📚 Year 12 CCEA Chemistry: Formulas and Theorems Quick Reference Handbook | Year 12 CCEA 化学：公式定理速查手册
This quick reference handbook brings together all the essential formulas, definitions and theorems needed for Year 12 CCEA Chemistry. Use it alongside your course notes to check relationships, perform calculations and deepen your grasp of core concepts.
这份速查手册汇集了 Year 12 CCEA 化学所需的所有基本公式、定义和定理。结合课堂笔记使用，可随时查阅关系式、完成计算并加深对核心概念的理解。
1. Amount of Substance and the Mole | 物质的量与摩尔
The mole is the SI unit for amount of substance. One mole contains exactly 6.02214076 × 10²³ specified elementary entities (Avogadro’s constant, Nₐ).
摩尔是物质的量的国际单位。1 摩尔恰好包含 6.02214076 × 10²³ 个指定的基本单元（阿伏伽德罗常数 Nₐ）。
Number of entities N = n × Nₐ, where n = amount (mol). Mass m = n × M, with M = molar mass (g mol⁻¹). n = m / M.
粒子数目 N = n × Nₐ，其中 n 为物质的量（mol）。质量 m = n × M，M 为摩尔质量（g mol⁻¹）。n = m / M。
For solutions: amount n = c × V, where c = concentration (mol dm⁻³) and V = volume (dm³). n = (c × V) / 1000 if V is in cm³.
溶液：物质的量 n = c × V，c 为浓度（mol dm⁻³），V 为体积（dm³）。若 V 以 cm³ 为单位，则 n = (c × V) / 1000。
2. Empirical and Molecular Formulae | 实验式与分子式
The empirical formula is the simplest whole-number ratio of atoms of each element in a compound. It is determined from percentage composition by mass or from combustion data.
实验式是化合物中各元素原子的最简整数比，通过质量百分组成或燃烧数据确定。
Molecular formula = (empirical formula)ₙ, where n = relative molecular mass / empirical formula mass.
分子式 = (实验式)ₙ，n = 相对分子质量 / 实验式质量。
Steps: convert % or mass to moles by dividing by Aᵣ, then divide by smallest number of moles to obtain ratio. Multiply to get whole numbers if necessary.
步骤：将百分数或质量除以相对原子质量 Aᵣ 转化为摩尔，再除以最小摩尔数得整数比，必要时乘以因子得整数。
Combustion analysis data: mass of CO₂ gives moles of C, mass of H₂O gives moles of H; moles of other elements from difference or direct measurement.
燃烧分析数据：CO₂ 的质量给出 C 的摩尔，H₂O 的质量给出 H 的摩尔；其他元素的摩尔通过差量或直接测定获得。
3. Gas Laws and the Ideal Gas Equation | 气体定律与理想气体方程
Boyle’s Law: p ∝ 1/V at constant T and n; Charles’s Law: V ∝ T at constant p and n; Avogadro’s Law: V ∝ n at constant p and T. These combine to the ideal gas equation: pV = nRT.
波义耳定律：恒温恒量下 p ∝ 1/V；查理定律：恒压恒量下 V ∝ T；阿伏伽德罗定律：恒温恒压下 V ∝ n。结合得理想气体方程：pV = nRT。
R = 8.31 J K⁻¹ mol⁻¹ when p in Pa, V in m³, T in K. Use consistent units: 1 atm = 101325 Pa, 1 dm³ = 0.001 m³, T(K) = T(°C) + 273.
R = 8.31 J K⁻¹ mol⁻¹（p 用 Pa，V 用 m³，T 用 K）。单位一致：1 atm = 101325 Pa，1 dm³ = 0.001 m³，T(K) = T(°C) + 273。
Molar volume at RTP (20 °C, 1 atm): approximately 24.0 dm³ mol⁻¹; at STP (0 °C, 1 atm): 22.4 dm³ mol⁻¹.
室温常压（20 °C, 1 atm）下气体摩尔体积约为 24.0 dm³ mol⁻¹；标准状况（0 °C, 1 atm）为 22.4 dm³ mol⁻¹。
Density of a gas: ρ = m/V = (pM) / (RT), where M = molar mass.
