📚 Entropy, Enthalpy Changes and Free Energy | 熵、焓变与自由能
In A-Level Chemistry, understanding why chemical reactions happen requires more than just measuring heat changes. Entropy, enthalpy changes and Gibbs free energy together give a powerful way to explain and predict the feasibility of chemical and physical processes.
在 A-Level 化学中，要理解化学反应为什么能够发生，仅仅测量热量变化是不够的。熵、焓变和吉布斯自由能共同提供了一种强有力的方法，用来解释和预测化学与物理过程的可行性。
1. What is Entropy? | 什么是熵？
Entropy, given the symbol S, is a measure of the number of ways that energy and particles can be arranged in a system. A system with high entropy has many possible arrangements and is more disordered or more random.
熵用符号 S 表示，是衡量系统中能量和粒子排列方式数量的物理量。熵值高的系统具有许多可能的排列方式，更加无序或更加随机。
The units of entropy are joules per kelvin per mole, written as J K⁻¹ mol⁻¹. Unlike enthalpy, absolute entropy values can be determined, because a perfectly ordered crystal at absolute zero (0 K) is assigned an entropy of zero.
熵的单位是焦耳每开尔文每摩尔，写作 J K⁻¹ mol⁻¹。与焓不同，熵的绝对值是可以测定的，因为理想有序晶体在绝对零度（0 K）时的熵被定义为零。
Entropy tends to increase when a solid melts, a liquid boils, or a solute dissolves. In each case, particles gain more freedom of movement and energy is spread over more possible states.
当固体熔化、液体沸腾或溶质溶解时，熵通常会增加。在这些过程中，粒子获得更多的运动自由，能量分散到更多可能的状态中。
2. Standard Entropy Values | 标准熵值
The standard entropy of a substance, S°, is the entropy of one mole of that substance under standard conditions: 298 K and 1 atm pressure. Standard entropy values are always positive because particles always have some disorder above 0 K.
物质的标准熵 S° 是在标准条件（298 K 和 1 atm 压力）下，一摩尔该物质的熵。标准熵值始终为正，因为在 0 K 以上粒子总是有一定程度的无序。
Gases generally have much higher standard entropy values than liquids, and liquids have higher values than solids. This reflects the increasing freedom of particle movement from solid to liquid to gas.
气体的标准熵值通常远高于液体，液体的标准熵值又高于固体。这反映了从固体到液体再到气体，粒子运动自由度的不断增加。
| Substance | 物质 | State | 状态 | S° / J K⁻¹ mol⁻¹ |
|---|---|---|
| Carbon, C | solid (graphite) | 5.7 |
| Water, H₂O | liquid | 69.9 |
| Water, H₂O | gas | 188.8 |
| Carbon dioxide, CO₂ | gas | 213.6 |
These data show the large increase in entropy when a liquid turns into a gas, which is a useful pattern when predicting entropy changes in reactions.
这些数据表明，液体变为气体时熵会大幅增加，这是预测反应熵变时一个非常有用的规律。
3. Predicting Entropy Changes in Reactions | 预测反应中的熵变
The entropy change of a reaction, ΔS, is calculated using the expression:
反应的熵变 ΔS 通过以下公式计算：
ΔS = ΣS°(products) − ΣS°(reactants)
A positive ΔS means the products are more disordered than the reactants. This often occurs when the number of gas molecules increases, when a solid or liquid produces a gas, or when a solid dissolves.
ΔS 为正值意味着产物比反应物更加无序。这通常发生在气体分子数增加、固体或液体生成气体、或固体溶解时。
A negative ΔS means the system becomes more ordered. This often occurs when gases react to form a solid or liquid, or when the number of gas molecules decreases.
ΔS 为负值意味着系统变得更加有序。这通常发生在气体反应生成固体或液体，或气体分子数减少时。
- CaCO₃(s) → CaO(s) + CO₂(g): ΔS is positive because a gas is produced.
- N₂(g) + 3H₂(g) → 2NH₃(g): ΔS is negative because 4 moles of gas become 2 moles of gas.
- CaCO₃(s) → CaO(s) + CO₂(g)：由于生成了气体，ΔS 为正值。
- N₂(g) + 3H₂(g) → 2NH₃(g)：由于 4 摩尔气体变为 2 摩尔气体，ΔS 为负值。
4. Calculating Entropy Changes | 计算熵变
To calculate ΔS for a reaction, multiply each standard entropy value by the stoichiometric coefficient in the balanced equation, then subtract the total for reactants from the total for products.
要计算反应的 ΔS，需要将配平方程式中每种物质的标准熵值乘以其化学计量数，然后用产物的总和减去反应物的总和。
Example: Calculate ΔS for the combustion of methane.
示例：计算甲烷燃烧的 ΔS。
CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l)
entropy values: CH₄(g) = 186.2, O₂(g) = 205.0, CO₂(g) = 213.6, H₂O(l) = 69.9 J K⁻¹ mol⁻¹.
