📚 Cambridge IGCSE Chemistry Formula & Theorem Quick Reference Handbook | 剑桥IGCSE化学公式定理速查手册
This handbook summarises the essential formulae and key theorems of Cambridge IGCSE Chemistry, providing a quick reference for Year 11 students. Each section pairs a clear English explanation with its Chinese counterpart, ensuring that concepts are fully understood in both languages. Mastery of these fundamentals is crucial for success in the examination.
本手册总结了剑桥IGCSE化学的核心公式与重要定理，为11年级学生提供一份速查指南。每个小节均以清晰的英文解释和对应的中文说明成对出现，确保双语理解。掌握这些基础知识是考试成功的关键。
1. Mole Concept & Avogadro’s Constant | 摩尔概念与阿伏伽德罗常数
The mole is the unit for amount of substance. One mole contains exactly 6.02 × 10²³ elementary entities (atoms, molecules, ions, etc.), known as Avogadro’s constant (Nₐ). The number of moles (n) is calculated by dividing the mass of the substance (m) by its molar mass (M):
摩尔是物质的量的单位。1摩尔精确包含6.02 × 10²³个基本单元（原子、分子、离子等），这个数值称为阿伏伽德罗常数（Nₐ）。物质的量（n）由物质的质量（m）除以它的摩尔质量（M）求得：
n = m / M
Molar mass (M) is the mass of one mole of a substance, expressed in g/mol. It is numerically equal to the relative atomic mass (Aᵣ) or relative formula mass (Mᵣ). To convert between number of particles (N) and moles, use N = n × Nₐ.
摩尔质量（M）是1摩尔物质的质量，单位为g/mol。它在数值上等于相对原子质量（Aᵣ）或相对化学式量（Mᵣ）。粒子数（N）与物质的量的换算公式为 N = n × Nₐ。
2. Empirical & Molecular Formula | 实验式与分子式
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 of each element in one molecule. To determine empirical formula from mass or percentage composition: convert masses to moles, then find the simplest ratio by dividing by the smallest number of moles.
实验式表示化合物中各元素原子的最简整数比。分子式则表示一个分子中各元素的实际原子数。由质量或质量分数求实验式的方法：将各元素的质量换算成物质的量，再除以最小物质的量，得到最简比。
Molecular formula = (Empirical formula) × n, where n = Mᵣ(compound) / Mᵣ(empirical formula). For example, glucose has an empirical formula CH₂O and a molecular formula C₆H₁₂O₆.
分子式 = (实验式) × n，其中 n = 化合物的Mᵣ / 实验式的Mᵣ。例如，葡萄糖的实验式为CH₂O，分子式为C₆H₁₂O₆。
3. Molar Gas Volume | 气体摩尔体积
At room temperature and pressure (rtp, 20 °C and 1 atm), one mole of any gas occupies a volume of 24 dm³. This is the molar gas volume (Vₘ). The volume of a gas (V) is related to moles by:
在常温常压下（rtp，20 °C和1 atm），1摩尔任何气体的体积为24 dm³，这就是气体摩尔体积（Vₘ）。气体体积（V）与物质的量的关系为：
n = V (dm³) / 24
For calculations involving gases in chemical reactions, the volume ratio of reacting gases is equal to the mole ratio, provided all gases are at the same temperature and pressure. This follows from Avogadro’s law: equal volumes of gases contain equal numbers of molecules.
在涉及气体的化学反应计算中，只要温度、压力相同，反应气体的体积比等于物质的量之比。这源于阿伏伽德罗定律：同温同压下，相同体积的气体含有相同数目的分子。
4. Concentration & Titration | 浓度与滴定
Concentration (c) is the amount of solute dissolved per unit volume of solution. It is most often expressed in mol/dm³. The key formula is:
浓度（c）表示单位体积溶液中所含溶质的物质的量，常用单位为mol/dm³。核心公式为：
n = c × V (dm³)
When volume is given in cm³, convert to dm³ by dividing by 1000. In a titration, the unknown concentration of an acid or base can be found using the relationship c₁V₁ / n₁ = c₂V₂ / n₂, where n is the stoichiometric coefficient from the balanced equation.
