📚 Year 13 CCEA Chemistry: Formula & Theorem Quick Reference Handbook | CCEA Year 13 化学公式定理速查手册
This quick reference guide consolidates all the essential formulas, equations, and key theoretical principles required for the CCEA Year 13 Chemistry course. It is designed for efficient revision, helping you to recall definitions, manipulate quantitative relationships, and apply concepts accurately in examinations. The material is organised into self-contained sections covering physical, inorganic, and organic chemistry, ensuring you have a one-stop resource for every critical calculation and law.
本速查手册汇集了 CCEA Year 13 化学课程中所有必备的公式、方程式和重点理论原理。手册旨在帮助同学们高效复习，快速回顾定义、运用定量关系，并在考试中准确应用相关概念。内容按物理化学、无机化学和有机化学自成模块编排，是一站式攻克所有关键计算与定律的备考利器。
1. Mole Calculations and the Ideal Gas Equation | 摩尔计算与理想气体状态方程
The mole is the central unit in chemistry, linking microscopic particles to measurable macroscopic quantities. The amount of substance n (in mol) can be determined from mass, concentration, or volume of a gas, depending on the data given.
物质的量 n（单位：mol）是化学的核心单位，它把微观粒子与可测量的宏观量联系起来。根据给定的数据，可以从质量、浓度或气体体积求得 n。
n = m / M n = c V n = V / Vₘ
me (dm³ mol⁻¹). At room temperature and pressure (RTP), Vₘ = 24 dm³ mol⁻¹. For non-standard conditions, the ideal gas equation applies.
式中 m 为质量（g），M 为摩尔质量（g mol⁻¹），c 为浓度（mol dm⁻³），V 为溶液体积（dm³），V 为气体体积（dm³），Vₘ 为摩尔体积（dm³ mol⁻¹）。在常温常压（RTP）下，Vₘ = 24 dm³ mol⁻¹。非标准状况时需使用理想气体状态方程。
pV = nRT
¹, T is absolute temperature in kelvin (K = °C + 273). Always convert units appropriately.
p 为压强，单位帕斯卡（Pa）；V 为体积，单位 m³（1 m³ = 1000 dm³）；n 为物质的量；R = 8.314 J K⁻¹ mol⁻¹；T 为热力学温度，单位 K（K = °C + 273）。务必统一单位。
2. Enthalpy Changes and Hess's Law | 焓变与赫斯定律
Enthalpy change, ΔH, is the heat energy transferred under constant pressure. Standard conditions are 100 kPa and a stated temperature, usually 298 K. The quantity is calculated using q = mcΔT and then converted to ΔH per mole.
焓变 ΔH 是在恒压条件下转移的热量。标准条件是 100 kPa 和指定温度（通常为 298 K）。计算时先通过 q = mcΔT 求得热量，再换算为每摩尔的 ΔH。
q = mcΔT ΔH = –q / n
tion (4.18 J g⁻¹ K⁻¹ for water), ΔT = temperature change (K). ΔH is expressed in kJ mol⁻¹.
q 为能量变化（J）；m 为溶液质量（g，对稀溶液可近似取体积 cm³）；c 为溶液比热容（水取 4.18 J g⁻¹ K⁻¹）；ΔT 为温度变化（K）。ΔH 以 kJ mol⁻¹ 表示。
Hess's Law states that the total enthalpy change for a reaction is independent of the route taken. It allows calculation of ΔH using enthalpies of formation or combustion.
赫斯定律指出，一个反应的总焓变与途径无关。由此可利用生成焓或燃烧焓数据计算 ΔH。
ΔH = ΣΔHf°(products) – ΣΔHf°(reactants)
ΔH = ΣΔHc°(reactants) – ΣΔHc°(products)
These are standard enthalpy changes at 298 K. Always balance the equations and account for stoichiometric coefficients.
以上为标准生成焓和标准燃烧焓在 298 K 下的计算式。注意配平方程式并按照计量系数计算。
3. Bond Enthalpy and Reaction Enthalpy | 键焓与反应焓
Mean bond enthalpy is the energy required to break one mole of a given covalent bond in the gaseous state, averaged over a range of compounds. Breaking bonds absorbs energy (endothermic), while making bonds releases energy (exothermic).
平均键焓是气态下断裂 1 mol 某共价键所需能量的平均值。断键吸热（吸热过程），成键放热（放热过程）。
ΔH ≈ Σ(bond enthalpies broken) – Σ(bond enthalpies made)
This calculation provides an estimate of ΔH because mean bond enthalpies are not exact for a specific molecule. Use it for gaseous reactions.
