📚 CIE IGCSE Chemistry: Quick Reference Formula & Theorem Handbook | CIE IGCSE 化学：公式定理速查手册
This article provides a concise, exam-focused summary of all essential formulae, definitions and common theorems required for the CIE IGCSE Chemistry syllabus. Use it for quick revision and to reinforce your quantitative chemistry skills.
本文为 CIE IGCSE 化学考纲所要求的全部核心公式、定义及常见定理提供一份简明、紧扣考点的总结。可用于快速复习并强化定量化学技能。
1. The Mole Concept | 摩尔概念
× 10²³ elementary entities (atoms, molecules, ions or electrons). This number is Avogadro's constant, Nₐ.
摩尔是物质的量单位，1 摩尔物质含有 6.02 × 10²³ 个基本粒子（原子、分子、离子或电子）。这个数字就是阿伏伽德罗常数，Nₐ。
n = m / M
ar mass is the mass of one mole of the substance and is numerically equal to the relative atomic or formula mass.
式中 n = 物质的量（摩尔），m = 质量（克），M = 摩尔质量（克/摩尔）。摩尔质量是 1 摩尔该物质的质量，数值上等于相对原子质量或相对式量。
tionship allows conversion between the number of atoms, molecules or formula units and the amount in moles.
微粒数 = n × Nₐ。通过这个关系可在原子、分子或化学式单元数量和摩尔数之间进行转换。
| Relationship | 关系 | Formula | 公式 |
|---|---|
| Mass to moles | 质量换算为摩尔 | n = m ÷ M |
| Particles to moles | 微粒数换算为摩尔 | n = number of particles ÷ Nₐ |
2. Empirical and Molecular Formulae | 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.
实验式表示化合物中各元素原子的最简整数比。分子式表示一个分子中各元素原子的实际数目。
To determine the empirical formula: convert the mass (or percentage) of each element to moles by dividing by its relative atomic mass; then divide each mole value by the smallest number of moles to obtain the simplest ratio.
确定实验式的方法：将每种元素的质量（或百分含量）除以各自的相对原子质量，换算成摩尔；然后用最小的摩尔数除以所有摩尔值，得到最简整数比。
ical formula) × n, where n = relative molecular mass ÷ relative mass of empirical formula.
分子式 = (实验式) × n，式中 n = 相对分子质量 ÷ 实验式的相对质量。
3. Molar Volume of Gases | 气体摩尔体积
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). This is known as the molar volume, Vₘ.
在常温常压下（r.t.p., 20 °C 和 1 atm），1 摩尔任何气体的体积为 24 dm³（24000 cm³）。这称为气体摩尔体积，Vₘ。
V = n × Vₘ
where V = volume of gas (dm³), n = amount of gas (mol), Vₘ = 24 dm³/mol at r.t.p.
式中 V = 气体体积（dm³），n = 气体的物质的量（摩尔），Vₘ = 24 dm³/摩尔（常温常压下）。
This formula is used to calculate the volume of gas produced or consumed in a reaction, or to find the number of moles from a measured gas volume.
此公式用于计算反应中产生或消耗的气体体积，或通过测量气体体积求出气体的摩尔数。
4. Concentration of Solutions | 溶液浓度
The concentration of a solution can be expressed either in mol/dm³ (molar concentration) or in g/dm³ (mass concentration).
溶液的浓度可以用 mol/dm³（摩尔浓度）或 g/dm³（质量浓度）表示。
c = n / V
f solution (dm³). Remember that 1 dm³ = 1000 cm³, so to convert cm³ to dm³ divide by 1000.
式中 c = 浓度（mol/dm³），n = 溶质的物质的量（摩尔），V = 溶液体积（dm³）。注意 1 dm³ = 1000 cm³，因此将 cm³ 转换为 dm³ 需要除以 1000。
m³). This can be linked to molar concentration via molar mass: mass concentration = c × M.