当体积以cm³给出时，需除以1000转化为dm³。在滴定中，酸或碱的未知浓度可利用关系式 c₁V₁ / n₁ = c₂V₂ / n₂ 求得，其中 n 是配平方程式中相应的化学计量数。
5. Mass Conservation & Stoichiometry | 质量守恒与化学计量
The law of conservation of mass states that total mass of reactants equals total mass of products in a chemical reaction. Stoichiometry uses the mole ratios from a balanced equation to calculate masses, volumes, and concentrations of substances involved.
质量守恒定律指出，化学反应中反应物的总质量等于生成物的总质量。化学计量法利用配平方程式中的物质的量之比来计算相关物质的质量、体积和浓度。
General steps: write a balanced equation; convert given data to moles; use the mole ratio to find moles of the unknown; convert moles to the required unit (mass, volume, concentration).
基本步骤：写出配平方程式；将已知量换算为物质的量；利用物质的量之比求出未知物的物质的量；再将物质的量换算为所需单位（质量、体积、浓度）。
6. Rate of Reaction | 反应速率
The rate of a reaction measures how quickly a reactant is used up or a product is formed. It is defined as the change in concentration of a reactant or product per unit time:
反应速率衡量反应物消耗或产物生成的快慢。其定义为反应物或产物的浓度在单位时间内的变化量：
Rate = Δ[concentration] / Δt
Experimentally, rate can be followed by measuring volume of gas evolved, mass loss, colour change, or pH change. Factors affecting rate include: concentration (pressure for gases), temperature, surface area of solids, and the presence of a catalyst. Collision theory explains these effects: reactions occur when particles collide with sufficient energy (activation energy) and correct orientation.
实验上可通过测量气体释放体积、质量减少、颜色变化或pH变化来追踪速率。影响速率的因素有：浓度（气体为压力）、温度、固体表面积和催化剂。碰撞理论解释了这些影响：粒子需以足够的能量（活化能）和正确的取向发生碰撞，反应才会进行。
7. Energetics & Bond Energy | 能量变化与键能
The enthalpy change (ΔH) of a reaction is the heat energy transferred at constant pressure. In an exothermic reaction, ΔH is negative (heat released); in an endothermic reaction, ΔH is positive (heat absorbed). Bond breaking is endothermic, bond making is exothermic.
反应的焓变（ΔH）是恒压条件下传递的热量。放热反应ΔH为负（释放热量），吸热反应ΔH为正（吸收热量）。断裂化学键吸热，形成化学键放热。
The overall enthalpy change can be estimated using average bond energies:
总焓变可通过平均键能估算：
ΔH = Σ (bond energies of bonds broken) − Σ (bond energies of bonds formed)
A negative result confirms an exothermic process. Activation energy (Eₐ) is the minimum energy colliding particles must have for a reaction to occur. Reaction profile diagrams illustrate ΔH and Eₐ.
计算结果为负值表明是放热过程。活化能（Eₐ）是发生反应时碰撞粒子必须具备的最低能量。反应进程图展示了ΔH和Eₐ。
8. Acids, Bases & pH | 酸、碱与pH
An acid is a proton (H⁺) donor; a base is a proton acceptor (Brønsted–Lowry theory). The pH scale measures the acidity of a solution: pH = −log₁₀[H⁺]. A low pH (0–6) indicates an acidic solution, pH 7 is neutral, and a high pH (8–14) indicates an alkaline solution.
酸是质子（H⁺）给予体，碱是质子接受体（布朗斯特–劳里理论）。pH标度用于衡量溶液的酸碱度：pH = −log₁₀[H⁺]。低pH（0–6）为酸性，pH 7为中性，高pH（8–14）为碱性。
Common strong acids fully ionise in water (e.g., HCl, H₂SO₄, HNO₃); weak acids partially ionise (e.g., CH₃COOH). Neutralisation: acid + base → salt + water. In terms of ions: H⁺ + OH⁻ → H₂O.
常见的强酸在水中完全电离（如HCl、H₂SO₄、HNO₃）；弱酸只部分电离（如CH₃COOH）。中和反应：酸 + 碱 → 盐 + 水。离子方程式：H⁺ + OH⁻ → H₂O。
9. Electrolysis & Faraday’s Laws | 电解与法拉第定律
Electrolysis is the decomposition of an ionic compound, when molten or in aqueous solution, by the passage of an electric current. The key principles: cations migrate to the cathode (negative electrode) and are reduced; anions migrate to the anode (positive electrode) and are oxidised.
