Entropy in A-Level Chemistry: Key Concepts | A-Level化学：熵考点精讲

📚 Entropy in A-Level Chemistry: Key Concepts | A-Level化学：熵考点精讲

Entropy, symbol S, is a fundamental thermodynamic quantity that measures the dispersal of energy within a system at a given temperature. In A-Level chemistry, mastering entropy is essential for understanding why reactions occur spontaneously and how temperature influences chemical feasibility. This article breaks down every key concept you need for exam success, from definition to calculation to Gibbs free energy.

熵（符号为 S）是一个基本的热力学量，用来衡量在给定温度下系统内能量的分散程度。在 A-Level 化学中，掌握熵对于理解反应为何能自发进行以及温度如何影响化学可行性至关重要。本文将从定义、计算到吉布斯自由能，逐一分解考试所需的所有关键概念。

1. What Is Entropy? | 什么是熵？

Entropy is a measure of the number of ways energy can be distributed among the particles in a system. The greater the number of possible arrangements (microstates), the higher the entropy. A solid has low entropy because particles are locked in fixed positions; a gas has high entropy because particles move randomly and occupy a much larger volume.

熵衡量的是系统内粒子之间能量分配的可能方式数。可能的排列方式（微态）越多，熵就越高。固体的熵较低，因为粒子被固定在一定的位置上；气体的熵较高，因为粒子随机运动并占据大得多的体积。

In thermodynamic terms, entropy is defined as the amount of energy dispersed or spread out in a process, divided by the temperature: dS = dq_rev / T. However, at A-Level, we focus on qualitative trends and changes in standard molar entropy, S°, measured in J K⁻¹ mol⁻¹.

从热力学角度，熵定义为过程中分散或扩散的能量除以温度：dS = dq_rev / T。但在 A-Level 阶段，我们重点关注定性趋势以及标准摩尔熵 (S°) 的变化，其单位为 J K⁻¹ mol⁻¹。

2. Entropy and Disorder | 熵与混乱度

A common, though slightly simplified, way to think about entropy is as a measure of ‘disorder’. When a system becomes more random or disordered, its entropy increases. For example, melting ice into liquid water increases entropy because H₂O molecules are freer to move. Boiling water to steam causes an even larger entropy jump.

一个常见但略显简化的理解方式是将熵视为“混乱度”的量度。当系统变得更随机或更无序时，其熵便会增加。例如，冰融化成液态水会使熵增加，因为水分子可以更自由地运动。水沸腾变成水蒸气则会引起更大的熵跃升。

This disorder idea helps predict changes: any process that increases the number of gas molecules or dissolves a solid will usually have a positive ΔS. However, a more accurate description is energy dispersal, which avoids misconceptions about ‘disorder’ in systems like crystalline salts.

这种混乱度的概念有助于进行预测：任何增加气体分子数或使固体溶解的过程通常都会具有正的 ΔS。然而，更精确的描述是能量分散，这可以避免对晶体盐等系统产生关于“混乱度”的误读。

3. The Second Law of Thermodynamics | 热力学第二定律

The Second Law states that the total entropy of the universe (system plus surroundings) always increases for a spontaneous process. In other words, for any feasible reaction, ΔS_total > 0. If ΔS_total = 0, the system is at equilibrium; if ΔS_total < 0, the reaction is not thermodynamically feasible under those conditions.

热力学第二定律指出，对于任何自发过程，宇宙（系统加环境）的总熵总是增加的。换句话说，对于任何可行的反应，ΔS_total > 0。如果 ΔS_total = 0，系统处于平衡状态；如果 ΔS_total < 0，则该反应在此条件下在热力学上不可行。

It is important to note that a reaction can proceed even if the entropy of the system decreases (ΔS_system < 0), provided that the entropy of the surroundings increases by an even greater amount. This is the key to understanding endothermic reactions that are spontaneous at high temperatures.

值得注意的是，即使系统的熵减少（ΔS_system < 0），只要环境的熵增加量更大，反应仍然可以进行。这是理解高温下能够自发的吸热反应的关键所在。

4. Total Entropy Change | 总熵变

The total entropy change for a reaction is the sum of the entropy change of the system and the entropy change of the surroundings:

反应的总熵变是系统熵变与环境熵变之和：

ΔS_total = ΔS_system + ΔS_surroundings

For a reaction to be thermodynamically feasible, ΔS_total must be positive. This equation effectively tells us that a decrease in the system’s order can be compensated by a large enough release of heat to the surroundings, which increases their entropy.

