📚 Covalent Bonding Models | 共价键模型
Covalent bonding is one of the most fundamental concepts in chemistry, describing how atoms share electron pairs to achieve stability. This article explores the key models—from Lewis structures to molecular orbital theory—that IB Chemistry students must master for both SL and HL examinations.
共价键是化学中最基本的概念之一，描述了原子如何通过共用电子对达到稳定状态。本文深入探讨IB化学SL和HL考试中必须掌握的各类模型——从路易斯结构到分子轨道理论。
1. The Nature of Covalent Bonds | 共价键的本质
A covalent bond forms when two atoms share one or more pairs of valence electrons. Unlike ionic bonds which involve electron transfer, covalent bonding arises from the electrostatic attraction between the positively charged nuclei and the shared negatively charged electrons. This sharing allows each atom to attain a noble gas electron configuration.
当两个原子共享一对或多对价电子时，共价键便形成了。与涉及电子转移的离子键不同，共价键源于带正电的原子核与共享的带负电的电子之间的静电吸引力。这种共享使每个原子能够达到稀有气体的电子构型。
Key characteristics of covalent bonds include:
- Directionality: Covalent bonds are directional, leading to specific molecular geometries.
- Bond strength: Typically 150–400 kJ mol⁻¹, stronger than intermolecular forces but weaker than ionic bonds in most cases.
- Localised electrons: Valence electrons are concentrated between the bonded nuclei.
共价键的关键特征包括：
- 方向性：共价键具有方向性，决定了特定的分子几何构型。
- 键强度：通常在150–400 kJ mol⁻¹，强于分子间作用力，但在多数情况下弱于离子键。
- 电子局域化：价电子集中在成键原子核之间。
2. Lewis Structures | 路易斯结构
The Lewis model, developed by Gilbert N. Lewis in 1916, represents valence electrons as dots surrounding the element symbol. A covalent bond is depicted as a shared pair of electrons—either as two dots or a single line between atoms. Lone pairs are shown as unshared dots.
路易斯模型由吉尔伯特·路易斯于1916年提出，用元素符号周围的点表示价电子。共价键被描绘为共享电子对——既可以画成两个点，也可以用原子之间的一条短线表示。孤对电子则以未共享的点来显示。
To construct a Lewis structure, follow these steps:
构建路易斯结构的步骤如下：
- Count valence electrons — Sum the valence electrons of all atoms; add electrons for negative charges and subtract for positive charges.
- Identify the central atom — Usually the least electronegative element (except hydrogen).
- Connect atoms — Use single bonds initially, placing remaining electrons as lone pairs.
- Complete octets — Assign lone pairs to terminal atoms first, then the central atom.
- Form multiple bonds — If the central atom lacks an octet, convert lone pairs into double or triple bonds.
- 计算价电子总数——将所有原子的价电子相加；负电荷加电子，正电荷减电子。
- 确定中心原子——通常选择电负性最小的元素（氢除外）。
- 连接原子——先用单键连接，剩余电子作为孤对电子分配。
- 满足八隅体——先给端基原子分配孤对电子，再分配中心原子。
- 形成多重键——若中心原子不满足八隅体，将孤对电子转为双键或三键。
CO₂: O=C=O (each O has 2 lone pairs; 16 valence electrons total)
CO₂：O=C=O（每个O有2对孤对电子；总价电子数为16）
3. The Octet Rule and Its Exceptions | 八隅体规则及其例外
The octet rule states that atoms tend to achieve eight valence electrons in their outermost shell, resembling a noble gas configuration. However, several exceptions are essential for IB examinations:
八隅体规则指出原子倾向于在最外层达到八个价电子，类似于稀有气体的电子构型。然而，有几个IB考试中必须掌握的重要例外：
- Incomplete octets: Beryllium (BeCl₂, 4 e⁻), Boron (BF₃, 6 e⁻) — common in compounds of elements from Groups 2 and 13.
- Expanded octets: Phosphorus (PCl₅), Sulfur (SF₆) — elements in Period 3 and beyond can utilise d-orbitals to accommodate more than 8 electrons.
- Odd-electron molecules: NO and NO₂ — contain an unpaired electron, making them paramagnetic.
- 不完整八隅体：铍（BeCl₂，4个电子）、硼（BF₃，6个电子）——常见于第2族和第13族元素的化合物中。
- 扩张八隅体：磷（PCl₅）、硫（SF₆）——第三周期及以后的元素可利用d轨道容纳超过8个电子。
- 奇电子分子：NO和NO₂——含有一个未配对电子，具有顺磁性。
Expanded octets: The ns and np orbitals are filled first; the vacant nd orbitals are then used to accommodate additional bonding pairs. For example, in SF₆, sulfur forms six bonds using 3s, 3p, and two 3d orbitals.