电解是用电流使熔融态或水溶液中的离子化合物分解的过程。基本原理：阳离子向阴极（负极）迁移并被还原；阴离子向阳极（正极）迁移并被氧化。
The amount of substance discharged is proportional to the quantity of charge passed. Faraday’s constant (F) is 96 500 C/mol. Charge (Q) = current (I) × time (t). Moles of electrons = Q / F. For example, to deposit 1 mol of a metal Mⁿ⁺, n mol of electrons are required.
析出物质的量与通过的电量成正比。法拉第常数（F）为96 500 C/mol。电量 Q = 电流 I × 时间 t。电子的物质的量 = Q / F。例如，要析出1 mol的金属 Mⁿ⁺，需要 n mol电子。
10. Reversible Reactions & Equilibrium | 可逆反应与平衡
In a reversible reaction, products can react to re-form reactants. Dynamic equilibrium is reached when the forward and reverse rates are equal, and the concentrations of all species remain constant. The equilibrium constant (Kc) is the ratio of product concentrations to reactant concentrations, each raised to the power of its stoichiometric coefficient.
在可逆反应中，生成物可重新反应生成反应物。当正逆反应速率相等，所有物质的浓度不再变化时，即达到动态平衡。平衡常数（Kc）是生成物浓度与反应物浓度的比值，各浓度以其化学计量数为指数。
Le Chatelier’s principle states that if a system at equilibrium is subjected to a change in concentration, pressure, or temperature, the equilibrium position shifts to counteract the change. For instance, increasing temperature favours the endothermic direction.
勒夏特列原理指出，如果改变处于平衡状态的体系的浓度、压强或温度，平衡将向减弱这种改变的方向移动。例如，升高温度会使平衡向吸热方向移动。
11. Redox & Oxidation Numbers | 氧化还原与氧化数
Oxidation is originally defined as gain of oxygen or loss of hydrogen; reduction is loss of oxygen or gain of hydrogen. The modern electron-based definition: oxidation is loss of electrons, reduction is gain of electrons (OIL RIG). Redox reactions always involve simultaneous oxidation and reduction.
氧化最初定义为得氧或失氢；还原定义为失氧或得氢。现代基于电子的定义：氧化是失去电子，还原是得到电子（失升氧，得降还）。氧化还原反应总是同时包含氧化与还原过程。
Oxidation numbers (states) help identify redox processes. Key rules: the oxidation number of an uncombined element is 0; for simple ions it equals the charge; oxygen is usually −2, hydrogen +1. The sum of oxidation numbers in a compound is zero; in a polyatomic ion it equals the ion charge.
氧化数（化合价）有助于识别氧化还原过程。主要规则：游离态单质的氧化数为0；简单离子的氧化数等于其所带电荷；氧通常为−2，氢为+1。化合物中各元素氧化数之和为零；多原子离子中各元素氧化数之和等于离子所带电荷。
12. Periodic Trends & Bonding Theories | 周期规律与键合理论
The Periodic Table arranges elements in order of increasing atomic number. Periods correspond to electron shells; groups contain elements with the same number of outer-shell electrons, leading to similar chemical properties. Key trends across a period: atomic radius decreases, ionisation energy generally increases, and electronegativity increases.
元素周期表按原子序数递增的顺序排列。周期对应于电子层；族的元素具有相同的最外层电子数，因此化学性质相似。同周期主要规律：原子半径减小，电离能总体增大，电负性增强。
Bonding theories: ionic bonding involves transfer of electrons between metals and non-metals, forming a giant ionic lattice. Covalent bonding involves sharing of electrons between non‑metals, creating molecules or giant covalent structures. Metallic bonding is the electrostatic attraction between positive metal ions and a sea of delocalised electrons.
键合理论：离子键涉及金属与非金属之间的电子转移，形成巨型离子晶格。共价键涉及非金属原子间共享电子，形成分子或巨型共价结构。金属键是带正电的金属离子与离域电子海之间的静电吸引力。
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