质量浓度（g/dm³）= 溶质质量（g）÷ 溶液体积（dm³）。通过摩尔质量可与摩尔浓度联系：质量浓度 = c × M。
5. Titration Calculations | 滴定计算
In an acid–base titration, the point at which the acid and base have reacted completely is the equivalence point. The key relationship for a 1:1 reaction is:
在酸碱滴定中，酸和碱恰好完全反应的点为等当点。对于 1:1 的反应，关键关系式为：
cₐVₐ = cₑVₑ
. All volumes must be in the same unit (usually dm³ or cm³) and concentrations in mol/dm³.
式中 cₐ = 酸的浓度，Vₐ = 酸的体积，cₑ = 碱的浓度，Vₑ = 碱的体积。所有体积必须使用相同单位（通常为 dm³ 或 cm³），浓度单位为 mol/dm³。
a₂SO₄ + 2H₂O, so n(NaOH) = 2 × n(H₂SO₄). Then c(NaOH) × V(NaOH) = 2 × c(H₂SO₄) × V(H₂SO₄).
若化学计量比不是 1:1，则须添加相应系数。例如 2NaOH + H₂SO₄ → Na₂SO₄ + 2H₂O，因此 n(NaOH) = 2 × n(H₂SO₄)。则 c(NaOH) × V(NaOH) = 2 × c(H₂SO₄) × V(H₂SO₄)。
6. Energy Changes in Reactions | 反应能量变化
The heat energy change in a reaction is often measured by recording the temperature change of the surrounding solution. The amount of heat transferred, q, is given by:
反应的热能变化通常通过测量周围溶液的温度变化来确定。传递的热量 q 由下式给出：
q = m c ΔT
(g), c = specific heat capacity (4.18 J g⁻¹ °C⁻¹ for water), ΔT = temperature change (°C).
式中 m = 溶液的质量（g），c = 比热容（水的比热容为 4.18 J g⁻¹ °C⁻¹），ΔT = 温度变化（°C）。
To find the molar enthalpy change, ΔH, divide the heat change by the number of moles reacting:
要得出摩尔焓变 ΔH，将热量变化除以反应的摩尔数：
ΔH = -q / n
The negative sign indicates whether the reaction is exothermic (q negative, ΔH negative) or endothermic (q positive, ΔH positive). ΔH is usually expressed in kJ/mol, so convert q (in J) to kJ by dividing by 1000.
负号表示反应是放热（q 为负，ΔH 为负）还是吸热（q 为正，ΔH 为正）。ΔH 通常以 kJ/mol 表示，因此需将 q（J）除以 1000 转换为 kJ。
7. Rates of Reaction | 反应速率
p or a product is formed. Average rate = change in amount (or concentration) ÷ time taken.
化学反应速率衡量反应物消耗或生成物形成的快慢。平均速率 = 物质的量（或浓度）的变化量 ÷ 所需时间。
rate = Δc / Δt
ate can also be expressed for a gas by measuring volume change per second: rate = ΔV / Δt.
式中 Δc = 浓度变化（mol/dm³），Δt = 时间变化（s）。对于气体反应，速率也可用每秒体积变化表示：rate = ΔV / Δt。
Factors affecting rate are explained by collision theory: particles must collide with sufficient energy (activation energy) and correct orientation. Increasing concentration, pressure (for gases), surface area (for solids) or temperature all increase the rate by increasing collision frequency or the energy of collisions. A catalyst increases the rate by providing an alternative reaction pathway with lower activation energy.
影响速率的因素可用碰撞理论解释：粒子必须以足够能量（活化能）和正确取向碰撞。增大浓度、压强（气体）、表面积（固体）或升高温度均能提高碰撞频率或碰撞能量，从而加快反应速率。催化剂通过提供活化能较低的替代反应路径来提高速率。
8. Reversible Reactions and Equilibrium | 可逆反应与平衡
In a closed system, a reversible reaction reaches dynamic equilibrium when the forward and reverse reactions occur at the same rate. The concentrations of reactants and products remain constant, but the reactions are still ongoing.
在密闭体系中，可逆反应当正逆反应速率相等时达到动态平衡。此时反应物和生成物浓度保持不变，但反应仍在持续进行。
Le Chatelier's principle states that if a system at equilibrium is subjected to a change in concentration, pressure or temperature, the position of equilibrium shifts to oppose that change.