要使反应在热力学上可行，ΔS_total 必须为正。这个方程实际上告诉我们，系统有序度的降低可以通过向环境释放足够多的热量来补偿，从而增加环境的熵。

In examinations, you may be asked to calculate ΔS_total using standard values, or to explain why some endothermic dissolving processes (like NH₄NO₃ in water) occur spontaneously despite a cooling effect: the increase in system entropy overcomes the decrease in surroundings entropy.

在考试中，你可能会被要求使用标准值计算 ΔS_total，或者解释为什么某些吸热的溶解过程（如 NH₄NO₃ 溶于水）尽管会产生降温效应却仍能自发进行：因为系统熵的增加克服了环境熵的减少。

5. Calculating Entropy Change of the System | 系统熵变的计算

The entropy change of the system, ΔS_system, is calculated from standard molar entropy values (S°) found in data tables. All values refer to 1 mole of substance at 298 K and 100 kPa. The formula is:

系统熵变 ΔS_system 可通过数据表中的标准摩尔熵值 (S°) 计算得出。所有数值均指 298 K 和 100 kPa 下 1 摩尔物质。其公式为：

ΔS_system = Σ S°(products) – Σ S°(reactants)

Remember to multiply each S° by the stoichiometric coefficient from the balanced equation. For example, in the reaction N₂(g) + 3H₂(g) → 2NH₃(g), the system entropy change is ΔS = [2×S°(NH₃)] – [1×S°(N₂) + 3×S°(H₂)]. The units are J K⁻¹ mol⁻¹, but the value is usually expressed per mole of the reaction as written.

请记住，需要将每个 S° 乘以配平方程式中相应的化学计量系数。例如，在反应 N₂(g) + 3H₂(g) → 2NH₃(g) 中，系统熵变为 ΔS = [2×S°(NH₃)] – [1×S°(N₂) + 3×S°(H₂)]。单位为 J K⁻¹ mol⁻¹，但该值通常表示为每摩尔如上书写的反应。

Because gases have much higher entropy than solids or liquids, a reaction that produces more gas molecules than it consumes will typically have a positive ΔS_system.

由于气体的熵远高于固体或液体，如果反应产生的气体分子多于消耗的气体分子，其 ΔS_system 通常为正。

6. Entropy Change of the Surroundings | 环境熵变

The entropy change of the surroundings depends on the heat transferred to them at constant pressure, which is essentially the negative of the enthalpy change of the reaction, -ΔH. It is given by the relationship:

环境的熵变取决于在恒压下传递给它的热量，这基本上等于反应焓变的负值 -ΔH。其关系式如下：

ΔS_surroundings = -ΔH / T

where T is the absolute temperature in kelvin. If the reaction is exothermic (ΔH is negative), then -ΔH is positive, so ΔS_surroundings is positive, meaning the heat released increases the entropy of the surroundings. Conversely, an endothermic reaction (positive ΔH) decreases the entropy of the surroundings.

其中 T 为以开尔文为单位的绝对温度。如果反应是放热的（ΔH 为负），则 -ΔH 为正，因此 ΔS_surroundings 为正，意味着释放的热量增加了环境的熵。相反，吸热反应（ΔH 为正）会降低环境的熵。

Make sure to convert ΔH from kJ mol⁻¹ to J mol⁻¹ when combining with ΔS_system, as entropy values are given in J K⁻¹ mol⁻¹. A common exam pitfall is mixing kJ and J, leading to an incorrect ΔS_total calculation.

在将 ΔH 与 ΔS_system 结合计算时，一定要将 ΔH 从 kJ mol⁻¹ 转换为 J mol⁻¹，因为熵值是以 J K⁻¹ mol⁻¹ 给出的。一个常见的考试陷阱就是混淆 kJ 和 J，导致计算出错误的 ΔS_total。

7. Gibbs Free Energy Equation | 吉布斯自由能方程

To avoid always having to calculate both ΔS_system and ΔS_surroundings, scientists combined the two into a single quantity called Gibbs free energy, ΔG. The equation is derived by substituting the expression for ΔS_surroundings into the total entropy condition:

为了避免总是需要同时计算 ΔS_system 和 ΔS_surroundings，科学家将两者合并为一个称为吉布斯自由能 ΔG 的量。该方程是通过将 ΔS_surroundings 的表达式代入总熵条件推导出来的：

ΔG = ΔH – TΔS_system

Notice that it uses ΔS_system, not ΔS_total. The reaction is feasible (spontaneous) when ΔG < 0. When ΔG = 0, the system is at equilibrium. When ΔG > 0, the forward reaction is not feasible under those conditions, though the reverse reaction may be.