气体密度：ρ = m/V = (pM) / (RT)，M 为摩尔质量。
4. Enthalpy Changes and Calorimetry | 焓变与量热法
Enthalpy change ΔH is the heat energy transferred at constant pressure. Exothermic: ΔH < 0; endothermic: ΔH > 0. Units: kJ mol⁻¹.
焓变 ΔH 是恒压下传递的热能。放热：ΔH < 0；吸热：ΔH > 0。单位 kJ mol⁻¹。
Measured by calorimetry: q = mcΔT, where q = heat energy (J), m = mass of solution (g), c = specific heat capacity (J g⁻¹ K⁻¹, usually 4.18 for water), ΔT = temperature change (K).
用量热法测定：q = mcΔT，q 为热量（J），m 为溶液质量（g），c 为比热容（J g⁻¹ K⁻¹，水通常取 4.18），ΔT 为温度变化（K）。
Molar enthalpy change ΔH = –q / n (exothermic gives negative sign). n = moles of limiting reactant.
摩尔焓变 ΔH = –q / n（放热得负值），n 为限量反应物的物质的量。
Standard conditions: 100 kPa, 298 K, solutions at 1 mol dm⁻³. Standard enthalpy of combustion (Δ_cH°) and standard enthalpy of formation (Δ_fH°) refer to formation of 1 mole of compound from its elements or complete combustion.
标准条件：100 kPa，298 K，溶液浓度 1 mol dm⁻³。标准燃烧焓（Δ_cH°）和标准生成焓（Δ_fH°）分别指 1 mol 物质完全燃烧或由元素生成 1 mol 化合物时的焓变。
5. Hess’s Law and Bond Enthalpies | 赫斯定律与键焓
Hess’s Law: the enthalpy change for a reaction is independent of the route taken, depending only on initial and final states. ΔH for a reaction can be found by combining known enthalpy changes of other reactions.
赫斯定律：反应的焓变与途径无关，只取决于始态和终态。可通过组合其他已知反应的焓变求出某反应的 ΔH。
ΔH_reaction = Σ Δ_fH°(products) – Σ Δ_fH°(reactants). Alternatively, ΔH = Σ (bond enthalpies broken) – Σ (bond enthalpies formed).
ΔH_反应 = Σ Δ_fH°(产物) – Σ Δ_fH°(反应物)。也可用键焓计算：ΔH = Σ (断裂键的键焓) – Σ (形成键的键焓)。
Bond enthalpy is the energy required to break 1 mole of a covalent bond in the gaseous state. Mean bond enthalpies are averaged over different compounds.
键焓是断裂气态中 1 摩尔共价键所需的能量。平均键焓是不同化合物中的平均值。
Use Hess cycle diagrams to visualise alternative paths, ensuring all substances are in correct states.
使用赫斯循环图直观展示不同路径，确保所有物质状态正确。
6. Rates of Reaction | 反应速率
Rate of reaction = change in concentration of a reactant or product / time. Units: mol dm⁻³ s⁻¹.
反应速率 = 反应物或产物浓度的变化量 / 时间，单位 mol dm⁻³ s⁻¹。
Rate equation: rate = k[A]^m[B]^n, where k = rate constant, m and n are orders of reaction with respect to A and B. Overall order = m + n.
速率方程：rate = k[A]^m[B]^n，k 为速率常数，m 和 n 分别为对 A 和 B 的反应级数。总级数 = m + n。
Zero order: rate independent of [A]; 1st order: rate ∝ [A]; 2nd order: rate ∝ [A]². Orders are determined experimentally, not from stoichiometry.
零级：速率与 [A] 无关；一级：速率 ∝ [A]；二级：速率 ∝ [A]²。级数由实验确定，不由化学计量数决定。
Temperature affects rate via Arrhenius equation: k = A e^(–Eₐ/RT) where Eₐ = activation energy, A = pre-exponential factor. A higher temperature gives a larger k and faster rate.
温度通过阿伦尼乌斯方程影响速率：k = A e^(–Eₐ/RT)，Eₐ 为活化能，A 为指前因子。温度升高，k 增大，反应更快。
Catalysts provide an alternative pathway with lower Eₐ, increasing rate without being consumed.
