Entropy and Spontaneity in IB Chemistry HL | IB化学（HL）：熵与自发反应判断要点

📚 Entropy and Spontaneity in IB Chemistry HL | IB化学（HL）：熵与自发反应判断要点

In IB Chemistry Higher Level, predicting whether a reaction is spontaneous requires more than just enthalpy change. The key lies in entropy and the total entropy change of the universe. This article covers the essential points you need to master: what entropy is, how to calculate entropy changes, and how to use Gibbs free energy to judge spontaneity.

在 IB 化学高级水平（HL）中，判断一个反应是否自发仅看焓变远远不够，关键在于熵以及宇宙总熵变。本文涵盖你需要掌握的核心要点：什么是熵、如何计算熵变，以及如何利用吉布斯自由能判断自发性。

1. What Is Entropy? | 什么是熵？

Entropy, symbol S, is a measure of the dispersal of energy or the number of possible microstates available to a system. In simple terms, it describes the degree of disorder or randomness of particles.

熵，符号为 S，是能量分散程度或系统可能微观状态数的量度。简单来说，它描述粒子无序性（混乱度）的大小。

A system with more possible arrangements has higher entropy. Gases have much higher entropy than liquids and solids. For example, solid NaCl has low entropy, while NaCl dissolved in water has higher entropy because the ions are spread throughout the solution.

具有更多可能排列方式的系统具有更高的熵。气体的熵远高于液体和固体。例如，固体 NaCl 的熵较低，而 NaCl 溶于水后熵较高，因为离子分散在整个溶液中。

The third law of thermodynamics states that the entropy of a perfectly ordered pure crystal at absolute zero (0 K) is zero. This allows chemists to define absolute standard molar entropies, S°, measured in J K⁻¹ mol⁻¹.

热力学第三定律指出，在绝对零度（0 K）下，完美有序的纯晶体熵为零。这使化学家能够定义绝对标准摩尔熵 S°，单位为 J K⁻¹ mol⁻¹。

2. Predicting the Sign of Entropy Change | 判断熵变的正负

Although exact calculation is useful, IB exam questions often ask you to predict whether ΔS is positive or negative. Check three major factors.

虽然精确计算很有用，但 IB 考试题常要求你判断 ΔS 是正还是负。可关注三大因素。

Change in number of gas molecules: More gas molecules means higher entropy. Example: 2H₂O₂(aq) → 2H₂O(l) + O₂(g), gas is produced, so ΔS is positive.
气体分子数变化：气体分子数增加，熵增大。例如：2H₂O₂(aq) → 2H₂O(l) + O₂(g)，生成了气体，所以 ΔS 为正。
Change of state: Melting and vaporization increase entropy; condensation and freezing decrease entropy.
状态变化：熔化、气化使熵增大；凝结、凝固使熵减小。
Dissolving a solid or gas: Dissolving a solid in water usually increases entropy; dissolving a gas decreases entropy because gas molecules become confined in solution.
溶解过程：固体溶于水通常使熵增大；气体溶于水使熵减小，因为气体分子被限制在溶液中。

In the reaction N₂(g) + 3H₂(g) → 2NH₃(g), four moles of gas become two moles of gas. The number of gas molecules decreases, so the sign of ΔS for the system is negative.

在反应 N₂(g) + 3H₂(g) → 2NH₃(g) 中，四摩尔气体变为两摩尔气体，气体分子数减少，所以系统熵变 ΔS 为负。

3. Calculating Standard Entropy Change | 计算标准熵变

For a chemical reaction, the standard entropy change of the system is calculated from standard molar entropies:

对于化学反应，系统的标准熵变由标准摩尔熵计算：

ΔS° = ΣS°(products) − ΣS°(reactants)

Remember to multiply each S° value by its stoichiometric coefficient. The result is in J K⁻¹ mol⁻¹ (per mole of reaction as written).

记得将每个 S° 值乘以其化学计量系数。结果的单位为 J K⁻¹ mol⁻¹（按所写反应式的每摩尔反应计）。

Example: Calculate ΔS° for CaCO₃(s) → CaO(s) + CO₂(g), given S° values in J K⁻¹ mol⁻¹: CaCO₃ = 92.9, CaO = 39.7, CO₂ = 213.7.

示例：计算 CaCO₃(s) → CaO(s) + CO₂(g) 的 ΔS°，已知各物质的 S°（J K⁻¹ mol⁻¹）：CaCO₃ = 92.9，CaO = 39.7，CO₂ = 213.7。

ΔS° = (39.7 + 213.7) − (92.9) = 160.5 J K⁻¹ mol⁻¹

The positive value matches the prediction that one mole of gas is produced from a solid, increasing disorder.

正值符合预测：固体产生了一摩尔气体，无序度增大。

4. Total Entropy Change and the Second Law | 总熵变与热力学第二定律

The second law of thermodynamics states that in any spontaneous process, the entropy of the universe increases. The universe includes the system and the surroundings.