请注意，这里使用的是 ΔS_system，而不是 ΔS_total。当 ΔG < 0 时，反应可行（自发）。当 ΔG = 0 时，系统处于平衡状态。当 ΔG > 0 时，正向反应在这些条件下不可行，但逆反应可能是可行的。

This equation is absolutely central to A-Level thermodynamic calculations and explanations. You will be expected to use it to determine the temperature at which a reaction becomes feasible (ΔG = 0) or to explain how temperature affects spontaneity.

这个方程是 A-Level 热力学计算和解释中绝对核心的内容。你需要用该方程来确定反应变得可行的温度（ΔG = 0），或用来解释温度如何影响反应的自发性。

8. Using ΔG to Predict Reaction Feasibility | 使用 ΔG 预测反应可行性

To decide if a reaction will ‘go’ under standard conditions (298 K, 100 kPa), you can calculate ΔG° directly from standard free energy of formation values, or more commonly, use the equation ΔG° = ΔH° – TΔS°_system. If ΔG° is negative, the reaction is thermodynamically feasible under standard conditions.

要判断一个反应在标准条件下（298 K, 100 kPa）是否能“进行”，你可以直接用标准生成自由能值计算 ΔG°，或更常见地用方程 ΔG° = ΔH° – TΔS°_system 来计算。如果 ΔG° 为负，则该反应在标准条件下热力学可行。

However, a negative ΔG does not guarantee that the reaction will happen at an observable rate. Kinetics also matter: a reaction may be thermodynamically feasible (ΔG < 0) but extremely slow without a suitable catalyst or high activation energy.

然而，ΔG 为负并不能保证反应会以可观察的速率发生。动力学也很重要：一个反应可能在热力学上可行（ΔG < 0），但由于活化能很高或缺乏合适的催化剂，其速率可能极其缓慢。

This distinction between thermodynamics and kinetics is a classic A-Level discussion point, particularly in the context of the Haber process or the combustion of diamond.

热力学和动力学之间的这种区别是一个经典的 A-Level 讨论点，尤其是在哈伯法或金刚石燃烧等情境中。

9. Effect of Temperature on Feasibility | 温度对可行性的影响

Temperature plays a decisive role in determining the sign of ΔG via the TΔS term. Depending on the signs of ΔH and ΔS_system, we can identify four scenarios:

温度通过 TΔS 项在决定 ΔG 的正负方面起着决定性作用。根据 ΔH 和 ΔS_system 的正负，我们可以识别出四种情况：

Sign of ΔH	Sign of ΔS_system	Feasibility
Negative (exothermic)	Positive	Always feasible (ΔG < 0 at all T)
Negative	Negative	Feasible only at low T (\|ΔH\| > \|TΔS\|)
Positive (endothermic)	Positive	Feasible only at high T (TΔS > ΔH)
Positive	Negative	Never feasible (ΔG > 0 at all T)

The temperature at which feasibility switches (ΔG = 0) can be found by setting T = ΔH / ΔS_system. If ΔH and ΔS_system have the same sign, there will be a specific ‘threshold temperature’ above or below which the reaction becomes spontaneous.

可行性发生切换的温度点（ΔG = 0）可通过设 T = ΔH / ΔS_system 求得。如果 ΔH 和 ΔS_system 符号相同，则会有一个特定的“阈值温度”，高于或低于该温度时反应变得自发。

10. Standard Entropy Values and Trends | 标准熵值与趋势

Standard molar entropy, S°, increases with the complexity of the molecule and with the physical state. Going from solid to liquid to gas dramatically increases S°. Even within the same state, larger molecules generally possess higher entropy because they have more vibrational and rotational energy levels.