催化剂提供低活化能的替代途径，加快反应而自身不被消耗。
7. Chemical Equilibrium and Kc | 化学平衡与 Kc
Dynamic equilibrium: in a closed system, the forward and reverse reactions occur at equal rates, concentrations remain constant. Le Chatelier’s principle: if a system at equilibrium is disturbed, it shifts to counteract the change.
动态平衡：封闭系统中正逆反应速率相等，浓度保持恒定。勒夏特列原理：若平衡体系受到扰动，平衡向减少扰动方向移动。
For a reaction aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration: Kc = [C]^c[D]^d / [A]^a[B]^b (only for homogeneous systems). [ ] = equilibrium concentration in mol dm⁻³.
对于反应 aA + bB ⇌ cC + dD，浓度平衡常数 Kc = [C]^c[D]^d / [A]^a[B]^b（仅适用均相体系）。[ ] 表示平衡浓度 mol dm⁻³。
Kc is temperature dependent; its value does not change with concentration or pressure (but equilibrium position can shift). A large Kc indicates products favoured at equilibrium.
Kc 只随温度变化；浓度或压力改变不改变 Kc 值（但平衡位置可移动）。Kc 值大表示平衡时产物占优。
For heterogeneous systems, solid and pure liquid concentrations are constant and omitted from the Kc expression.
非均相体系中，固体和纯液体的浓度为常数，不出现在 Kc 表达式中。
8. Acid-Base Equilibria: pH, Ka, Kw | 酸碱平衡：pH、Ka、Kw
pH = –log₁₀[H⁺]; [H⁺] = 10^(–pH). Similarly, pOH = –log₁₀[OH⁻]; pH + pOH = 14 at 298 K.
pH = –log₁₀[H⁺]；[H⁺] = 10^(–pH)。类似地，pOH = –log₁₀[OH⁻]；298 K 时 pH + pOH = 14。
Ionic product of water: Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K. pKw = –log₁₀ Kw = 14. Kw increases with temperature.
水的离子积：Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ (298 K)。pKw = –log₁₀ Kw = 14。Kw 随温度升高而增大。
For weak acids HA ⇌ H⁺ + A⁻, acid dissociation constant Ka = [H⁺][A⁻] / [HA]. pKa = –log₁₀ Ka. Assumptions for weak acid calculations: [H⁺] = [A⁻], [HA]_equilibrium ≈ [HA]_initial.
弱酸 HA ⇌ H⁺ + A⁻，酸解离常数 Ka = [H⁺][A⁻] / [HA]。pKa = –log₁₀ Ka。弱酸计算假设：[H⁺] = [A⁻]，[HA]_平衡 ≈ [HA]_初始。
[H⁺] ≈ √(Ka × c) for a weak monoprotic acid of initial concentration c.
一元弱酸初始浓度 c 时，[H⁺] ≈ √(Ka × c)。
Buffer solutions resist pH change; for acidic buffer, pH = pKa + log₁₀([salt]/[acid]) (Henderson-Hasselbalch equation in logarithmic form).
缓冲溶液抵抗 pH 改变；酸性缓冲液 pH = pKa + log₁₀([盐]/[酸])（亨德森-哈塞尔巴尔赫方程对数形式）。
9. Redox Reactions and Oxidation Numbers | 氧化还原反应与氧化数
Oxidation is loss of electrons; reduction is gain of electrons (OIL RIG). Oxidation number (ON) is the charge an atom would have if all bonds were ionic.
氧化是失电子，还原是得电子（OIL RIG）。氧化数（ON）是假设所有键均为离子键时原子所带的电荷。
Rules: element = 0; H usually +1 (except metal hydrides –1); O usually –2 (except peroxides –1, OF₂ +2); sum of ONs in a neutral compound = 0; in a polyatomic ion, sum equals ion charge.
规则：单质为 0；H 通常 +1（金属氢化物中为 –1）；O 通常 –2（过氧化物 –1，OF₂ 中 +2）；中性化合物中 ON 代数和为 0；多原子离子中 ON 代数和等于离子电荷。
Balancing redox using oxidation numbers: identify atoms that change ON, balance electron transfer, then balance change by coefficients, finally add H⁺/OH⁻ and H₂O as needed.
用氧化数配平氧化还原反应：识别 ON 变化原子，平衡电子转移，用系数平衡变化，最后按需添加 H⁺/OH⁻ 和 H₂O。
Half-equations: show electron transfer separately for oxidation and reduction. Combine to give overall equation, ensuring electrons cancel.
