Lattice Energy and Born-Haber Cycles | 晶格能与玻恩-哈伯循环

📚 Lattice Energy and Born-Haber Cycles | 晶格能与玻恩-哈伯循环

In Edexcel A Level Chemistry Topic 13.1, lattice energy and Born-Haber cycles pull together many earlier enthalpy ideas: ionisation energy, electron affinity, atomisation and enthalpy of formation. This topic is highly numerical and definition-heavy, so examiners reward precise language and a clear sign convention.

在 Edexcel A Level 化学 13.1 中，晶格能和玻恩-哈伯循环将之前学过的许多焓变概念——电离能、电子亲和能、原子化焓和生成焓——整合在一起。本节高度量化、定义密集，考官尤其看重准确表述和清晰的符号约定。

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1. Defining Lattice Energy | 晶格能的定义

Lattice energy is the enthalpy change when one mole of an ionic solid is formed from its gaseous ions under standard conditions. The ions are initially separated and in the gas phase, so lattice energy measures the strength of the ionic bonding in the solid lattice.

晶格能是在标准条件下，由气态离子生成 1 mol 离子固体时的焓变。离子最初彼此分离并处于气相，因此晶格能衡量离子固体中离子键的强度。

Na⁺(g) + Cl⁻(g) → NaCl(s) ΔH°lattice is negative

Because the ionic lattice is much more stable than free gaseous ions, energy is released when the lattice forms. Lattice energy is therefore always exothermic, so ΔH°lattice is always negative.

由于离子晶格远比自由气态离子稳定，晶格形成时会释放能量。因此晶格能总是放热的，所以 ΔH°lattice 总是负值。

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2. Standard Conditions and Sign Convention | 标准条件与符号约定

Standard conditions mean 298 K, 100 kPa and all substances in their standard states. In lattice energy questions, the gaseous ion states are always specified, so you do not need to assume states for the ions.

标准条件指 298 K、100 kPa，且所有物质处于标准状态。在晶格能题目中，气态离子状态总会明确给出，因此无需自行假设离子的状态。

A negative lattice energy means the process is exothermic. A common mistake is to reverse the sign or to use the process NaCl(s) → Na⁺(g) + Cl⁻(g), which is the lattice dissociation process and is endothermic.

晶格能为负值表示该过程放热。常见错误是颠倒符号，或误用 NaCl(s) → Na⁺(g) + Cl⁻(g) 这一相反过程，后者是晶格解离过程，为吸热。

Lattice dissociation enthalpy is the enthalpy change when one mole of an ionic solid is broken apart into its gaseous ions. It has the same magnitude as lattice energy but the opposite sign, so it is always positive.

晶格解离焓是 1 mol 离子固体解离为气态离子时的焓变。它与晶格能大小相同但符号相反，因此总为正值。

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3. Born-Haber Cycle: An Energy Ledger | 玻恩-哈伯循环：能量账本

A Born-Haber cycle is an application of Hess’s Law. It shows two routes from elements in their standard states to an ionic lattice: one direct route via enthalpy of formation, and one indirect route via atomisation, ionisation, electron affinity and lattice energy.

玻恩-哈伯循环是赫斯定律的应用。它展示了从标准状态元素到离子晶格的两条路径：一条通过生成焓的直接路径，另一条通过原子化、电离、电子亲和和晶格能的间接路径。

The sum of enthalpy changes around any complete cycle is zero, or equivalently the direct route equals the sum of the indirect steps. This allows you to calculate an unknown enthalpy change if all other values are known.

完整循环中所有焓变之和为零，或者说直接路径等于各间接步骤之和。只要已知其他数值，就可以计算未知的焓变。

Drawing a clear cycle with state symbols on every species is the most reliable way to avoid sign errors and missing steps.

画出清晰的循环，并在每种物质上标注状态符号，是避免符号错误和遗漏步骤的最可靠方法。

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4. Enthalpy of Formation | 生成焓

Enthalpy of formation is the enthalpy change when one mole of a compound is formed from its elements in their standard states under standard conditions. For sodium chloride, this is the direct route in the Born-Haber cycle.

生成焓是在标准条件下，由标准状态元素生成 1 mol 化合物时的焓变。对于氯化钠，这是玻恩-哈伯循环中的直接路径。

Na(s) + ½Cl₂(g) → NaCl(s) ΔH°f = -411 kJ mol⁻¹

The negative value shows that forming NaCl from its elements is exothermic. In calculations, ΔH°f is often the value you use to anchor the whole cycle.

负值说明由元素生成 NaCl 是放热过程。在计算中，ΔH°f 通常是用于锚定整个循环的数值。

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5. Enthalpy of Atomisation | 原子化焓

Enthalpy of atomisation is the enthalpy change when one mole of gaseous atoms is formed from the element in its standard state. For metals such as sodium, this is simply sublimation of the solid metal.

原子化焓是由标准状态元素生成 1 mol 气态原子时的焓变。对于钠等金属，这实际上就是固态金属的升华。

Na(s) → Na(g) ΔH°at = +107 kJ mol⁻¹

For diatomic non-metals such as chlorine, atomisation enthalpy is half the bond dissociation enthalpy because only one mole of gaseous atoms is produced from the standard state molecule.

对于氯等双原子非金属，原子化焓是键解离焓的一半，因为从标准状态分子只生成 1 mol 气态原子。

½Cl₂(g) → Cl(g) ΔH°at = +122 kJ mol⁻¹

Atomisation is always endothermic because bonds or intermolecular forces must be overcome to form separate gaseous atoms.

原子化总是吸热的，因为必须克服化学键或分子间作用力才能形成分离的气态原子。

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6. Ionisation Energy and Electron Affinity |

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