标准摩尔熵 S° 随着分子复杂性的增加和物理状态的变化而增大。从固体到液体再到气体，S° 会显著增加。即使在同一种状态下，较大的分子通常也具有较高的熵，因为它们拥有更多的振动和转动能级。

For example, S° of I₂(s) is much lower than I₂(g). For alkanes, S° increases from methane to octane due to the increasing number of atoms and degrees of freedom. Students should be comfortable comparing S° values and predicting relative magnitudes based on structure.

例如，I₂(s) 的 S° 远低于 I₂(g)。对于烷烃，从甲烷到辛烷，S° 因原子数和自由度的增加而增大。学生应能熟练比较 S° 值，并根据结构预测相对大小。

Standard entropy of elements is not zero, unlike standard enthalpy of formation. Only at absolute zero (0 K) would a perfect crystal have zero entropy, according to the Third Law of Thermodynamics.

与标准生成焓不同，元素的标准熵并非为零。根据热力学第三定律，只有在绝对零度 (0 K) 时，完美的晶体才具有零熵。

11. Exam Tips and Common Mistakes | 考试技巧与常见错误

Always check your units: ΔH is typically given in kJ mol⁻¹, but entropy is in J K⁻¹ mol⁻¹. You must convert kJ to J (×1000) before plugging into ΔG = ΔH – TΔS. Forgetting this leads to completely wrong feasibility conclusions.

务必检查单位：ΔH 通常以 kJ mol⁻¹ 给出，而熵的单位是 J K⁻¹ mol⁻¹。在代入 ΔG = ΔH – TΔS 之前，必须将 kJ 转换为 J（×1000）。忘记这点会导致完全错误的可行性结论。

When calculating ΔS_system, use absolute standard entropy values and remember stoichiometric coefficients. For ΔS_surroundings, use -ΔH/T. And never confuse the two: ΔS_surroundings does not involve standard entropy data.

在计算 ΔS_system 时，使用绝对标准熵值并记住化学计量系数。对于 ΔS_surroundings，使用 -ΔH/T。永远不要混淆这两者：ΔS_surroundings 的计算不涉及标准熵数据。

Interpret ‘spontaneous’ and ‘feasible’ correctly: a negative ΔG means a reaction is thermodynamically possible, but not necessarily fast. Answers that suggest a reaction ‘does not occur’ based solely on a positive ΔG may lose marks if kinetics or equilibrium contexts are given.

正确理解“自发”和“可行”：ΔG 为负仅意味着反应在热力学上是可能的，但速度不一定快。如果题目给出了关于动力学或平衡的背景，仅凭 ΔG 为正就回答反应“不会发生”可能会丢分。

Practice writing clear explanations that link entropy to energy dispersal, not just vague ‘disorder’. Use phrases like ‘more ways to distribute energy’ to gain full credit.

练习写出清晰的解释，将熵与能量分散联系起来，而不仅仅是模糊的“混乱度”。使用诸如“更多的能量分布方式”这样的表述来获得满分。

12. Summary and Key Takeaways | 总结与要点回顾

Entropy measures energy dispersal, and total entropy change must increase for a spontaneous process. The Gibbs free energy equation elegantly combines system entropy and enthalpy to predict feasibility, with temperature acting as the critical switch. Memorise ΔG = ΔH – TΔS_system, understand the four ΔH/ΔS sign combinations, and always watch your units. With these tools, any entropy question on the A-Level paper becomes manageable.

熵衡量的是能量分散，自发过程的总熵必定增加。吉布斯自由能方程巧妙地将系统熵和焓结合起来以预测可行性，而温度则充当了关键的切换要素。牢记 ΔG = ΔH – TΔS_system，理解四种 ΔH/ΔS 符号组合，并始终注意单位。掌握了这些工具，A-Level 试卷上任何关于熵的问题都将变得迎刃而解。

Keep a chart of standard entropies handy and practice calculating threshold temperatures (T = ΔH/ΔS) until the process is automatic. In essays, connect microscopic particle behaviour to macroscopic thermodynamic quantities for top-grade responses.

在复习时，将一张标准熵值表放在手边，并练习计算阈值温度 (T = ΔH/ΔS)，直到成为自然反应。在写论述题时，将微观粒子行为与宏观热力学量联系起来，以获得高分。

Published by TutorHao | Chemistry Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Entropy in A-Level Chemistry: Key Concepts | A-Level化学：熵 考点精讲