半反应式：分别表示氧化和还原中的电子转移。组合成全反应式，确保电子数相等而抵消。
10. Shapes of Molecules and VSEPR | 分子形状与价层电子对互斥理论
VSEPR theory: electron pairs (bonding and lone) around a central atom repel to positions of minimum repulsion. Shape is determined by the number of bonding pairs and lone pairs.
价层电子对互斥（VSEPR）理论：中心原子周围的电子对（成键和孤对）彼此排斥，采取斥力最小的排布。分子形状取决于成键对和孤对数目。
| Bonding pairs / 成键对 | Lone pairs / 孤对 | Shape / 形状 | Bond angle / 键角 |
|---|---|---|---|
| 2 | 0 | Linear / 直线形 | 180° |
| 3 | 0 | Trigonal planar / 平面三角形 | 120° |
| 4 | 0 | Tetrahedral / 四面体形 | 109.5° |
| 3 | 1 | Trigonal pyramidal / 三角锥形 | ≈ 107° |
| 2 | 2 | Bent / V形 | ≈ 104.5° |
| 5 | 0 | Trigonal bipyramidal / 三角双锥形 | 90°, 120° |
| 6 | 0 | Octahedral / 八面体形 | 90° |
Lone pairs repel more strongly than bonding pairs, reducing bond angles by about 2.5° per lone pair.
孤对电子的排斥力强于成键电子对，每有一对孤对电子，键角减小约 2.5°。
11. Nomenclature and Functional Groups in Organic Chemistry | 有机化学命名与官能团
IUPAC naming: identify the longest carbon chain, number to give lowest numbers to functional groups or substituents, use prefixes/suffixes.
IUPAC 命名：找出最长碳链，从靠近官能团或取代基的一端编号，使用前缀/后缀。
| Homologous series / 同系列 | Functional group / 官能团 | Suffix / 后缀 |
|---|---|---|
| Alkane / 烷烃 | C–C single bonds | -ane |
| Alkene / 烯烃 | C=C | -ene |
| Alcohol / 醇 | –OH (hydroxyl) | -ol |
| Aldehyde / 醛 | –CHO (carbonyl at end) | -al |
| Ketone / 酮 | >C=O (carbonyl, not at end) | -one |
| Carboxylic acid / 羧酸 | –COOH | -oic acid |
| Halogenoalkane / 卤代烷 | –F, –Cl, –Br, –I | prefix fluoro-, chloro-, bromo-, iodo- |
Isomerism: structural isomers (chain, position, functional group) have same molecular formula but different structural formula. Stereoisomerism (E/Z, optical) arises from different spatial arrangement.
异构现象：构造异构（碳链异构、位置异构、官能团异构）分子式相同但结构式不同。立体异构（E/Z、光学异构）来自不同的空间排列。
12. Key Data and Common Units | 关键数据与常用单位
Memorise these physical constants and conversions for CCEA chemistry calculations:
牢记以下用于 CCEA 化学计算的物理常数和换算：
- Avogadro’s number Nₐ = 6.02 × 10²³ mol⁻¹ | 阿伏伽德罗常数 Nₐ = 6.02 × 10²³ mol⁻¹
- Molar gas volume at RTP ≈ 24.0 dm³ mol⁻¹ | 室温常压下气体摩尔体积 ≈ 24.0 dm³ mol⁻¹
- Gas constant R = 8.31 J K⁻¹ mol⁻¹ | 气体常数 R = 8.31 J K⁻¹ mol⁻¹
- Specific heat capacity of water c = 4.18 J g⁻¹ K⁻¹ (or J °C⁻¹ g⁻¹) | 水的比热容 c = 4.18 J g⁻¹ K⁻¹
- 1 atm = 101 325 Pa = 101 kPa | 1 atm = 101 325 Pa = 101 kPa
- 1 dm³ = 1000 cm³ = 0.001 m³ | 1 dm³ = 1000 cm³ = 0.001 m³
- Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K | 298 K 时 Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶
Always convert temperature to kelvin and volumes to dm³ or m³ as required by the formula.
始终根据公式要求将温度转换为开尔文，体积转换为 dm³ 或 m³。
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