Thermodynamics | 热力学

📚 Thermodynamics | 热力学

Thermodynamics in A-Level Chemistry is the study of energy changes that accompany chemical reactions. It brings together enthalpy, entropy, and Gibbs free energy to explain why reactions happen and whether they are feasible under given conditions.

A-Level 化学中的热力学研究伴随化学反应发生的能量变化。它将焓、熵和吉布斯自由能结合起来，解释反应为何发生，以及在给定条件下反应是否可行。

1. Enthalpy Changes Revisited | 焓变回顾

Enthalpy (H) is the total heat content of a system at constant pressure. The change in enthalpy, ΔH, is positive for endothermic reactions (heat absorbed) and negative for exothermic reactions (heat released). Standard enthalpy changes are measured under standard conditions, 298 K and 1 atm.

焓（H）是系统在恒压下的总热含量。焓变 ΔH 在吸热反应中为正（吸收热量），在放热反应中为负（释放热量）。标准焓变是在标准条件下（298 K 和 1 atm）测定的。

Key standard enthalpy terms include: standard enthalpy of formation (ΔHf°) — the enthalpy change when one mole of a compound forms from its elements in their standard states; and standard enthalpy of combustion (ΔHc°) — the enthalpy change when one mole of substance burns completely in oxygen.

关键的标准焓术语包括：标准生成焓（ΔHf°）——由标准状态下的元素生成 1 摩尔化合物时的焓变；以及标准燃烧焓（ΔHc°）——1 摩尔物质在氧气中完全燃烧时的焓变。

2. Hess’s Law and Enthalpy Cycles | 赫斯定律与焓循环

Hess’s law states that the total enthalpy change for a reaction is independent of the route taken, provided the initial and final conditions are the same. This allows us to calculate ΔH for reactions that are difficult to measure directly.

赫斯定律指出，只要初始和最终条件相同，反应的总焓变与路径无关。这使我们能够计算难以直接测量的反应的 ΔH。

For example, the enthalpy of formation of propan-1-ol can be calculated from its combustion enthalpy and the combustion enthalpies of carbon and hydrogen. Using a Hess cycle:

例如，可以通过丙-1-醇的燃烧焓以及碳和氢的燃烧焓，利用赫斯循环计算其生成焓：

ΔHf°(C₃H₈O) = 3ΔHc°(C) + 4ΔHc°(H₂) − ΔHc°(C₃H₈O)

Remember to balance equations carefully; the coefficients in the Hess cycle must match the stoichiometric quantities.

请务必仔细配平方程；赫斯循环中的系数必须与化学计量数量匹配。

3. Born-Haber Cycles | 玻恩-哈伯循环

Born-Haber cycles are a specific application of Hess’s law for ionic compounds. They break down the lattice formation enthalpy into a series of well-defined steps: atomisation, ionisation, electron affinity, and formation.

玻恩-哈伯循环是赫斯定律在离子化合物中的具体应用。它将晶格形成焓分解为一系列明确的步骤：原子化、电离、电子亲和和生成。

For sodium chloride, the cycle includes: enthalpy of atomisation of Na, ionisation energy of Na, enthalpy of atomisation of Cl, electron affinity of Cl, and the lattice enthalpy. The overall ΔHf° of NaCl is given by:

对于氯化钠，该循环包括：Na 的原子化焓、Na 的电离能、Cl 的原子化焓、Cl 的电子亲和能以及晶格焓。NaCl 的总 ΔHf° 由下式给出：

ΔHf°(NaCl) = ΔHat°(Na) + IE₁(Na) + ΔHat°(Cl) + EA₁(Cl) − ΔHlattice°(NaCl)

Lattice enthalpy is defined as the enthalpy change when one mole of an ionic compound is formed from its gaseous ions (exothermic, negative value). The opposite process (breaking the lattice) is endothermic.

晶格焓定义为由气态离子形成 1 摩尔离子化合物时的焓变（放热，负值）。相反的过程（破坏晶格）是吸热的。

4. Factors Affecting Lattice Enthalpy | 影响晶格焓的因素

Two main factors determine the magnitude of lattice enthalpy: ionic charge and ionic radius. Higher charge and smaller radius lead to stronger electrostatic attraction between ions, resulting in a more exothermic lattice enthalpy.

决定晶格焓大小的两个主要因素是离子电荷和离子半径。更高的电荷和更小的半径导致离子间更强的静电吸引，从而使晶格焓更放热。

For example, MgO has a much more exothermic lattice enthalpy than NaCl because Mg²⁺ and O²⁻ carry higher charges. Similarly, LiF has a more exothermic lattice enthalpy than KBr due to smaller ionic radii.