扩张八隅体：ns和np轨道首先被填满；然后利用空的nd轨道容纳额外的成键电子对。例如，在SF₆中，硫利用3s、3p和两个3d轨道形成六个共价键。
4. VSEPR Theory | VSEPR理论（价层电子对互斥理论）
Valence Shell Electron Pair Repulsion (VSEPR) theory predicts molecular geometry by minimising the repulsion between electron pairs in the valence shell of a central atom. Both bonding pairs and lone pairs are considered — lone pairs repel more strongly than bonding pairs because they occupy more space.
价层电子对互斥理论（VSEPR，即Valence Shell Electron Pair Repulsion的缩写）通过最小化中心原子价层中电子对之间的排斥力来预测分子几何构型。成键电子对和孤对电子都要考虑——孤对电子的排斥力比成键电子对更强，因为它们占据更大的空间。
The repulsion order is: lone pair–lone pair > lone pair–bonding pair > bonding pair–bonding pair.
排斥力的大小顺序为：孤对电子–孤对电子 > 孤对电子–成键电子对 > 成键电子对–成键电子对。
| Electron domains 电子域数 |
Lone pairs 孤对电子数 |
Molecular shape 分子形状 |
Bond angle 键角 |
Example 实例 |
| 2 | 0 | Linear 直线形 | 180° | BeCl₂, CO₂ |
| 3 | 0 | Trigonal planar 平面三角形 |
120° | BF₃, SO₃ |
| 4 | 0 | Tetrahedral 正四面体 | 109.5° | CH₄, NH₄⁺ |
| 4 | 1 | Trigonal pyramidal 三角锥形 |
107° | NH₃ |
| 4 | 2 | Bent / V-shaped 角形 / V形 |
104.5° | H₂O |
| 5 | 0 | Trigonal bipyramidal 三角双锥形 |
90° / 120° | PCl₅ |
| 6 | 0 | Octahedral 八面体 | 90° | SF₆ |
It is crucial to distinguish between electron domain geometry (the arrangement of all electron pairs) and molecular geometry (the arrangement of atoms only). For example, NH₃ has tetrahedral electron domain geometry but trigonal pyramidal molecular geometry.
务必区分电子域几何（所有电子对的排列）和分子几何（仅原子的排列）。例如，NH₃的电子域几何为正四面体，但分子几何为三角锥形。
5. Hybridisation | 杂化轨道理论
Hybridisation explains how atomic orbitals mix to form new, equivalent hybrid orbitals that match observed molecular geometries. The number of hybrid orbitals equals the number of electron domains around the central atom.
杂化轨道理论解释了原子轨道如何混合形成新的、等价的杂化轨道，从而与观察到的分子几何构型相匹配。杂化轨道的数目等于中心原子周围的电子域数。
| Electron domains 电子域数 |
Hybridisation 杂化方式 |
Geometry 几何构型 |
Angle 键角 |
| 2 | sp | Linear 直线形 | 180° |
| 3 | sp² | Trigonal planar 平面三角形 | 120° |
| 4 | sp³ | Tetrahedral 正四面体 | 109.5° |
| 5 | sp³d | Trigonal bipyramidal 三角双锥形 | 90° / 120° |
| 6 | sp³d² | Octahedral 八面体 | 90° |
For example, the carbon atom in CH₄ is sp³ hybridised: one 2s orbital and three 2p orbitals mix to create four equivalent sp³ orbitals. Each orbital overlaps with a hydrogen 1s orbital, yielding four identical C–H σ bonds.
例如，CH₄中的碳原子为sp³杂化：一个2s轨道和三个2p轨道混合形成四个等价的sp³杂化轨道。每个轨道与氢的1s轨道重叠，形成四个完全相同的C–H σ键。
In ethene (C₂H₄), each carbon is sp² hybridised with one unhybridised p orbital used for the π bond. In ethyne (C₂H₂), each carbon is sp hybridised with two unhybridised p orbitals forming two π bonds.
