📚 Year 11 CIE Chemistry Formula & Theorem Quick Reference Handbook | CIE 化学公式定理速查手册
This handbook brings together every essential formula, law, and numerical relationship required for the Year 11 CIE IGCSE Chemistry syllabus. Keep it to hand for quick revision of quantitative chemistry, energetics, rates, equilibrium, and more. All expressions are written in plain Unicode, matching the working you will use in Cambridge IGCSE Chemistry (0620) examinations.
本手册汇集了 CIE IGCSE 化学（0620）Year 11 阶段必须掌握的公式、定律与数量关系，涵盖定量化学、能量学、速率、平衡等核心模块。所有表达式均以 Unicode 写成，与你在试卷中实际使用的格式完全一致，方便考前快速查阅与巩固。
1. Relative Mass & the Mole | 相对质量与摩尔
The relative atomic mass (Aᵣ) of an element is the average mass of its atoms compared to 1/12th of the mass of a carbon‑12 atom. Relative formula mass (Mᵣ) is the sum of Aᵣ values for all atoms in a formula unit.
元素的相对原子质量 (Aᵣ) 是其原子平均质量与碳‑12 原子质量的 1/12 的比值。相对分子式质量 (Mᵣ) 则是化学式中所有原子的 Aᵣ 之和。
The mole is the unit of amount of substance. One mole contains 6.02 × 10²³ particles (Avogadro constant, L). The mass of one mole of a substance is its molar mass in g mol⁻¹, numerically equal to Mᵣ.
摩尔是物质的量的单位。1 mol 物质含有 6.02 × 10²³ 个微粒（阿伏伽德罗常数 L）。1 摩尔物质的质量即其摩尔质量，单位为 g mol⁻¹，数值上等于 Mᵣ。
n = m / M
其中 n: 物质的量 (mol), m: 质量 (g), M: 摩尔质量 (g mol⁻¹)
Always convert mass to grams and use the correct Mᵣ calculated from the latest periodic table provided in the exam.
务必先将质量换算为克，并使用试卷所附周期表计算正确的 Mᵣ。
2. Molar Volume & Gas Calculations | 摩尔体积与气体计算
At room temperature and pressure (r.t.p., 20 °C and 1 atm), one mole of any gas occupies a volume of 24 dm³ (24,000 cm³).
在常温常压下（r.t.p., 20 °C, 1 atm），1 mol 任何气体的体积为 24 dm³（24000 cm³）。
V (dm³) = n × 24
V (dm³) = n × 24，或 V (cm³) = n × 24000
| Volume units | Conversion |
| 1 dm³ | 1000 cm³ |
| 1 m³ | 1000 dm³ |
When reacting gases at the same temperature and pressure, volumes are directly proportional to the number of moles (Avogadro’s law). This allows simple whole‑number volume ratios to be used in calculations.
在相同温度和压强下，气体体积与物质的量成正比（阿伏伽德罗定律）。因此化学方程式中气体的计量系数之比可直接用作体积比进行计算。
3. Concentration & Titration | 浓度与滴定
Concentration is usually expressed in mol dm⁻³ or g dm⁻³. The two are linked by the molar mass.
浓度通常以 mol dm⁻³ 或 g dm⁻³ 表示，两者通过摩尔质量联系。
c (mol dm⁻³) = n / V (dm³) = m / (M × V)
c (mol dm⁻³) = n / V (dm³) = m / (M × V)，其中 V 为溶液体积
Mass concentration (g dm⁻³) = molarity (mol dm⁻³) × molar mass (g mol⁻¹).
质量浓度 (g dm⁻³) = 物质的量浓度 (mol dm⁻³) × 摩尔质量 (g mol⁻¹)。
In titrations, the key relationship is: (c₁V₁)/n₁ = (c₂V₂)/n₂, where n₁, n₂ are the stoichiometric coefficients of the reactants. For a 1:1 reaction, it simplifies to c₁V₁ = c₂V₂.