使用标准熵值：CH₄(g) = 186.2，O₂(g) = 205.0，CO₂(g) = 213.6，H₂O(l) = 69.9 J K⁻¹ mol⁻¹。
ΔS = [213.6 + 2(69.9)] − [186.2 + 2(205.0)] = 353.4 − 596.2 = −242.8 J K⁻¹ mol⁻¹
The negative value is expected because three moles of gas are converted into one mole of gas and two moles of liquid, so the system becomes more ordered.
负值是符合预期的，因为三摩尔气体转化为一摩尔气体和两摩尔液体，系统变得更加有序。
5. Total Entropy Change and the Second Law | 总熵变与热力学第二定律
For a reaction to be feasible, it is not enough to consider only the entropy change of the chemical system. The total entropy change of the universe must be positive.
要判断一个反应是否可行，只考虑化学系统本身的熵变是不够的。宇宙的总熵变必须为正值。
ΔS(total) = ΔS(system) + ΔS(surroundings)
The second law of thermodynamics states that a spontaneous process increases the total entropy of the universe. If ΔS(total) is positive, the process is thermodynamically feasible.
热力学第二定律指出，自发过程会增加宇宙的总熵。如果 ΔS(total) 为正，则该过程在热力学上是可行的。
The entropy change of the surroundings is related to the enthalpy change of the reaction and the temperature:
周围的熵变与反应的焓变和温度有关：
ΔS(surroundings) = −ΔH / T
An exothermic reaction (ΔH negative) releases heat to the surroundings, increasing the entropy of the surroundings. An endothermic reaction (ΔH positive) decreases the entropy of the surroundings.
放热反应（ΔH 为负）向周围释放热量，使周围的熵增加。吸热反应（ΔH 为正）会使周围的熵减少。
6. Introducing Gibbs Free Energy | 引入吉布斯自由能
Combining the entropy changes of the system and surroundings leads to a much more convenient quantity called the Gibbs free energy change, ΔG.
将系统和周围的熵变结合起来，可以得到一个更方便使用的物理量，称为吉布斯自由能变 ΔG。
ΔG = ΔH − TΔS(system)
In this equation, T is the absolute temperature in kelvin. The derivation shows that the condition ΔS(total) > 0 is equivalent to ΔG < 0 for a reaction at constant temperature and pressure.
在该方程中，T 是以开尔文为单位的绝对温度。推导表明，在恒温恒压条件下，ΔS(total) > 0 这一条件等价于 ΔG < 0。
When ΔG is negative, the reaction is said to be thermodynamically feasible. When ΔG is positive, the reaction is not feasible under the stated conditions.
当 ΔG 为负值时，反应在热力学上可行。当 ΔG 为正值时，在给定条件下反应不可行。
7. Standard Gibbs Free Energy Change | 标准吉布斯自由能变
The standard Gibbs free energy change, ΔG°, refers to reactions carried out under standard conditions of 298 K and 1 atm pressure, with all substances in their standard states.
标准吉布斯自由能变 ΔG° 是指在 298 K 和 1 atm 压力、所有物质均处于标准状态下的反应。
ΔG° = ΔH° − TΔS°
Because ΔG depends on temperature, a reaction that is not feasible at 298 K may become feasible at a higher or lower temperature. The standard symbol only fixes the pressure and concentration conditions, not necessarily the temperature, but in A-Level calculations 298 K is usually used unless stated otherwise.
由于 ΔG 与温度有关，在 298 K 下不可行的反应可能在更高或更低温度下变得可行。标准符号只固定压力和浓度条件，并不一定固定温度，但在 A-Level 计算中通常使用 298 K，除非另有说明。
When calculating ΔG°, it is essential to convert ΔH° from kJ mol⁻¹ to J mol⁻¹ or convert ΔS° from J K⁻¹ mol⁻¹ to kJ K⁻¹ mol⁻¹ so that both terms have the same energy unit.
计算 ΔG° 时，必须将 ΔH° 从 kJ mol⁻¹ 转换为 J mol⁻¹，或将 ΔS° 从 J K⁻¹ mol⁻¹ 转换为 kJ K⁻¹ mol⁻¹，使两项具有相同的能量单位。
8. Temperature Dependence of Feasibility | 温度对可行性的影响
The sign of ΔG depends on the relative sizes of ΔH and TΔS. Since T is always positive in kelvin, the effect of the entropy term increases as temperature increases.