在乙烯（C₂H₄）中，每个碳为sp²杂化，一个未杂化的p轨道用于形成π键。在乙炔（C₂H₂）中，每个碳为sp杂化，两个未杂化的p轨道形成两个π键。
6. Sigma (σ) and Pi (π) Bonds | σ键与π键
When atomic orbitals overlap head-on along the internuclear axis, a σ bond forms. When parallel p orbitals overlap laterally, a π bond forms. A single bond consists of one σ bond; a double bond has one σ and one π bond; a triple bond has one σ and two π bonds.
当原子轨道沿核间轴方向“头碰头”重叠时，形成σ键。当平行的p轨道从侧面“肩并肩”重叠时，形成π键。单键包含一个σ键；双键包含一个σ键和一个π键；三键包含一个σ键和两个π键。
| Property 性质 |
σ bond σ键 |
π bond π键 |
| Formation 形成方式 | Head-on overlap 头碰头重叠 | Sideways overlap 肩并肩重叠 |
| Electron density 电子密度 | Concentrated between nuclei 集中在核间 |
Above and below the bond axis 分布在键轴上下 |
| Free rotation 自由旋转 | Allowed 允许 | Restricted (breaks π bond) 受限（会破坏π键） |
| Strength 强度 | Stronger 较强 | Weaker 较弱 |
The presence of π bonds restricts rotation around the double bond, giving rise to cis-trans (geometric) isomerism in alkenes such as 2-butene.
π键的存在限制了双键周围的自由旋转，从而在诸如2-丁烯之类的烯烃中产生了顺反（几何）异构现象。
7. Bond Order, Bond Length, and Bond Energy | 键级、键长与键能
Bond order is the number of shared electron pairs between two atoms. Higher bond order corresponds to a shorter bond length and greater bond energy, because more shared electrons draw the nuclei closer and strengthen the bond.
键级是两个原子之间共享的电子对数。键级越高，键长越短，键能越大，因为更多的共享电子将原子核拉得更近并增强键的强度。
| Bond 键型 |
Bond order 键级 |
Bond length (pm) 键长（pm） |
Bond energy (kJ mol⁻¹) 键能（kJ mol⁻¹） |
| C–C | 1 | 154 | 347 |
| C=C | 2 | 134 | 614 |
| C≡C | 3 | 120 | 839 |
Note that the relationship is not linear — a double bond is not exactly twice as strong as a single bond. This is because a π bond is weaker than a σ bond due to less effective orbital overlap.
注意这种关系并非线性——双键的强度并非恰好是单键的两倍。这是因为π键的重叠效率较低，其强度弱于σ键。
8. Electronegativity and Bond Polarity | 电负性与键的极性
Electronegativity is the ability of an atom to attract shared electrons in a covalent bond. When two atoms with different electronegativities form a covalent bond, the electron density shifts toward the more electronegative atom, creating a polar covalent bond.
电负性是原子在共价键中吸引共享电子的能力。当电负性不同的两个原子形成共价键时，电子密度向电负性较大的原子偏移，从而形成极性共价键。
Electronegativity difference (Δχ) can be used to estimate bond type:
电负性差值（Δχ）可用于判断键的类型：
| Δχ 电负性差值 |
Bond type 键型 |
Example 实例 |
| 0 | Non-polar covalent 非极性共价键 | Cl–Cl, C–H |
| 0.1 – 1.7 | Polar covalent 极性共价键 | H–Cl, C–O |
| > 1.8 | Ionic (usually) 离子键（通常） | Na–Cl |
These thresholds are approximate — bond type exists on a continuum rather than as discrete categories.
这些界限只是近似值——键的类型实际上是一个连续谱，而非绝对的分类。
A molecule is polar if it has polar bonds and an asymmetric arrangement of bond dipoles. For example, CO₂ has two polar C=O bonds, but the linear geometry cancels the dipoles, making the molecule non-polar. Water, however, has a bent shape, so its bond dipoles do not cancel, resulting in a permanent dipole moment.
分子是否具有极性取决于两个条件：含有极性键且键偶极矩的排列不对称。例如，CO₂含有两个极性C=O键，但直线形几何使得偶极相互抵消，因此分子为非极性。然而，水的弯曲形状使键偶极无法抵消，从而产生永久偶极矩。
9. Resonance Structures | 共振结构
When a single Lewis structure cannot adequately represent a molecule, resonance structures are used. The true structure is a hybrid of all contributing resonance forms, with delocalised electrons spread across multiple atoms.
当单一路易斯结构无法充分表示一个分子时，需要使用共振结构。真实结构是所有共振形式的杂化体，电子离域分布在多个原子之间。
Classic examples include:
经典实例如下：
- Ozone (O₃): The two O–O bonds are identical, with a bond order of 1.5, intermediate between a single and double bond.