勒夏特列原理指出，如果处于平衡态的体系受到浓度、压强或温度变化的影响，平衡会朝着减弱该变化的方向移动。
For example, increasing temperature favours the endothermic direction. Increasing pressure favours the side with fewer moles of gas. Adding a reactant favours the forward reaction, producing more product.
例如，升高温度有利于吸热方向；增大压强有利于气体摩尔数较少的一侧；加入反应物则有利于正向反应，生成更多产物。
Although a quantitative equilibrium constant (Kc) is not required at IGCSE level, you should be able to predict the shift in equilibrium position qualitatively according to Le Chatelier's principle.
虽然 IGCSE 阶段不要求定量计算平衡常数 Kc，但应能根据勒夏特列原理定性判断平衡移动方向。
9. Acids, Bases and pH | 酸碱与 pH
An acid is a substance that donates protons (H⁺ ions) when dissolved in water. A base is a substance that accepts protons (or releases OH⁻ ions). The strength of an acid depends on the extent of its dissociation: strong acids fully ionise in water (e.g. HCl, H₂SO₄, HNO₃), while weak acids partially ionise (e.g. ethanoic acid).
酸是溶于水时释放质子（H⁺）的物质。碱是接受质子（或释放 OH⁻）的物质。酸的强弱取决于其在水中电离的程度：强酸完全电离（如 HCl、H₂SO₄、HNO₃），弱酸部分电离（如乙酸）。
The pH scale is a measure of hydrogen ion concentration:
pH 标度是氢离子浓度的量度：
pH = -log₁₀[H⁺]
so [H⁺] = 10⁻ᵖᴴ ion of H⁺ ions. In pure water at 25 °C, [H⁺] = 1 × 10⁻⁷ mol/dm³, giving a neutral pH of 7.
故此 [H⁺] = 10⁻ᵖᴴ mol/dm³。pH 越小，H⁺ 浓度越高。在 25 °C 纯水中，[H⁺] = 1 × 10⁻⁷ mol/dm³，中性 pH = 7。
t 25 °C. This relationship links the concentrations of H⁺ and OH⁻ in any aqueous solution.
水的离子积 Kw = [H⁺][OH⁻] = 1 × 10⁻¹⁴ mol²/dm⁶（25 °C）。此关系将任何水溶液中的 H⁺ 和 OH⁻ 浓度联系起来。
10. Redox Reactions and Oxidation Numbers | 氧化还原反应与氧化数
Oxidation is the loss of electrons; reduction is the gain of electrons. An oxidising agent (oxidant) is reduced; a reducing agent (reductant) is oxidised. The transfer of electrons can be tracked using oxidation numbers (states).
氧化是失去电子，还原是得到电子。氧化剂（氧化剂）本身被还原，还原剂（还原剂）本身被氧化。电子转移可通过氧化数（氧化态）来追踪。
Key rules for assigning oxidation numbers:
确定氧化数的主要规则：
- Uncombined element: oxidation number = 0 (e.g. O₂, Mg).
单质元素：氧化数 = 0（如 O₂、Mg）。 - Simple monatomic ion: oxidation number equals its charge (e.g. Cl⁻ → -1, Al³⁺ → +3).
简单单原子离子：氧化数等于其所带电荷（如 Cl⁻ → -1，Al³⁺ → +3）。 - Oxygen in compounds is usually -2, except in peroxides (e.g. H₂O₂) where it is -1.
化合物中的氧通常为 -2，但在过氧化物（如 H₂O₂）中为 -1。 - Hydrogen in compounds is usually +1, except in metal hydrides (e.g. NaH) where it is -1.
化合物中的氢通常为 +1，但在金属氢化物（如 NaH）中为 -1。 - The sum of oxidation numbers in a neutral compound is 0; in a polyatomic ion it equals the ion's charge.
中性化合物中氧化数总和为 0；多原子离子中氧化数总和等于离子所带电荷。
In a redox reaction, oxidation is an increase in oxidation number; reduction is a decrease in oxidation number. Identifying these changes helps balance half-equations and overall equations in terms of both mass and charge.
在氧化还原反应中，氧化数升高为氧化，氧化数降低为还原。识别这些变化有助于配平半反应方程式和总方程式，同时兼顾质量守恒和电荷守恒。
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