ΔG 的符号取决于 ΔH 与 TΔS 的相对大小。由于开尔文温度 T 始终为正，熵项的影响会随着温度的升高而增大。
| ΔH | ΔS | Feasibility | 可行性 |
|---|---|---|
| Negative (exothermic) | Positive | Always feasible at all temperatures |
| Positive (endothermic) | Negative | Never feasible at any temperature |
| Negative | Negative | Feasible below a certain temperature |
| Positive | Positive | Feasible above a certain temperature |
The temperature at which a reaction becomes just feasible is found by setting ΔG = 0:
反应刚好变得可行的温度可以通过令 ΔG = 0 求得：
T = ΔH / ΔS
This is especially important for endothermic reactions that produce a gas, such as thermal decomposition of carbonates.
这对于产生气体的吸热反应尤其重要，例如碳酸盐的热分解。
9. Worked Example: Decomposition of Calcium Carbonate | 计算示例：碳酸钙分解
Consider the thermal decomposition of calcium carbonate:
考虑碳酸钙的热分解反应：
CaCO₃(s) → CaO(s) + CO₂(g)
H° = +178 kJ mol⁻¹ and ΔS° = +160 J K⁻¹ mol⁻¹, the minimum temperature for feasibility is:
已知 ΔH° = +178 kJ mol⁻¹，ΔS° = +160 J K⁻¹ mol⁻¹，求反应可行的最低温度：
T = ΔH / ΔS = 178000 J mol⁻¹ / 160 J K⁻¹ mol⁻¹ = 1112.5 K
Below this temperature, ΔG is positive and the reaction is not thermodynamically feasible. Above this temperature, ΔG becomes negative and decomposition can occur.
低于该温度时，ΔG 为正，反应在热力学上不可行。高于该温度时，ΔG 变为负值，分解反应可以发生。
This calculation explains why heating limestone strongly is necessary to produce quicklime in industry.
这一计算解释了为什么工业上生产生石灰需要强烈加热石灰石。
10. Limitations of Feasibility Predictions | 可行性预测的局限性
A negative ΔG indicates that a reaction is thermodynamically possible, but it does not guarantee that the reaction will happen at a measurable rate. Kinetics also plays a vital role.
ΔG 为负表明反应在热力学上是可能发生的，但并不能保证反应会以可测量的速率进行。动力学也起着至关重要的作用。
Many thermodynamically feasible reactions have a high activation energy and are therefore very slow at room temperature. For example, graphite is thermodynamically more stable than diamond, yet diamond does not spontaneously convert to graphite under normal conditions.
许多热力学上可行的反应具有较高的活化能，因此在室温下非常缓慢。例如，石墨在热力学上比金刚石更稳定，但在正常条件下金刚石并不会自发转化为石墨。
For this reason, exam answers should use the phrase "thermodynamically feasible" rather than simply saying that a reaction will definitely occur.
因此，考试答案应使用“热力学上可行”这一表述，而不是简单地说反应一定会发生。
11. Free Energy and Equilibrium | 自由能与平衡
When a reversible reaction reaches equilibrium, the Gibbs free energy change is zero. At this point, the forward and reverse reactions are occurring at equal rates, and there is no net tendency for the reaction to proceed in either direction.
当可逆反应达到平衡时，吉布斯自由能变为零。此时正反应和逆反应以相等的速率进行，反应没有向任一方向进行的净趋势。
If ΔG is negative, the forward reaction is favoured and the equilibrium position lies towards the products. If ΔG is positive, the reverse reaction is favoured and the equilibrium position lies towards the reactants.
如果 ΔG 为负，正反应受到促进，平衡位置偏向产物。如果 ΔG 为正，逆反应受到促进，平衡位置偏向反应物。
This link between free energy and equilibrium helps to explain why some reactions shift direction as temperature changes, especially those where ΔH and ΔS have the same sign.
自由能与平衡之间的这种联系有助于解释为什么某些反应会随着温度变化而改变方向，特别是那些 ΔH 和 ΔS 同号的反应。
12. Exam Tips for Entropy and Free Energy | 熵与自由能的考试技巧
- nvert kJ to J before using ΔG = ΔH − TΔS unless both terms are converted to the same unit.
- Always use temperature in kelvin, not degrees Celsius.
- Remember that standard entropy values are always positive, but ΔS can be positive or negative.
- When predicting entropy change, focus on gas moles and state changes.
- Use "thermodynamically feasible" instead of "will react" when discussing the sign of ΔG.
- 在使用 ΔG = ΔH − TΔS 之前，务必先将 kJ 转换为 J，或者将两项换算为同一单位。
- 温度必须使用开尔文，而不是摄氏度。
- 记住标准熵值始终为正，但 ΔS 可以为正或负。
- 预测熵变时，重点关注气体摩尔数和状态变化。
- 讨论 ΔG 符号时，使用“热力学上可行”而不是“会反应”。
Mastering these ideas will give you a clear understanding of why some reactions occur and others do not, and how temperature can change the direction of chemical change.
掌握这些概念将使你清楚地理解为什么有些反应能够发生而有些不能，以及温度如何改变化学变化的方向。
Published by TutorHao | Chemistry Revision Series | aleveler.com
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