例如，MgO 的晶格焓比 NaCl 放热得多，因为 Mg²⁺ 和 O²⁻ 带有更高的电荷。类似地，LiF 的晶格焓比 KBr 更放热，因为离子半径更小。

Application: Lattice enthalpy helps explain trends in melting points, hardness, and solubility of ionic compounds.

应用：晶格焓有助于解释离子化合物的熔点、硬度和溶解度的变化趋势。

5. Entropy | 熵

Entropy (S) measures the degree of disorder or randomness of a system. The units are J K⁻¹ mol⁻¹. A system with more possible arrangements of particles has higher entropy. Gases have much higher entropy than liquids and solids because particles are free to move randomly.

熵（S）衡量系统的无序度或随机程度。单位是 J K⁻¹ mol⁻¹。粒子可能排列方式越多的系统，熵越高。气体的熵远高于液体和固体，因为粒子可以自由地随机运动。

Standard entropy values (S°) are tabulated at 298 K and 1 atm. The standard entropy change for a reaction, ΔS°, is calculated as:

标准熵值（S°）在 298 K 和 1 atm 下列成表格。反应的标准熵变 ΔS° 计算如下：

ΔS° = ΣS°(products) − ΣS°(reactants)

Remember to multiply each entropy value by its stoichiometric coefficient.

请记得将每个熵值乘以其化学计量系数。

6. Predicting Entropy Changes | 预测熵变

You can often predict the sign of ΔS without calculations. If a reaction produces more gas molecules than it consumes, entropy increases (positive ΔS). If the number of gas molecules decreases, entropy decreases.

通常无需计算即可预测 ΔS 的符号。如果反应产生的气体分子数多于消耗的，熵增加（ΔS 为正）。如果气体分子数减少，熵减少。

Dissolving a solid in water often increases entropy because the solute particles become more dispersed. However, gas dissolving in a liquid decreases entropy. Phase changes also affect entropy: melting and boiling increase entropy, while freezing and condensing decrease it.

固体溶于水通常增加熵，因为溶质粒子变得更加分散。然而，气体溶于液体会降低熵。相变也影响熵：熔化和沸腾增加熵，而凝固和冷凝降低熵。

Example: The thermal decomposition of calcium carbonate, CaCO₃(s) → CaO(s) + CO₂(g), has a positive ΔS because one mole of solid produces one mole of gas.

例如：碳酸钙的热分解，CaCO₃(s) → CaO(s) + CO₂(g)，ΔS 为正，因为 1 摩尔固体产生了 1 摩尔气体。

7. Gibbs Free Energy | 吉布斯自由能

Gibbs free energy (G) combines enthalpy and entropy to determine whether a reaction is feasible at a given temperature. The change in Gibbs free energy, ΔG, is given by the equation:

吉布斯自由能（G）结合焓和熵来判断反应在给定温度下是否可行。吉布斯自由能变 ΔG 由方程给出：

ΔG = ΔH − TΔS

where T is the temperature in kelvin. A reaction is feasible (spontaneous) when ΔG is negative. If ΔG is zero, the system is at equilibrium. If ΔG is positive, the reaction is not feasible under those conditions.

其中 T 是开尔文温度。当 ΔG 为负时，反应可行（自发）。若 ΔG 为零，系统处于平衡。若 ΔG 为正，则反应在该条件下不可行。

Note: ΔH must be in joules per mole for consistency with TΔS (J K⁻¹ mol⁻¹ × K = J mol⁻¹).

注意：ΔH 必须以焦耳每摩尔为单位，以与 TΔS（J K⁻¹ mol⁻¹ × K = J mol⁻¹）保持一致。

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

The sign of ΔG can change with temperature depending on the signs of ΔH and ΔS. There are four cases to consider:

ΔG 的符号会随温度变化，其变化方式取决于 ΔH 和 ΔS 的符号。需要考虑四种情况：

ΔH negative, ΔS positive: ΔG is always negative — feasible at all temperatures.
ΔH positive, ΔS negative: ΔG is always positive — not feasible at any temperature.
ΔH negative, ΔS negative: ΔG becomes less negative as T increases; feasible at low temperatures only.
ΔH positive, ΔS positive: ΔG becomes more negative as T increases; feasible at high temperatures only.