- Nitrate ion (NO₃⁻): Three equivalent N–O bonds, each with a bond order of 1⅓.
- Benzene (C₆H₆): Six equivalent C–C bonds (bond order 1.5), delocalised above and below the ring plane.
- 臭氧（O₃）：两个O–O键完全相同，键级为1.5，介于单键和双键之间。
- 硝酸根离子（NO₃⁻）：三个等价的N–O键，每个键级为1⅓。
- 苯（C₆H₆）：六个等价的C–C键（键级为1.5），电子离域于环平面上方和下方。
Resonance structures are connected by a double-headed arrow (↔), not a single arrow. They are not in equilibrium — the actual molecule is a weighted average of all resonance forms.
共振结构之间用双头箭头（↔）连接，而不是单箭头。它们不是处于平衡状态——真实分子是所有共振形式的加权平均。
10. Bond Enthalpy and Lattice Enthalpy | 键焓与晶格焓
Bond enthalpy (or bond dissociation energy) is the energy required to break one mole of a specific bond in gaseous molecules. Average bond enthalpies are used in calculations because the exact value depends on the molecular environment.
键焓（也称键解离能）是在气态分子中断裂一摩尔特定化学键所需的能量。由于精确值取决于分子环境，计算中通常使用平均键焓。
For the reaction: CH₄ + 2O₂ → CO₂ + 2H₂O, the enthalpy change can be estimated as:
对于反应：CH₄ + 2O₂ → CO₂ + 2H₂O，其焓变可通过以下方式估算：
ΔH = Σ(Bond enthalpies of reactants) − Σ(Bond enthalpies of products)
ΔH = Σ(反应物的键焓之和) − Σ(生成物的键焓之和)
An important detail: bond breaking is endothermic (requires energy), while bond formation is exothermic (releases energy).
一个重要细节：断键是吸热过程（需要吸收能量），而成键是放热过程（释放能量）。
11. Molecular Polarity and Intermolecular Forces | 分子极性与分子间作用力
The polarity of molecules directly influences their physical properties, such as boiling point, solubility, and surface tension. Polar molecules experience dipole-dipole interactions; non-polar molecules experience only London dispersion forces.
分子的极性直接影响其物理性质，如沸点、溶解度和表面张力。极性分子之间存在偶极-偶极相互作用；非极性分子之间仅存在伦敦色散力。
For molecules of similar molar mass, stronger intermolecular forces lead to higher boiling points. For example, among the hydrogen halides:
对于摩尔质量相近的分子，分子间作用力越强，沸点越高。例如，在卤化氢中：
HF (19.5 °C) > HI (−35.4 °C) > HBr (−67.0 °C) > HCl (−85.0 °C)
HF（19.5 °C）> HI（−35.4 °C）> HBr（−67.0 °C）> HCl（−85.0 °C）
Despite having the lowest molar mass, HF has the highest boiling point due to hydrogen bonding—a particularly strong type of dipole-dipole interaction between a hydrogen atom bonded to N, O, or F and a lone pair on another electronegative atom.
尽管HF的摩尔质量最低，但其沸点最高，这是因为氢键的存在——氢键是氢原子与N、O或F成键后，与另一个电负性原子上的孤对电子之间形成的一种特别强的偶极-偶极相互作用。
12. Common Pitfalls and Exam Tips | 常见错误与考试技巧
IB Chemistry students frequently lose marks on covalent bonding questions due to a few recurring errors. Pay attention to the following:
IB化学考生在共价键题目中常因一些反复出现的错误而失分。请注意以下几点：
- Hybridisation vs. geometry: Always match the hybridisation to the total number of electron domains (bonding + lone pairs), not just the number of atoms attached.
- Lone pairs affect angles: Remember that lone pairs compress bond angles (e.g., H₂O at 104.5° instead of 109.5°).
- Polarity versus polar bonds: A molecule can have polar bonds but be non-polar overall if the dipoles cancel (e.g., CCl₄).
- Resonance is not real: Draw accurate hybrid structures and avoid implying that the molecule “flips” between resonance forms.
- Formal charge: When multiple Lewis structures are possible, the most stable one minimises formal charges.
- 杂化与几何的区别：杂化方式要对应电子域总数（成键电子对+孤对电子），而不仅仅是连接的原子数量。
- 孤对电子影响键角：孤对电子会压缩键角（例如H₂O为104.5°而非109.5°）。
- 分子极
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