该计算仅为 ΔH 的估算值，因为平均键焓并非特定分子的精确数值。通常用于气相反应。
4. Kinetics and the Rate Equation | 动力学与速率方程
The rate of reaction measures how quickly reactants are consumed or products are formed. The rate equation relates rate to the concentrations of reactants, each raised to a power called the order.
反应速率衡量反应物消耗或产物生成的快慢。速率方程将反应速率与反应物浓度的幂乘积相联系，该幂指数即为反应级数。
rate = k [A]ᵐ [B]ⁿ
k is the rate constant, m and n are partial orders with respect to A and B. The overall order is m + n. The units of k depend on the overall order.
k 为速率常数，m 和 n 分别为反应物 A 和 B 的分级数，总级数为 m + n。k 的单位取决于总级数。
- Zero order: rate = k, units mol dm⁻³ s⁻¹
- First order: rate = k[A], units s⁻¹
- Second order: rate = k[A]² or rate = k[A][B], units dm³ mol⁻¹ s⁻¹
- 零级反应：rate = k，单位 mol dm⁻³ s⁻¹
- 一级反应：rate = k[A]，单位 s⁻¹
- 二级反应：rate = k[A]² 或 rate = k[A][B]，单位 dm³ mol⁻¹ s⁻¹
The rate-determining step is the slowest step in a multi-step mechanism; the rate equation includes only the species (and their orders) involved in or before this step.
速率决定步骤是多步机理中最慢的一步；速率方程仅包含参与该步骤或之前步骤的物种（及其反应级数）。
5. Equilibrium and the Equilibrium Constant | 化学平衡与平衡常数
For a reversible reaction at equilibrium, the concentrations of reactants and products remain constant. The equilibrium constant Kc expresses the ratio of product concentrations to reactant concentrations, each raised to the power of its stoichiometric coefficient.
可逆反应达到平衡时，反应物和产物的浓度保持不变。平衡常数 Kc 表示产物浓度幂乘积与反应物浓度幂乘积之比，幂指数等于计量系数。
aA + bB ⇌ cC + dD
Kc = [C]ᶜ [D]ᵈ / ([A]ᵃ [B]ᵇ)
Kc has no units only when the sum of exponents on top equals that on bottom; otherwise units are derived. Temperature changes alter Kc; catalysts do not.
Kc 只有在分子和分母的总幂指数相等时才无单位，否则需推导单位。温度改变会引起 Kc 变化，催化剂不改变 Kc。
For gases, Kp uses partial pressures p (in Pa or atm) in place of concentrations.
对于气相反应，Kp 使用各组分的分压 p（单位 Pa 或 atm）代替浓度。
Kp = (pC)ᶜ (pD)ᵈ / (pA)ᵃ (pB)ᵇ
Partial pressure pₐ = mole fraction × total pressure.
分压 pₐ = 摩尔分数 × 总压。
6. Le Chatelier's Principle | 勒夏特列原理
If a system at dynamic equilibrium is subjected to a change in concentration, pressure, or temperature, the position of equilibrium shifts to oppose the change.
如果处于动态平衡的体系受到浓度、压强或温度的变化，平衡位置会向削弱该变化的方向移动。
- Concentration increase of a reactant: equilibrium shifts to product side to use it up.
- Pressure increase: equilibrium shifts to side with fewer gas molecules.
- Temperature increase: endothermic direction is favoured; Kc (or Kp) changes accordingly.
- 增大反应物浓度：平衡向生成物方向移动以消耗增加的反应物。
- 增大压强：平衡向气体分子总数更少的方向移动。
- 升高温度：平衡向吸热方向移动；Kc 或 Kp 随之变化。
Catalysts have no effect on position; they merely speed up attainment of equilibrium.
催化剂不影响平衡位置，仅加快达到平衡的速率。
7. Acids, Bases and pH Calculations | 酸碱与 pH 计算
A Brønsted–Lowry acid is a proton (H⁺) donor; a base is a proton acceptor. pH is defined as the negative logarithm (base 10) of hydrogen ion concentration.