ΔH 为负，ΔS 为正：ΔG 始终为负——所有温度下均可行。

ΔH 为正，ΔS 为负：ΔG 始终为正——任何温度下均不可行。

ΔH 为负，ΔS 为负：随 T 增大，ΔG 负值减小；仅低温下可行。

ΔH 为正，ΔS 为正：随 T 增大，ΔG 负值增大；仅高温下可行。

The temperature at which a reaction becomes feasible can be found by setting ΔG = 0:

T = ΔH / ΔS

9. Worked Example: Decomposition of Calcium Carbonate | 例题：碳酸钙的分解

For the reaction CaCO₃(s) → CaO(s) + CO₂(g), given ΔH° = +178 kJ mol⁻¹ and ΔS° = +160 J K⁻¹ mol⁻¹. Determine the minimum temperature at which this reaction becomes feasible.

对于反应 CaCO₃(s) → CaO(s) + CO₂(g)，已知 ΔH° = +178 kJ mol⁻¹，ΔS° = +160 J K⁻¹ mol⁻¹。求该反应变得可行的最低温度。

Convert ΔH to joules: ΔH = 178 × 1000 = 178,000 J mol⁻¹. Set ΔG = 0:

T = 178,000 / 160 = 1112.5 K

So the decomposition becomes feasible above approximately 1113 K (840 °C).

因此，该分解在约 1113 K（840 °C）以上变得可行。

10. Limitations of ΔG Predictions | ΔG 预测的局限性

While ΔG tells us whether a reaction is thermodynamically feasible, it says nothing about the rate of the reaction. A reaction with negative ΔG may proceed extremely slowly if it has a high activation energy.

虽然 ΔG 告诉我们反应在热力学上是否可行，但它不涉及反应速率。ΔG 为负的反应如果活化能很高，可能进行得非常缓慢。

For example, the combustion of diamond to form carbon dioxide has a negative ΔG at room temperature, yet diamonds do not burn visibly at 25 °C because the reaction rate is negligible. Kinetics, not thermodynamics, controls the speed.

例如，金刚石燃烧生成二氧化碳在室温下 ΔG 为负，但在 25 °C 时金刚石不会明显燃烧，因为反应速率可忽略。控制速率的是动力学，而非热力学。

Also, ΔG values assume standard conditions and complete conversion; real systems may reach equilibrium before full reaction, and side reactions can occur.

此外，ΔG 值假设标准条件和完全转化；实际系统可能在完全反应之前就达到平衡，并且可能发生副反应。

11. Application: Thermal Stability of Group 2 Carbonates | 应用：第二主族碳酸盐的热稳定性

The trend in thermal stability of Group 2 carbonates can be understood using thermodynamics. As you go down the group, the carbonate ion (CO₃²⁻) becomes less polarised by the larger, less polarising cation (e.g., Ba²⁺ vs Mg²⁺).

第二主族碳酸盐的热稳定性趋势可以用热力学来理解。从同族上到下，较大的、极化能力较弱的阳离子（如 Ba²⁺ 对比 Mg²⁺）使碳酸根离子（CO₃²⁻）极化程度降低。

The decomposition reaction MCO₃(s) → MO(s) + CO₂(g) is endothermic. The lattice enthalpy of the oxide (MO) becomes less exothermic down the group, but the difference between oxide and carbonate lattice enthalpies increases, making the overall ΔH more endothermic. Consequently, heavier carbonates require higher temperatures to decompose.

分解反应 MCO₃(s) → MO(s) + CO₂(g) 是吸热的。氧化物（MO）的晶格焓沿同族向下变得不那么放热，但氧化物与碳酸盐晶格焓之差增大，使得总 ΔH 更吸热。因此，较重的碳酸盐需要更高的温度才能分解。

This is why MgCO₃ decomposes easily on heating, while BaCO₃ requires very high temperatures.

这就是为什么 MgCO₃ 加热时容易分解，而 BaCO₃ 需要很高的温度。

12. Summary and Exam Tips | 总结与考试技巧

Thermodynamics links energy, disorder, and feasibility. Always check units (kJ vs J), use correct stoichiometric coefficients in entropy and enthalpy calculations, and remember that a negative ΔG indicates feasibility but not speed.

热力学将能量、无序和可行性联系起来。始终检查单位（kJ 与 J），在熵和焓计算中使用正确的化学计量系数，并记住 ΔG 为负表示可行但不表示速度快。

For AQA exam questions, practice drawing Born-Haber cycles and Hess cycles with correct arrows, label each step clearly, and show all calculations step by step. When asked about feasibility, quote the equation ΔG = ΔH − TΔS and explain how temperature affects the sign of ΔG.

针对 AQA 考试题目，练习绘制玻恩-哈伯循环和赫斯循环，箭头方向正确，清晰标注每一步，并逐步展示所有计算。当被问及可行性时，引用方程 ΔG = ΔH − TΔS，并解释温度如何影响 ΔG 的符号。

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Thermodynamics | 热力学