热力学第二定律指出，任何自发过程中，宇宙的熵增大。宇宙包括系统和环境。

ΔS_total = ΔS_system + ΔS_surroundings

For a spontaneous change, ΔS_total > 0. This rule is absolute; there are no exceptions.

自发变化要求 ΔS_total > 0。这一规则是绝对的，没有例外。

At constant pressure, the entropy change of the surroundings is related to the enthalpy change of the system:

在恒压下，环境的熵变与系统的焓变有关：

ΔS_surroundings = −ΔH_system / T

An exothermic reaction (ΔH < 0) releases heat into the surroundings, increasing the entropy of the surroundings. An endothermic reaction (ΔH > 0) absorbs heat from the surroundings, decreasing the entropy of the surroundings.

放热反应（ΔH < 0）向环境释放热量，使环境熵增大；吸热反应（ΔH > 0）从环境吸收热量，使环境熵减小。

5. Gibbs Free Energy and Spontaneity | 吉布斯自由能与自发性

Combining the equations gives the Gibbs free energy change:

将以上方程合并可得吉布斯自由能变：

ΔG = ΔH − TΔS

This is effectively a measure of the total entropy change of the universe, expressed in energy units. At constant temperature and pressure:

这实际上是宇宙总熵变的能量表达形式。在恒温恒压下：

ΔG < 0	Spontaneous (product-favoured)
ΔG = 0	At equilibrium
ΔG > 0	Non-spontaneous as written

注意：ΔG < 0 并不等于反应快。热力学只判断可能性，动力学决定速度。

Note: ΔG < 0 does not mean the reaction is fast. Thermodynamics judges possibility; kinetics determines rate.

ΔG = ΔG° + RT ln Q

At equilibrium, ΔG = 0 and Q = K, giving:

在平衡时，ΔG = 0 且 Q = K，由此可得：

ΔG° = −RT ln K

6. How ΔH and ΔS Signs Control Spontaneity | ΔH 与 ΔS 的正负如何控制自发性

The sign of ΔG depends on the signs of ΔH and ΔS, as well as the temperature T. This gives four general cases.

ΔG 的符号取决于 ΔH 与 ΔS 的正负，以及温度 T。这给出了四种常见情形。

ΔH	ΔS	Spontaneity	自发性
Negative	Positive	Spontaneous at all temperatures	所有温度下自发
Positive	Negative	Non-spontaneous at all temperatures	所有温度下不自发
Negative	Negative	Spontaneous at low T only	仅在低温下自发
Positive	Positive	Spontaneous at high T only	仅在高温下自发

例：水结冰 H₂O(l) → H₂O(s) 放热（ΔH < 0）且无序度减小（ΔS < 0）。低温时 |TΔS| 较小，ΔG < 0，所以低温下自发；高温时 |TΔS| 超过 ΔH，ΔG > 0，所以高温下不自发。

Example: For freezing of water H₂O(l) → H₂O(s), the process is exothermic (ΔH < 0) and has decreasing disorder (ΔS < 0). At low temperature, |TΔS| is small so ΔG < 0 and it is spontaneous; at high temperature, |TΔS| dominates and ΔG > 0, so it becomes non-spontaneous.

7. Calculating the Temperature of Transition | 计算转变温度

When ΔH and ΔS have the same sign, spontaneity changes at the temperature where ΔG = 0:

当 ΔH 与 ΔS 同号时，在 ΔG = 0 的温度处自发性发生转变：

T = ΔH / ΔS

For CaCO₃(s) → CaO(s) + CO₂(g), ΔH° = +178 kJ mol⁻¹ and ΔS° = +160.5 J K⁻¹ mol⁻¹. Convert ΔH to J: 178000 J mol⁻¹.

对于 CaCO₃(s) → CaO(s) + CO₂(g)，ΔH° = +178 kJ mol⁻¹，ΔS° = +160.5 J K⁻¹ mol⁻¹。将 ΔH 转换为 J：178000 J mol⁻¹。

T = 178000 / 160.5 ≈ 1109 K

Above about 1109 K, the decomposition of calcium carbonate becomes spontaneous because the positive TΔS term overcomes the positive ΔH. This is why limestone decomposes only when heated strongly.

大约在 1109 K 以上，碳酸钙分解变为自发，因为正的 TΔS 项超过了正的 ΔH。这就是为什么石灰石只有在强热条件下才分解。

Be careful with units: ΔH is usually given in kJ mol⁻¹, while ΔS is in J K⁻¹ mol⁻¹. Convert one of them before calculating T or ΔG.

务必注意单位：ΔH 通常以 kJ mol⁻¹ 给出，而 ΔS 以 J K⁻¹ mol⁻¹ 给出。计算 T 或 ΔG 之前须先统一单位。

8. Worked Example: Is the Reaction Spontaneous? | 综合例题：反应是否自发？

Consider the reaction 2NO(g) + O₂(g) → 2NO₂(g) at 298 K. Data: ΔH° = −114 kJ mol⁻¹; ΔS° = −146 J K⁻¹ mol⁻¹.