布朗斯特-劳里酸是质子（H⁺）给予体，碱是质子接受体。pH 定义为氢离子浓度的负常用对数。
pH = –log₁₀[H⁺] [H⁺] = 10⁻ᴾᴴ
t 298 K, [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³, so pH = 7, and the ionic product of water is:
对于强一元酸，[H⁺] 等于酸的浓度。298 K 下纯水中 [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³，pH = 7。水的离子积为：
Kₒᵥ = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ (at 298 K)
Thus pKₒᵥ = 14, and pOH = –log[OH⁻]. The relationship pH + pOH = 14 always holds.
因此 pKₒᵥ = 14，pOH = –log[OH⁻]，并且恒有 pH + pOH = 14。
For weak acids, an acid dissociation constant Ka applies. For a weak acid HA dissociating:
对于弱酸，适用酸离解常数 Ka。弱酸 HA 的解离：
HA ⇌ H⁺ + A⁻ Ka = [H⁺][A⁻] / [HA]
Using the approximation [H⁺] << [HA]₀, the pH of a weak acid can be found from:
利用近似条件 [H⁺] << [HA]₀，弱酸 pH 计算公式：
[H⁺] = √Ka × [HA]₀
For buffer solutions, the Henderson–Hasselbalch equation is useful:
对于缓冲溶液，可使用 Henderson–Hasselbalch 方程：
pH = pKa + log₁₀([salt] / [acid])
d its conjugate base (salt). Similarly for weak bases, pOH = pKb + log₁₀([salt] / [base]).
适用于弱酸及其共轭碱（盐）组成的缓冲体系。同理，弱碱缓冲溶液：pOH = pKb + log₁₀([salt] / [base])。
8. Redox Reactions and Oxidation Numbers | 氧化还原反应与氧化数
Redox reactions involve simultaneous oxidation (loss of electrons, increase in oxidation number) and reduction (gain of electrons, decrease in oxidation number). Assign oxidation numbers using rules to identify what is oxidised and what is reduced.
氧化还原反应同时发生氧化（失去电子，氧化数升高）和还原（得到电子，氧化数降低）。通过规则确定氧化数，可辨识反应中被氧化和被还原的物质。
Key oxidation number rules:
- Elements in their standard state: 0
- Monatomic ions: charge on the ion
- Oxygen: –2 (except in peroxides where it is –1 and with fluorine where it is positive)
- Hydrogen: +1 (except in metal hydrides where it is –1)
- Sum of oxidation numbers in a neutral compound: 0; in a polyatomic ion: equals the ion charge
氧化数的主要规则：单质为 0；单原子离子为离子电荷；氧通常为 –2（过氧化物中为 –1，与氟结合时为正）；氢通常为 +1（金属氢化物中为 –1）；中性化合物中各元素氧化数和为 0，多原子离子中等于离子电荷。
Half-equations balance atoms and charge; electrons appear on the more positive side. Combine half-equations so that electrons cancel.
半反应式同时配平原子与电荷；电子写在电势较高的一侧。合并半反应式时电子相互抵消。
9. Electrochemical Cells and the Nernst Equation | 电化学电池与能斯特方程
The electromotive force (emf) of a cell is given by E°cell = E°(right-hand electrode) – nd electrode) under standard conditions. The cell reaction is spontaneous when E°cell > 0.
标准状态下，电池电动势（emf）E°电池 = E°（右电极）– E°（左电极）。当 E°电池 > 0 时，电池反应自发进行。
When concentrations are not 1 mol dm⁻³, the Nernst equation allows calculation of the electrode potential E or cell emf at 298 K.
当浓度不是 1 mol dm⁻³ 时，可使用能斯特方程计算 298 K 下的电极电势 E 或电池电动势。
E = E° + (RT / zF) ln([oxidised] / [reduced])
At 298 K, RT/F = 0.0257 V, so the equation becomes:
在 298 K 时，RT/F = 0.0257 V，因此方程简化为：
E = E° + (0.0257 / z) ln([ox] / [red])
2 / z) log₁₀([ox] / [red]). z is the number of electrons transferred in the half-equation.
或使用 log₁₀：E = E° + (0.0592 / z) log₁₀([氧化态] / [还原态])。z 为半反应中转移的电子数。
10. Organic Isomerism and Functional Groups | 有机化学同分异构与官能团
Isomers are compounds with the same molecular formula but different arrangement of atoms. Structural isomers differ in the connectivity of atoms, for example chain, position, and functional group isomers. Stereoisomers have the same structural formula but different spatial arrangement.
