📚 Energy Cycles and Hess’s Law | 能量循环与赫斯定律
Thermochemistry is the study of energy changes that accompany chemical reactions and physical transformations. A key concept is enthalpy (H), which describes the heat content of a system at constant pressure. Chemists use ΔH to represent the change in enthalpy, and they often rely on indirect methods to determine these values when direct measurement is impossible or difficult.
热化学研究伴随化学反应和物理转变的能量变化。其核心概念是焓（H），它描述恒压条件下系统的热量含量。化学家用ΔH表示焓变，并且在无法或难以直接测量时，常常依赖间接方法来确定这些数值。
1. Enthalpy and Energy Changes | 焓与能量变化
In any chemical reaction, energy is either released to the surroundings (exothermic, ΔH < 0) or absorbed from the surroundings (endothermic, ΔH > 0). For example, the combustion of methane is exothermic, while the thermal decomposition of calcium carbonate is endothermic.
在任何化学反应中，能量要么释放到环境（放热，ΔH < 0），要么从环境吸收（吸热，ΔH > 0）。例如，甲烷燃烧是放热的，而碳酸钙热分解是吸热的。
Enthalpy is a state function, meaning its value depends only on the current state of the system, not on the path taken. This property forms the basis of Hess’s law and allows chemists to calculate enthalpy changes using algebraic combinations of known reactions.
焓是状态函数，这意味着它的值只取决于系统的当前状态，而不取决于所经历的路径。这一性质构成了赫斯定律的基础，也使化学家能够通过已知反应的代数组合来计算焓变。
2. What is Hess’s Law? | 什么是赫斯定律？
Hess’s law states that the total enthalpy change for a reaction is the same regardless of the number of steps or the specific reaction pathway, provided the initial and final conditions are identical. In other words, enthalpy change depends only on the initial and final states of the system.
赫斯定律指出，只要初始和最终条件相同，反应的总焓变与反应的步骤数量或具体路径无关。换句话说，焓变只取决于系统的初始状态和最终状态。
Mathematically, if a reaction can be expressed as the sum of two or more reactions, then the overall enthalpy change is the sum of the individual enthalpy changes:
用数学表达，如果一个反应可以表示为两个或多个反应之和，则总焓变等于各个焓变之和：
ΔHreaction = ΔH₁ + ΔH₂ + ΔH₃ + …
3. Constructing Energy Cycles | 构建能量循环
An energy cycle is a diagram that shows the relationship between the reactants and products through alternative pathways. One common form is a triangle where the direct reaction and an indirect route through an intermediate compound both connect the same initial and final states. According to Hess’s law, the enthalpy change along each path is identical.
能量循环是一种通过替代路径展示反应物与产物关系的示意图。常见形式是三角形，其中直接反应和经由中间化合物的间接路线连接相同的初始状态和最终状态。根据赫斯定律，每条路径上的焓变是相同的。
Consider the formation of carbon monoxide from carbon and oxygen:
考虑由碳和氧气生成一氧化碳的过程：
C(s) + ½O₂(g) → CO(g) ΔHr = ?
This reaction is difficult to measure directly because CO₂ also forms. Instead, we can measure the combustion of carbon and the combustion of CO:
该反应难以直接测量，因为同时也会生成CO₂。然而，我们可以测量碳的燃烧和CO的燃烧：
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C(s) + O₂(g) → CO₂(g) ΔH₁ = −393.5 kJ/mol
C(s) + O₂(g) → CO₂(g) ΔH₁ = −393.5 kJ/mol
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CO(g) + ½O₂(g) → CO₂(g) ΔH₂ = −283.0 kJ/mol
CO(g) + ½O₂(g) → CO₂(g) ΔH₂ = −283.0 kJ/mol
Using Hess’s law, the target reaction is obtained by reversing the second reaction and adding it to the first:
利用赫斯定律，将第二个反应逆向并与第一个反应相加，即可得到目标反应：
ΔHr = ΔH₁ − ΔH₂ = −393.5 − (−283.0) = −110.5 kJ/mol
4. Standard Enthalpy Changes | 标准焓变
Standard enthalpy changes are defined under standard conditions: 100 kPa pressure, a specified temperature (usually 298 K), and all substances in their standard states. Two important types are standard enthalpy of formation and standard enthalpy of combustion.
