成焓不同——元素在标准状态下生成焓定义为零。实际上，完美晶体在 0 K 时熵为零，但在标准条件下所有物质均具有熵。

Entropy increases with temperature, because particles vibrate, rotate and translate more energetically. It also increases when a solid melts or a liquid boils, because these phase changes involve large increases in disorder.

熵随温度升高而增大，因为粒子振动、转动和平动更剧烈。固体熔化或液体沸腾时熵也会增大，因为这些相变使无序程度大幅增加。

For simple molecules, heavier molecules or those with more atoms often have greater standard entropy because they have more ways to distribute energy among vibrational and rotational modes.

对于简单分子，较重的分子或含更多原子的分子通常具有更大的标准熵，因为它们有更多方式在振动和转动模式中分配能量。

---

3. Calculating Entropy Changes | 计算熵变

The entropy change for a reaction is the difference between the total entropy of the products and the total entropy of the reactants:

反应的熵变等于生成物总熵与反应物总熵之差：

ΔS° = ΣS°(products) − ΣS°(reactants)

If the products are more disordered than the reactants, ΔS° is positive. If the products are more ordered, ΔS° is negative.

如果生成物比反应物更无序，则 ΔS° 为正；如果生成物更有序，则 ΔS° 为负。

Reactions that produce more gas molecules than they consume usually have a positive entropy change, whereas reactions that convert gases into solids or liquids usually have a negative entropy change.

生成气体分子数多于消耗气体分子数的反应通常熵变为正；将气体转化为固体或液体的反应通常熵变为负。

Example: in CaCO₃(s) → CaO(s) + CO₂(g), ΔS° is positive because a gas is produced from a single solid reactant.

例如：CaCO₃(s) → CaO(s) + CO₂(g)，ΔS° 为正，因为由一种固体反应物生成了气体。

---

4. Introducing Gibbs Free Energy | 吉布斯自由能导论

Gibbs free energy, symbol G, is a thermodynamic potential that combines enthalpy and entropy to determine whether a process is spontaneous at constant temperature and pressure. A spontaneous process is one that can proceed on its own once started, without continuous external energy input.

吉布斯自由能（符号 G）是结合焓和熵的热力学势，用于判断恒温恒压过程能否自发进行。自发过程指一旦开始，无需持续外部能量输入即可进行的过程。

The change in Gibbs free energy ΔG tells us the maximum non-expansion work that can be obtained from a chemical reaction. In chemistry, however, its main use is as a feasibility criterion.

吉布斯自由能变化 ΔG 表示从化学反应可获得的最大非体积功。在化学中，其主要用途是作为可行性判据。

For a reaction under standard conditions, ΔG° can be calculated from standard Gibbs free energy of formation values, but at A-level it is often found from ΔH° and ΔS° using the Gibbs equation.

对于标准条件下的反应，ΔG° 可由标准生成吉布斯自由能计算，但在A-level中通常利用 ΔH° 和 ΔS° 通过吉布斯方程求得。

---

5. The Gibbs Equation ΔG = ΔH − TΔS | 吉布斯方程 ΔG = ΔH − TΔS

The central relationship is:

核心关系式为：

ΔG = ΔH − TΔS

Here ΔH is the enthalpy change, T is the absolute temperature in kelvin, and ΔS is the entropy change. The term TΔS represents the energy associated with the entropy change at temperature T.

式中 ΔH 为焓变，T 为开尔文温度，ΔS 为熵变。TΔS 项表示在温度 T 下与熵变相关的能量。

Because ΔH is usually quoted in kJ mol⁻¹ while ΔS is quoted in J K⁻¹ mol⁻¹, you must convert one of them before combining. For example, convert ΔH to J mol⁻¹ by multiplying by 1000, or convert ΔS to kJ K⁻¹ mol⁻¹ by dividing by 1000.

由于 ΔH 通常以 kJ mol⁻¹ 表示，而 ΔS 以 J K⁻¹ mol⁻¹ 表示，必须先统一单位再计算。例如将 ΔH 乘以 1000 转换为 J mol⁻¹，或将 ΔS 除以 1000 转换为 kJ K⁻¹ mol⁻¹。

A negative ΔG means the forward reaction is feasible, a positive ΔG means the forward reaction is not feasible under those conditions, and ΔG = 0 indicates the system is at equilibrium.

ΔG 为负表示正向反应可行，ΔG 为正表示该条件下正向反应不可行，ΔG = 0 表示体系处于平衡状态。

---

6. Predicting Feasibility: Sign of ΔG | 预测可行性：ΔG 的符号

The sign of ΔG depends on the signs of ΔH and ΔS. Four combinations are possible.

ΔG 的符号取决于 ΔH 和 ΔS 的符号，共有四种组合。

If ΔH is negative and ΔS is positive, ΔG is negative at all temperatures, so the reaction is always feasible.

若 ΔH 为负且 ΔS

Published by TutorHao | A-Level Chemistry Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）