同分异构体是分子式相同但原子排列不同的化合物。构造异构体的原子连接顺序不同，例如碳链异构、位置异构和官能团异构。立体异构体构造式相同而空间排列不同。
bond, where two different groups are attached to each carbon of the double bond. The Cahn–Ingold– n same side) or E (entgegen, opposite sides). Optical isomerism (enantiomers) occurs when a molecule contains a chiral centre – imposable mirror images and rotate plane-polarised light in equal but opposite directions.
E-Z 异构源于 C=C 双键的旋转受阻，且双键的每个碳上连接两个不同的基团。根据 Cahn–Ingold–Prelog 优先规则，优先级高的基团在同侧为 Z，在对侧为 E。手性异构（对映异构）源于分子含手性中心——即连接四个不同基团的碳原子。对映体互为不可重叠的镜像，可使平面偏振光发生等量但反向的旋转。
Key functional groups encountered in Year 13 include alkenes, haloalkanes, alcohols, aldehydes, ketones, carboxylic acids, esters, amines, and nitriles. Their characteristic reactions and interconversions form a large part of organic synthesis pathways.
Year 13 涉及的官能团主要包括烯烃、卤代烷、醇、醛、酮、羧酸、酯、胺和腈。其特性反应与相互转化构成了有机合成路线的重要部分。
11. Shapes of Molecules and VSEPR | 分子形状与价层电子对互斥理论
Valence Shell Electron Pair Repulsion (VSEPR) theory states that electron pairs around a central atom repel each other and adopt an arrangement that minimises repulsion. The shape is determined by the number of bonding pairs and lone pairs.
价层电子对互斥理论（VSEPR）认为，中心原子周围的电子对相互排斥，并采取使斥力最小的排布方式。分子形状取决于成键电子对和孤电子对的数目。
| Bonding Pairs | Lone Pairs | Shape | Bond Angle (°) |
|---|---|---|---|
| 2 | 0 | Linear | 180 |
| 3 | 0 | Trigonal planar | 120 |
| 2 | 1 | Bent / V-shaped | ~118 |
| 4 | 0 | Tetrahedral | 109.5 |
| 3 | 1 | Trigonal pyramidal | ~107 |
| 2 | 2 | Bent / V-shaped | 104.5 |
| 5 | 0 | Trigonal bipyramidal | 90, 120 |
| 6 | 0 | Octahedral | 90 |
Lone pairs repel more strongly than bonding pairs, reducing bond angles from the ideal values. Always count electron pairs, draw a Lewis structure first.
孤对电子的排斥力大于成键电子对，因而使键角偏离理想值。务必先画出路易斯结构，再计算电子对数。
12. Energetics of Ionic Bonding and Born–Haber Cycles | 离子键能学与玻恩–哈伯循环
The Born–Haber cycle is an energy cycle applying Hess's Law to ionic compounds. It relates lattice enthalpy (the enthalpy change when one mole of solid ionic compound is formed from its gaseous ions) to experimental enthalpies such as atomisation, ionisation energy, electron affinity, and formation.
玻恩–哈伯循环是应用于离子化合物的赫斯定律能量循环。它将晶格焓（1 mol 固态离子化合物由气态离子形成时的焓变）与原子化焓、电离能、电子亲和能和生成焓等实验数据相关联。
The general cycle for NaCl is represented as:
以 NaCl 为例的通用循环如下：
Na(s) → Na(g) ΔHₐₜ (atomisation of sodium)
½Cl₂(g) → Cl(g) ΔHₐₜ (atomisation of chlorine)
Na(g) → Na⁺(g) + e⁻ IE (first ionisation energy)
Cl(g) + e⁻ → Cl⁻(g) EA (electron affinity)
Na⁺(g) + Cl⁻(g) → NaCl(s) ΔHₗₐₜₜ (lattice enthalpy)
The standard enthalpy of formation ΔHf°(NaCl) equals the sum of all the above steps by Hess's Law. Lattice enthalpy can thus be calculated or compared with a theoretical value from the perfect ionic model to assess covalent character.
根据赫斯定律，标准生成焓 ΔHf°(NaCl) 等于上述各步的焓变之和。由此可计算晶格焓，并与纯离子模型的理论值比较，以判断共价性程度。
Key sign conventions: atomisation and ionisation are endothermic (positive ΔH); electron affinity is usually exothermic (negative); lattice enthalpy is exothermic (negative).
符号惯例：原子化和电离为吸热过程（ΔH 为正）；电子亲和能通常放热（负值）；晶格焓为放热（负值）。
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