标准焓变是在标准条件下定义的：压力100 kPa，特定温度（通常为298 K），所有物质处于其标准状态。两种重要的类型是标准生成焓和标准燃烧焓。
The standard enthalpy of formation, ΔHf°, is the enthalpy change when one mole of a compound is formed from its elements in their standard states. The standard enthalpy of combustion, ΔHc°, is the enthalpy change when one mole of a substance is completely burned in oxygen under standard conditions.
标准生成焓ΔHf°是指一摩尔化合物从其标准状态下的元素形成时的焓变。标准燃烧焓ΔHc°是指一摩尔物质在标准条件下于氧气中完全燃烧时的焓变。
For a general reaction aA + bB → cC + dD, using standard enthalpies of formation, the reaction enthalpy is:
对于一般反应 aA + bB → cC + dD，使用标准生成焓，反应焓为：
ΔHr° = ΣΔHf°(products) − ΣΔHf°(reactants)
5. Using Formation Enthalpies | 利用生成焓计算反应焓
Standard enthalpies of formation are widely used because they allow direct calculation of reaction enthalpies from tabulated data. Consider the hydrogenation of ethene:
标准生成焓被广泛使用，因为它们允许通过表格数据直接计算反应焓。以乙烯加氢为例：
C₂H₄(g) + H₂(g) → C₂H₆(g)
| Substance | ΔHf° (kJ/mol) |
| C₂H₄(g) | +52.3 |
| H₂(g) | 0 |
| C₂H₆(g) | −84.7 |
Applying the formula:
代入公式：
ΔHr° = (−84.7) − [(+52.3) + 0] = −137.0 kJ/mol
The negative value indicates that hydrogenation is exothermic, which is consistent with the fact that double bonds are less stable than the corresponding single-bond framework.
负值表明加氢反应是放热的，这与双键比相应单键框架稳定性更低的事实一致。
6. Using Combustion Enthalpies | 利用燃烧焓计算反应焓
When formation enthalpy data are not available, combustion enthalpies provide an alternative route. For a reaction that does not involve oxygen, the standard enthalpy change can be obtained from the difference between the combustion enthalpies of the reactants and products:
当无法获得生成焓数据时，燃烧焓提供了另一条途径。对于不含氧的反应，标准焓变可以通过反应物与产物燃烧焓之差获得：
ΔHr° = ΣΔHc°(reactants) − ΣΔHc°(products)
Why the sign is reversed: combusting the reactants releases a certain amount of heat, and combusting the products releases another. Because both combustion processes go to the same fully oxidised products (CO₂ and H₂O), the difference gives the reaction enthalpy.
为什么会反转符号：反应物燃烧释放一定热量，产物燃烧释放另一热量。由于两个燃烧过程都生成完全氧化的产物（CO₂和H₂O），其差值即为反应焓。
Using the same hydrogenation reaction, with ΔHc°(C₂H₄) = −1411 kJ/mol, ΔHc°(H₂) = −286 kJ/mol, ΔHc°(C₂H₆) = −1560 kJ/mol:
使用相同的加氢反应，已知ΔHc°(C₂H₄) = −1411 kJ/mol，ΔHc°(H₂) = −286 kJ/mol，ΔHc°(C₂H₆) = −1560 kJ/mol：
ΔHr° = (−1411) + (−286) − (−1560) = −137 kJ/mol
This agrees with the result obtained from formation enthalpies, demonstrating the power of Hess’s law.
这一结果与由生成焓所得一致，充分体现了赫斯定律的威力。
7. Bond Enthalpies | 键焓与键能
Bond enthalpy (or bond dissociation energy) is the energy required to break one mole of a particular covalent bond in the gaseous state. Average bond enthalpies are tabulated from many compounds and can be used to estimate reaction enthalpies for gaseous reactions.
键焓（或称键解离能）是使一摩尔特定共价键在气态下断裂所需的能量。平均键焓由多种化合物汇总而得，可用于估算气相反应的焓变。
For a reaction, the approximate enthalpy change is the sum of bond enthalpies of bonds broken in the reactants minus the sum of bond enthalpies of bonds formed in the products:
对于某个反应，近似焓变等于反应物中断裂键的键焓之和减去产物中形成键的键焓之和：
ΔH ≈ ΣBE(bonds broken) − ΣBE(bonds formed)
For example, in the reaction H₂(g) + Cl₂(g) → 2HCl(g):
例如，在反应 H₂(g) + Cl₂(g) → 2HCl(g) 中：
ΔH = (BEH–H + BECl–Cl) − 2(BEH–Cl) = (436 + 243) − 2(432) = −185 kJ/mol
This is a reasonable estimate; actual experimental values may differ slightly because average bond enthalpies are not exact for every molecular environment.