滴定计算的核心关系为：(c₁V₁)/n₁ = (c₂V₂)/n₂，其中 n₁、n₂ 为反应物的化学计量数。若化学计量比为 1:1，则简化为 c₁V₁ = c₂V₂。
4. Empirical & Molecular Formulae | 经验式与分子式
The empirical formula gives the simplest whole‑number ratio of atoms of each element in a compound. The molecular formula shows the actual number of atoms in a molecule.
经验式表示化合物中各元素原子最简整数比。分子式给出一个分子中实际的原子数目。
To find empirical formula: divide the mass or percentage of each element by its Aᵣ, then divide all results by the smallest value obtained.
求经验式：将各元素的质量或百分含量除以各自的 Aᵣ，再将所得比值同时除以最小值。
Molecular formula = (Empirical formula)n, where n = Mᵣ / (empirical formula mass)
分子式 = (经验式)n，其中 n = Mᵣ / 经验式质量
You may be required to use combustion data (masses of CO₂ and H₂O produced) to deduce the empirical formula of a hydrocarbon. Here, all carbon ends up in CO₂ and all hydrogen in H₂O.
考试可能要求根据燃烧数据（生成的 CO₂ 和 H₂O 质量）推求碳氢化合物的经验式，此时所有碳转化为 CO₂，所有氢转化为 H₂O。
5. Energy Changes & Enthalpy | 能量变化与焓
Exothermic reactions release heat (ΔH negative), endothermic reactions absorb heat (ΔH positive).
放热反应释放热量（ΔH 为负值），吸热反应吸收热量（ΔH 为正值）。
Q = m c ΔT
Q = m c ΔT，其中 Q: 热量 (J), m: 溶液质量 (g), c: 比热容 (4.2 J g⁻¹ °C⁻¹ 用于水), ΔT: 温度变化 (°C)
Enthalpy change per mole is then calculated: ΔH = −Q / n (in J mol⁻¹, usually converted to kJ mol⁻¹ by dividing by 1000). The negative sign is used for exothermic reactions because the surroundings gain energy.
随后计算每摩尔的焓变：ΔH = −Q / n（单位为 J mol⁻¹，通常除以 1000 转换为 kJ mol⁻¹）。放热反应带负号，因为体系向环境释放能量。
Bond energy calculations: ΔH = total energy absorbed for bond breaking − total energy released for bond forming. A negative overall value indicates an exothermic reaction.
键能计算：ΔH = 断裂化学键吸收的总能量 − 形成化学键释放的总能量。若总结果为负值，说明反应放热。
6. Rate of Reaction | 反应速率
Rate of reaction is the change in concentration of a reactant or product per unit time. It can be measured by following the volume of gas produced, change in mass, colour change, or appearance of a precipitate.
反应速率是单位时间内反应物或产物浓度的变化。实验中可以通过跟踪气体体积、质量变化、颜色变化或沉淀出现的时间来测量。
Average rate = change in quantity / time taken
平均速率 = 量的变化 / 时间
Factors affecting rate: concentration (pressure for gases), surface area of solids, temperature, and the presence of a catalyst. A catalyst provides an alternative pathway with lower activation energy, without being consumed.
影响速率的因素：浓度（气体用压强）、固体表面积、温度以及催化剂。催化剂通过提供活化能较低的替代路径来加快反应，自身在反应前后质量和化学性质不变。
The collision theory states that for a reaction to occur, particles must collide with energy equal to or greater than the activation energy and with the correct orientation.
碰撞理论指出，发生反应必须满足：粒子间的碰撞能量不低于活化能，且碰撞取向合适。
7. Chemical Equilibrium | 化学平衡
Reversible reactions can reach a dynamic equilibrium in a closed system, where the forward and reverse rates are equal and the macroscopic properties remain constant.
