Enthalpy Changes in Solution | 溶解焓变

📚 Enthalpy Changes in Solution | 溶解焓变

When an ionic solid dissolves in water, the ordered crystal lattice is dismantled and individual ions are released into solution, where they become surrounded by water molecules. This physical change is accompanied by an energy transfer that we quantify as the enthalpy change of solution. Understanding the balance between the energy required to break the lattice and the energy released during ion hydration is central to predicting solubility trends and thermal effects observed when salts dissolve.

当离子固体溶解在水中时，有序的晶格结构会被拆散，单个离子释放到溶液中并被水分子包围。这个物理变化伴随着能量转移，我们用量热法测定的溶解焓变来量化这一过程。理解拆散晶格所需的能量与离子水合释放的能量之间的平衡，是预测盐类溶解的热效应和溶解度趋势的核心。

1. Introduction to Dissolution Energetics | 溶解过程能量学简介

Dissolving an ionic compound involves two main energetic steps: the endothermic separation of ions from the giant lattice and the exothermic hydration of the separated ions by solvent molecules. The net enthalpy change is the sum of these contributions and determines whether the overall process feels hot or cold to the touch.

离子化合物的溶解涉及两个主要能量步骤：从巨型晶格中分离离子需要吸热，以及溶剂分子对分离后离子的水合过程释放能量。净焓变是这两部分贡献的总和，决定了整个溶解过程在宏观上是放热升温还是吸热降温。

A dilute solution is assumed to be infinitely dilute so that ion–ion interactions are negligible; the measured enthalpy change then corresponds to the standard enthalpy change of solution, ΔH°(sol). This value is quoted for one mole of solute in its standard state at 298 K and 100 kPa.

通常假设溶液为无限稀释，使得离子间相互作用可以忽略不计；此时测得的焓变对应于标准溶解焓变 ΔH°(sol)。该数值是指在 298 K 和 100 kPa 下，一摩尔溶质在其标准状态下的溶解焓变。

2. Defining Standard Enthalpy Change of Solution | 定义标准溶解焓变

The standard enthalpy change of solution, ΔH°(sol), is the enthalpy change when one mole of a substance dissolves in a large excess of solvent to form an infinitely dilute solution under standard conditions. For ionic solids, the equation is typically written as MX(s) + aq → M⁺(aq) + X⁻(aq).

标准溶解焓变 ΔH°(sol) 是指在标准条件下，一摩尔物质溶解在大量溶剂中、形成无限稀释溶液时的焓变。对于离子固体，通常表示为 MX(s) + aq → M⁺(aq) + X⁻(aq)。

The symbol ‘aq’ denotes that the ions are solvated, and the term ‘infinitely dilute’ means adding more solvent causes no further enthalpy change. ΔH°(sol) can be exothermic (negative) or endothermic (positive), depending on the relative magnitudes of lattice and hydration enthalpies.

符号‘aq’表示离子被溶剂化，‘无限稀释’意味着继续加入溶剂也不会引起进一步的焓变。ΔH°(sol) 可以是放热的（负值）或吸热的（正值），取决于晶格焓和水合焓的相对大小。

3. Lattice Enthalpy and Its Role | 晶格焓及其作用

Lattice enthalpy, ΔH°(latt), is the enthalpy change when one mole of an ionic solid is formed from its gaseous ions. It is always negative (exothermic) because strong electrostatic attractions release energy as the lattice is built. For NaCl, ΔH°(latt) ≈ −787 kJ mol⁻¹.

晶格焓 ΔH°(latt) 是指从气态离子生成一摩尔离子固体时的焓变。由于晶格形成过程中强静电吸引力释放能量，该值总是负值（放热）。以 NaCl 为例，ΔH°(latt) ≈ −787 kJ mol⁻¹。

To dissolve the solid, the reverse process must occur first: the lattice must be broken into free gaseous ions. The enthalpy input for this dissociation is the negative of lattice enthalpy, i.e. −ΔH°(latt), which is positive and numerically equal to the lattice energy required to overcome the ionic bonding.

要实现溶解，首先必须发生逆过程：将晶格拆散成游离的气态离子。破坏晶格所需的能量输入是晶格焓的相反数，即 −ΔH°(latt)，为正值，数值上等于克服离子键所需的晶格能。

The magnitude of ΔH°(latt) depends on ionic charge and ionic radius. Greater charges and smaller radii produce more exothermic lattice enthalpies, making the dissociation step more endothermic and harder to overcome.

ΔH°(latt) 的大小取决于离子电荷和离子半径。电荷越大、半径越小，晶格焓越负（放热越多），导致解离步骤吸热更多，更难打破晶格。

4. Enthalpy Change of Hydration | 水合焓变

The standard enthalpy change of hydration, ΔH°(hyd), is the enthalpy change when one mole of gaseous ions dissolves in water to form an infinitely dilute aqueous solution. Hydration enthalpies are always negative because ion–dipole interactions between the ion and water molecules release energy.