这是一个合理的估算；实际实验值可能略有差异，因为平均键焓并非对每个分子环境都完全精确。
8. Limitations of Mean Bond Enthalpies | 平均键焓的局限
Mean bond enthalpies are average values obtained from a range of compounds, so they are not exact for a specific molecule. The bond energy in a particular compound depends on the surrounding atoms, electron density, and molecular geometry.
平均键焓是从一系列化合物中获得的平均值，因此对于特定分子并不精确。特定化合物中的键能取决于周围的原子、电子云密度和分子几何构型。
Another limitation is that bond enthalpy calculations assume all species are in the gas phase. If a reaction involves liquids or solids, additional enthalpy changes such as vaporisation, fusion, or sublimation must be included. Therefore, bond enthalpies are best used for simple gaseous molecules and only provide approximate values.
另一个局限性在于键焓计算假设所有物质均处于气相。如果反应涉及液体或固体，则必须包括汽化、熔化或升华等额外焓变。因此，键焓最适合用于简单气体分子，且仅能提供近似值。
9. Hess’s Law in Practice: Measuring Difficult Reactions | 赫斯定律的实际应用：测定困难反应
Many reactions cannot be measured directly in a calorimeter. For example, the formation of carbon monoxide from carbon and oxygen is complicated by the simultaneous formation of carbon dioxide. Hess’s law allows us to determine this enthalpy change indirectly.
许多反应无法在量热计中直接测量。例如，由碳和氧气生成一氧化碳的过程因同时生成二氧化碳而变得复杂。赫斯定律使我们能够间接确定这一焓变。
Similarly, the enthalpy change of formation of a compound that is unstable such as ethyne can be calculated using combustion data of the elements and the compound. This approach is standard in IB Chemistry data-based questions.
类似地，对于像乙炔这样不稳定的化合物，其生成焓可以使用元素和该化合物的燃烧数据计算。这是IB化学数据分析题中的常见方法。
In practice, students should draw a clear energy cycle, label the known enthalpies, assign signs carefully (reverse a reaction changes the sign of ΔH), and then sum the values algebraically.
在实际操作中，学生应当画出清晰的能量循环，标出已知焓变，仔细确定符号（逆转反应需要改变ΔH的符号），然后进行代数求和。
10. Born–Haber Cycles (HL) | 玻恩-哈伯循环（HL）
For ionic compounds, a special type of energy cycle called a Born–Haber cycle is used to calculate lattice enthalpy, which cannot be measured directly. This cycle combines several enthalpy changes: formation, atomisation, ionisation energy, electron affinity, and lattice enthalpy.
对于离子化合物，一种特殊类型的能量循环被称为玻恩-哈伯循环，用于计算无法直接测量的晶格焓。该循环结合了多种焓变：生成焓、原子化焓、电离能、电子亲和能和晶格焓。
Consider sodium chloride. The overall reaction is:
以氯化钠为例，总反应为：
Na(s) + ½Cl₂(g) → NaCl(s) ΔHf° = −411 kJ/mol
The alternative path involves:
替代路径包括：
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Atomisation of sodium: Na(s) → Na(g), ΔHat = +107.3 kJ/mol
钠的原子化：Na(s) → Na(g)，ΔHat = +107.3 kJ/mol
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Atomisation of chlorine: ½Cl₂(g) → Cl(g), ΔHat = +121.7 kJ/mol
氯的原子化：½Cl₂(g) → Cl(g)，ΔHat = +121.7 kJ/mol
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First ionisation energy of sodium: Na(g) → Na⁺(g) + e⁻, ΔHIE = +496 kJ/mol
钠的第一电离能：Na(g) → Na⁺(g) + e⁻，ΔHIE = +496 kJ/mol
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Electron affinity of chlorine: Cl(g) + e⁻ → Cl⁻(g), ΔHEA = −349 kJ/mol
氯的电子亲和能：Cl(g) + e⁻ → Cl⁻(g)，ΔHEA = −349 kJ/mol
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Lattice enthalpy: Na⁺(g) + Cl⁻(g) → NaCl(s), ΔHlattice = ?
晶格焓：Na⁺(g) + Cl⁻(g) → NaCl(s)，ΔHlattice = ?
By Hess’s law, the sum of all steps equals the formation enthalpy:Published by TutorHao | IB Chemistry Revision Series | aleveler.com
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