考虑反应 2NO(g) + O₂(g) → 2NO₂(g)，温度为 298 K。数据：ΔH° = −114 kJ mol⁻¹；ΔS° = −146 J K⁻¹ mol⁻¹。

Step 1: Convert ΔS to kJ: −0.146 kJ K⁻¹ mol⁻¹.

第一步：将 ΔS 换算为 kJ：−0.146 kJ K⁻¹ mol⁻¹。

ΔG = −114 − (298)(−0.146) = −114 + 43.5 = −70.5 kJ mol⁻¹

Because ΔG < 0, the reaction is spontaneous at 298 K. In this case, ΔH is negative but ΔS is negative, so the reaction becomes less spontaneous at higher temperatures. It would be non-spontaneous above T = 114 / 0.146 ≈ 781 K.

因为 ΔG < 0，该反应在 298 K 下自发。此例中 ΔH 为负而 ΔS 为负，因此温度升高时自发性降低。当温度高于 T = 114 / 0.146 ≈ 781 K 时变为不自发。

9. Common Exam Mistakes and Tips | 常见错误与考试技巧

Unit errors: Mixing kJ and J is the most common mistake. Always convert ΔS to kJ or ΔH to J before using ΔG = ΔH − TΔS.
单位错误：混用 kJ 和 J 是最常见错误。使用 ΔG = ΔH − TΔS 前，务必将 ΔS 换成 kJ 或将 ΔH 换成 J。
Confusing ΔG and ΔG°: ΔG° refers to standard conditions (1 bar, 1 mol dm⁻³, usually 298 K). ΔG at non-standard conditions requires the reaction quotient Q.
混淆 ΔG 与 ΔG°：ΔG° 指标准状况（1 bar，1 mol dm⁻³，通常 298 K）。非标准状况下的 ΔG 需要用到反应商 Q。
Forgetting stoichiometric coefficients: When calculating ΔS° or ΔH°, multiply each substance’s value by its coefficient in the balanced equation.
忽略化学计量系数：计算 ΔS° 或 ΔH° 时，必须将各物质的数值乘以其在平衡方程式中的系数。
Thinking spontaneous means fast: A diamond is thermodynamically unstable relative to graphite at room temperature, but the conversion is extremely slow. Spontaneity says nothing about rate.
认为自发等于快速：在室温下，金刚石相对石墨在热力学上不稳定，但转化极慢。自发性与反应速率无关。

10. Entropy in Electrochemistry and Equilibrium | 电化学与平衡中的熵

In electrochemistry, the relationship ΔG° = −nFE° connects Gibbs free energy to cell potential. Therefore, a positive E° indicates a spontaneous redox reaction.

在电化学中，关系式 ΔG° = −nFE° 将吉布斯自由能与电池电动势联系起来。因此，正的 E° 表明氧化还原反应自发。

Also, since ΔG° = −RT ln K, a large negative ΔG° corresponds to an equilibrium constant much greater than 1, meaning the reaction strongly favours products.

同时，由于 ΔG° = −RT ln K，越负的 ΔG° 对应越大的平衡常数 K，说明反应强烈偏向生成物。

When answering exam questions, identify whether you are asked about the system, the surroundings, or the total entropy. Many marks are lost by describing only ΔS_system when the question asks for the second law of thermodynamics and ΔS_total.

答题时，先确认题目问的是系统熵、环境熵还是总熵。很多同学只讨论 ΔS_system 而忽略题目要求的是热力学第二定律与 ΔS_total，因而失分。

11. Quick Revision Checklist | 快速复习清单

熵的定义与单位 J K⁻¹ mol⁻¹。Definition and unit of entropy.
从分子数、状态、溶解等定性判断 ΔS 正负。Qualitative prediction of ΔS sign.
利用 ΔS° = ΣS°(产物) − ΣS°(反应物) 计算。Calculation using ΔS°.
热力学第二定律：ΔS_total > 0 为自发。Second law: ΔS_total > 0 for spontaneous change.
ΔS_surroundings = −ΔH/T。Surroundings entropy change.
ΔG = ΔH − TΔS 及正负判据。Gibbs free energy criterion.
四类 ΔH/ΔS 组合与温度的关系。Four combinations of ΔH and ΔS.
T = ΔH/ΔS 求转变温度。Transition temperature.
ΔG° = −RT ln K 与电化学关系。Link to equilibrium and electrochemistry.

By mastering entropy and Gibbs free energy, you can reliably predict spontaneity in any IB HL thermodynamics question. Remember to check units, use the correct equations, and always connect the calculation back to the fundamental rule: the entropy of the universe must increase.

掌握熵与吉布斯自由能后，你就能可靠地判断 IB HL 热力学题中任何反应的自发性。切记检查单位、选用正确公式，并将计算始终回归到基本规律：宇宙的总熵必须增大。

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Entropy and Spontaneity in IB Chemistry HL | IB化学（HL）：熵与自发反应判断要点