标准水合焓变 ΔH°(hyd) 是指一摩尔气态离子溶于水、形成无限稀释溶液时的焓变。水合焓总是负值，因为离子与水分子之间的离子-偶极作用会释放能量。

For example, ΔH°(hyd) for Na⁺ is about −406 kJ mol⁻¹ and for Cl⁻ is about −363 kJ mol⁻¹. The sum of the individual hydration enthalpies of the cation and anion gives the total hydration enthalpy for the salt.

例如，Na⁺ 的水合焓约为 −406 kJ mol⁻¹，Cl⁻ 的约为 −363 kJ mol⁻¹。阳离子和阴离子各自的水合焓之和即为该盐的总水合焓。

The more highly charged and the smaller the ion, the stronger the attraction for water molecules, leading to a more exothermic ΔH°(hyd). Thus, Al³⁺ has a much more negative hydration enthalpy than Na⁺.

离子电荷越高、半径越小，对水分子的吸引力就越强，导致 ΔH°(hyd) 更负（放热更多）。因此，Al³⁺ 的水合焓比 Na⁺ 负得多。

5. The Energy Cycle: ΔH°(sol) = −ΔH°(latt) + ΣΔH°(hyd) | 能量循环公式

The overall enthalpy change for dissolution is the sum of two steps: breaking the lattice (endothermic) and hydrating the ions (exothermic). Because lattice enthalpy is defined for formation, the bond-breaking step equals −ΔH°(latt). Therefore, ΔH°(sol) = −ΔH°(latt) + ΣΔH°(hyd).

溶解过程的净焓变是两步之和：拆散晶格（吸热）和离子水合（放热）。由于晶格焓是形成晶格时的焓变，断键步骤的能量等于 −ΔH°(latt)。因此，ΔH°(sol) = −ΔH°(latt) + ΣΔH°(hyd)。

If the hydration enthalpy released is larger in magnitude than the lattice dissociation energy required, ΔH°(sol) will be negative and the dissolution is exothermic. Conversely, if more energy is absorbed to break the lattice than is released upon hydration, ΔH°(sol) is positive and the process is endothermic.

如果水合焓放出的热量大于拆散晶格所需的能量，ΔH°(sol) 为负值，溶解过程放热。反之，如果拆散晶格吸收的能量多于水合释放的能量，ΔH°(sol) 为正值，溶解过程吸热。

6. Constructing Solution Born-Haber Cycles | 构建溶解过程的玻恩-哈伯循环

A Born-Haber cycle for solution is an energy level diagram that links the solid salt to the aqueous ions via the gaseous ions. The top of the diagram is the gaseous ions, with the solid lattice at a lower energy and the hydrated ions at the bottom if the overall process is exothermic.

溶解过程的玻恩-哈伯循环是一个能量级图，通过气态离子将固态盐与溶液中的水合离子联系起来。图中气态离子位于高处，固态晶格位于较低能量位置，如果总过程放热，水合离子位于最底部。

The cycle follows: Ionic solid → gaseous ions (energy input = −ΔH°(latt)); then gaseous ions → aqueous ions (energy output = ΣΔH°(hyd)). The enthalpy change directly from solid to solution is ΔH°(sol), and Hess’s law gives the relationship above.

循环路径为：离子固体 → 气态离子（能量输入 = −ΔH°(latt)）；然后气态离子 → 水合离子（能量输出 = ΣΔH°(hyd)）。直接从固体到溶液的能量变化是 ΔH°(sol)，通过赫斯定律可得出上述关系式。

In an examination, you may be given two of the three enthalpy values and asked to calculate the third, or you may need to construct the cycle to check the consistency of experimental data.

在考试中，你可能会被给定三个焓值中的两个，要求计算第三个，或者需要构建该循环来验证实验数据的一致性。

7. Worked Calculation: Dissolving NaCl | 计算示例：氯化钠溶解

Consider sodium chloride: ΔH°(latt) = −787 kJ mol⁻¹, ΔH°(hyd)(Na⁺) = −406 kJ mol⁻¹, ΔH°(hyd)(Cl⁻) = −363 kJ mol⁻¹. The expected ΔH°(sol) is therefore: −(−787) + (−406 −363) = 787 − 769 = +18 kJ mol⁻¹.

以氯化钠为例：ΔH°(latt) = −787 kJ mol⁻¹，ΔH°(hyd)(Na⁺) = −406 kJ mol⁻¹，ΔH°(hyd)(Cl⁻) = −363 kJ mol⁻¹。预期 ΔH°(sol) = −(−787) + (−406 −363) = 787 − 769 = +18 kJ mol⁻¹。

The small positive value indicates that the dissolution of NaCl is slightly endothermic, which matches the observation that adding salt to water causes hardly any noticeable temperature change. The values used here are typical data from A-level chemistry specifications.