可逆反应在封闭体系中可达到动态平衡，此时正逆反应速率相等，宏观性质不再改变。
Le Chatelier’s principle: if a system at equilibrium is subjected to a change in concentration, pressure, or temperature, the position of equilibrium shifts to oppose that change.
勒夏特列原理：若改变影响平衡的浓度、压强或温度，平衡将向削弱这种改变的方向移动。
For the Haber process (N₂ + 3H₂ ⇌ 2NH₃, ΔH = −92 kJ mol⁻¹): low temperature favours the forward exothermic reaction (higher yield), but in practice 450 °C is used to maintain a reasonable rate. High pressure favours the side with fewer gas molecules, so 200 atm is used. Iron catalyst speeds up the attainment of equilibrium.
以哈伯法合成氨为例（N₂ + 3H₂ ⇌ 2NH₃，ΔH = −92 kJ mol⁻¹）：低温有利于放热的正反应（产率更高），但实际使用 450 °C 以保证一定速率；高压有利于气体分子数减少的方向，故采用 200 atm；铁催化剂可加快达到平衡。
8. Acids, Bases & pH | 酸、碱与 pH
An acid is a proton (H⁺) donor; a base is a proton acceptor. The pH scale measures the concentration of H⁺ ions: pH = −log₁₀[H⁺]. In IGCSE, pH is simply interpreted qualitatively: lower pH means stronger acid.
酸是质子 (H⁺) 的给体，碱是质子受体。pH 是 H⁺ 浓度的负对数：pH = −log₁₀[H⁺]。在 IGCSE 层面，pH 只需定性理解：pH 越低，酸性越强。
Universal indicator and litmus are common indicators. Neutralisation: acid + base → salt + water. The formation of water can be shown by the ionic equation: H⁺ (aq) + OH⁻ (aq) → H₂O (l).
通用指示剂与石蕊是常用指示剂。中和反应：酸 + 碱 → 盐 + 水。水的生成可通过离子方程式 H⁺ (aq) + OH⁻ (aq) → H₂O (l) 表示。
Strong acids fully ionise in water (e.g. HCl, HNO₃, H₂SO₄); weak acids partially ionise (e.g. CH₃COOH, ethanoic acid). Concentration refers to the amount of acid per volume, whereas strength refers to the degree of ionisation.
强酸在水中完全电离（如 HCl、HNO₃、H₂SO₄），弱酸部分电离（如 CH₃COOH，乙酸）。浓度指单位体积溶液中酸的含量，而强度指电离程度。
9. Electrolysis & Electrochemistry | 电解与电化学
Electrolysis is the decomposition of an ionic compound by passing direct current through its molten or aqueous state. Cations (positive ions) move to the cathode (negative electrode); anions move to the anode (positive electrode).
电解是通过直流电使熔融态或水溶液中的离子化合物分解的过程。阳离子移向阴极（负极），阴离子移向阳极（正极）。
At the cathode: reduction takes place (gain of electrons). At the anode: oxidation takes place (loss of electrons). Remember OIL RIG: Oxidation Is Loss, Reduction Is Gain.
阴极发生还原（得电子），阳极发生氧化（失电子）。可记 OIL RIG: Oxidation Is Loss, Reduction Is Gain。
In aqueous solutions, the products depend on the relative ease of discharge of the ions present. The reactivity series determines the discharge order: the less reactive the metal, the easier its ions are discharged at the cathode. At the anode, simple halide ions (Cl⁻, Br⁻, I⁻) are discharged in preference to OH⁻, but in their absence, OH⁻ is discharged to give oxygen.
在水溶液中，电解产物取决于离子的放电顺序。金属活动性顺序决定阴极放电顺序：越不活泼的金属，其离子越易在阴极放电。阳极上，卤素离子（Cl⁻、Br⁻、I⁻）优先于 OH⁻ 放电；若无卤素离子，则 OH⁻ 放电产生氧气。
10. Metals & Reactivity | 金属与反应性
The reactivity series orders metals by their tendency to form positive ions. A more reactive metal will displace a less reactive metal from its oxide or salt solution.