小幅正值表明 NaCl 的溶解略为吸热，这与食盐溶于水几乎观察不到温度变化的实际现象一致。这里所用数值是 A-Level 化学大纲中的典型数据。

For MgCl₂, the lattice enthalpy is much more negative (around −2526 kJ mol⁻¹) but the sum of hydration enthalpies for Mg²⁺ and two Cl⁻ ions is also very large (around −1920 + 2×(−363) = −2646 kJ mol⁻¹). This can result in an exothermic ΔH°(sol) near −120 kJ mol⁻¹.

对于 MgCl₂，晶格焓更负（约 −2526 kJ mol⁻¹），但 Mg²⁺ 和两个 Cl⁻ 的水合焓之和也非常大（约 −1920 + 2×(−363) = −2646 kJ mol⁻¹），这使得 ΔH°(sol) 为负值，约 −120 kJ mol⁻¹，溶解过程放热。

8. Factors Affecting Lattice and Hydration Enthalpies | 影响晶格焓和水合焓的因素

Both lattice and hydration enthalpies become more exothermic as the ionic charge increases and the ionic radius decreases. For lattice enthalpy, the electrostatic attraction is proportional to (q⁺ × q⁻) / (r⁺ + r⁻), while for hydration, the ion–dipole strength depends on charge density (charge/radius).

随着离子电荷增加、半径减小，晶格焓和水合焓都变得更负。晶格焓中的静电引力与 (q⁺ × q⁻) / (r⁺ + r⁻) 成正比，而水合焓中离子-偶极作用的强弱取决于电荷密度（电荷/半径）。

However, the difference between the two trends determines the solubility pattern. For small, highly charged ions, both lattice dissociation and hydration involve large energy magnitudes; the net ΔH°(sol) can be positive, zero or negative. This is why many sulfates and carbonates show differing solubilities down a group.

然而，两种趋势之间的差异决定了溶解性规律。对于半径小、电荷高的离子，晶格解离和水合都涉及很大的能量幅度；净 ΔH°(sol) 可以是正值、零或负值。这就是为什么许多硫酸盐和碳酸盐在同族中的溶解度变化不同。

A useful comparison is between group 2 hydroxides: the lattice enthalpy becomes less exothermic down the group (larger cation radius) while the hydration enthalpy also becomes less exothermic, but the change in hydration dominates, leading to an increase in solubility although ΔH°(sol) becomes more positive — solubility does not depend on enthalpy alone.

一个有用的对比是第 2 族氢氧化物：随着阳离子半径增大，晶格焓的放热程度减弱，水合焓放热也减弱，但水合焓的变化起主导作用，导致溶解度增加，尽管 ΔH°(sol) 变得更正——溶解度并不只取决于焓变。

9. Exothermic and Endothermic Dissolution | 放热与吸热溶解实例

Common laboratory examples illustrate the two cases. Dissolving anhydrous calcium chloride is strongly exothermic: the hydration enthalpy of Ca²⁺ and Cl⁻ releases more energy than is needed to break the CaCl₂ lattice, and the test tube becomes noticeably hot.

常见的实验室实例可以说明这两种情况。无水氯化钙的溶解是强放热的：Ca²⁺ 和 Cl⁻ 的水合焓释放的能量多于拆散 CaCl₂ 晶格所需的能量，试管明显变热。

In contrast, dissolving ammonium nitrate is endothermic: NH₄NO₃(s) → NH₄⁺(aq) + NO₃⁻(aq) has a positive ΔH°(sol). The container feels cold because the hydration energy is insufficient to compensate for the lattice breakage, and the dissolving mixture takes in heat from the surroundings.

相比之下，硝酸铵的溶解是吸热的：NH₄NO₃(s) → NH₄⁺(aq) + NO₃⁻(aq) 的 ΔH°(sol) 为正值。容器会变冷，因为水合能不足以补偿晶格的破坏，溶解混合物从周围环境吸收热量。

Yet both salts dissolve spontaneously. This tells us that entropy changes are also crucial in determining whether a solid will dissolve.

然而，这两种盐都能自发溶解。这说明熵变在决定固体能否溶解方面同样至关重要。

10. Enthalpy versus Entropy: Why Some Solids Dissolve Endothermically | 焓与熵：为何某些固体吸热溶解

The thermodynamic feasibility of dissolution is determined by the Gibbs free energy change: ΔG° = ΔH° − TΔS°. For an endothermic dissolution to be spontaneous at room temperature, the entropy change ΔS° must be positive and large enough to make TΔS° > ΔH°.

溶解过程的热力学可行性由吉布斯自由能变决定：ΔG° = ΔH° − TΔS°。要使吸热溶解在室温下自发进行，熵变 ΔS° 必须为正值且足够大，使得 TΔS° > ΔH°。

When an ionic lattice dissolves, the highly ordered solid is replaced by freely moving aqueous ions, causing a significant increase in disorder. This positive ΔS° helps drive dissolution even when ΔH° is positive, as seen with NH₄NO₃. As temperature increases, the TΔS° term becomes larger and endothermic dissolutions become more favoured.

当离子晶格溶解时，高度

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Enthalpy Changes in Solution | 溶解焓变