金属活动性顺序根据金属形成阳离子的趋势排列。活泼金属可将较不活泼金属从其氧化物或盐溶液中置换出来。
Key displacement reactions: e.g., Zn(s) + CuSO₄(aq) → ZnSO₄(aq) + Cu(s). The blue colour of Cu²⁺ fades as copper is deposited. Heat is often released (exothermic).
典型的置换反应：Zn(s) + CuSO₄(aq) → ZnSO₄(aq) + Cu(s)。Cu²⁺ 的蓝色逐渐褪去并在锌表面析出铜，反应通常放热。
Rusting of iron requires both oxygen and water. Barrier protection (paint, grease) and sacrificial protection (coating with a more reactive metal such as zinc – galvanising) are common methods of preventing corrosion.
铁生锈需同时存在氧气和水。防护方法包括隔离层（油漆、油脂）和牺牲保护（用更活泼的金属如锌镀层——镀锌）。
11. Important Constants & Conversions | 重要常数与换算
Memorise these constants for quantitative problems; they are not always given on the formula sheet.
下列常数为定量计算的基石，考试中不总是提供，需熟记。
| Constant | Value |
| Avogadro constant (L) | 6.02 × 10²³ mol⁻¹ |
| Molar gas volume at r.t.p. | 24 dm³ mol⁻¹ (24000 cm³ mol⁻¹) |
| Specific heat capacity of water | 4.2 J g⁻¹ °C⁻¹ |
| 1 dm³ | 1000 cm³ = 1 L |
| 1 tonne | 10⁶ g |
Percentage yield = (actual yield / theoretical yield) × 100%. Percentage purity = (mass of pure substance / total mass of sample) × 100%. Atom economy = (Mᵣ of desired products / total Mᵣ of all reactants) × 100%.
产率百分比 = （实际产量 / 理论产量）× 100%。纯度百分比 = （纯物质质量 / 样品总质量）× 100%。原子经济性 = （目标产物的 Mᵣ / 所有反应物的总 Mᵣ）× 100%。
12. Organic Chemistry Essentials | 有机化学基础
Hydrocarbons contain only carbon and hydrogen. Alkanes (CₙH₂ₙ₊₂) are saturated; alkenes (CₙH₂ₙ) are unsaturated and contain at least one C=C double bond. The test for unsaturation is the addition of bromine water: an orange‑to‑colourless change confirms an alkene.
烃类仅含碳和氢。烷烃 (CₙH₂ₙ₊₂) 为饱和烃；烯烃 (CₙH₂ₙ) 为不饱和烃，至少含有一个 C=C 双键。检验不饱和键的方法为加入溴水：橙色褪为无色即证明存在烯烃。
Functional groups determine the chemical properties of organic compounds. Key homologous series:
官能团决定有机化合物的化学性质。重要的同系物包括：
| Homologous series | Functional group | General formula |
| Alcohols | –OH | CₙH₂ₙ₊₁OH |
| Carboxylic acids | –COOH | CₙH₂ₙ₊₁COOH |
| Esters | –COO– | Derived from acid + alcohol |
Petroleum is separated by fractional distillation based on boiling points. Cracking breaks long‑chain alkanes into shorter alkanes and alkenes, using heat and a catalyst (cat cracking) or steam (steam cracking).
石油通过分馏按沸点分离。裂化将长链烷烃断裂为短链烷烃和烯烃，可使用加热和催化剂（催化裂化）或水蒸气（蒸汽裂化）。
Addition polymerisation: many small alkene monomers (e.g., ethene, C₂H₄) join to form a long saturated polymer chain, without any by‑products. The repeating unit has the formula –(CH₂–CH₂)– for poly(ethene).
加聚反应：众多烯烃单体（如乙烯 C₂H₄）连接成长链饱和聚合物，不产生其他副产物。聚(乙烯) 的重复单元为 –(CH₂–CH₂)–。
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