📚 Year 10 Cambridge Chemistry: Formula & Theorem Quick Reference Handbook | 十年级剑桥化学：公式定理速查手册
This quick reference handbook brings together every essential formula, equation and calculation skill covered in the Year 10 Cambridge IGCSE Chemistry course. Use it to support your homework, test revision and practical write‑ups. Each section presents the key idea first in English and then in Chinese, so you can master the concepts and terminology in both languages.
本速查手册汇集了十年级剑桥 IGCSE 化学课程中所有必备的公式、方程式和计算技巧。你可以用它辅助作业、备考复习和实验报告撰写。每个小节先用英文阐述核心要点，再用中文配对讲解，帮助你同时掌握中英文的概念与术语。
1. Relative Atomic Mass (Aᵣ) & Isotopes | 相对原子质量 (Aᵣ) 与同位素
The relative atomic mass Aᵣ of an element is the weighted average mass of its isotopes relative to 1/12th the mass of a carbon‑12 atom. It is calculated from the percentage abundances and mass numbers of the isotopes.
元素的相对原子质量 Aᵣ 是其各种同位素相对于碳‑12 原子质量的 1/12 的加权平均质量。它根据同位素的丰度百分比和质量数计算得出。
Aᵣ = Σ (isotopic mass × % abundance) / 100
Aᵣ = Σ (同位素质量 × 丰度百分比) / 100
Example: chlorine has two stable isotopes, ³⁵Cl (75%) and ³⁷Cl (25%). Aᵣ(Cl) = (35 × 75 + 37 × 25) / 100 = 35.5.
例如：氯有两种稳定同位素，³⁵Cl (75%) 和 ³⁷Cl (25%)。 Aᵣ(Cl) = (35 × 75 + 37 × 25) / 100 = 35.5。
2. Relative Formula Mass (Mᵣ) & Percentage Composition | 相对式量 (Mᵣ) 与质量百分组成
The relative formula mass Mᵣ is the sum of the relative atomic masses of all atoms in a chemical formula. For ionic compounds we still call it the relative formula mass.
相对式量 Mᵣ 是化学式中所有原子的相对原子质量之和。对于离子化合物，我们仍称其为相对式量。
Mᵣ = Σ Aᵣ of atoms present
Mᵣ = 各原子 Aᵣ 之和
Percentage by mass of an element = (mass of that element in 1 formula unit / Mᵣ) × 100%. For example, in H₂O, Mᵣ = (2 × 1) + 16 = 18. %H = (2/18) × 100 = 11.1%.
元素的质量百分数 = (一个式单元中该元素的质量 / Mᵣ) × 100%。例如，水中 Mᵣ = (2 × 1) + 16 = 18，氢的质量百分比 = (2/18) × 100 = 11.1%。
3. The Mole & the Avogadro Constant | 摩尔与阿伏伽德罗常数
cles (atoms, molecules, ions or electrons). This number is the Avogadro constant, L or Nₐ.
1 摩尔任何物质恰好含有 6.02 × 10²³ 个微粒（原子、分子、离子或电子）。这个数字就是阿伏伽德罗常数，记作 L 或 Nₐ。
umber of moles × 6.02 × 10²³. The mole links the microscopic world to masses we can weigh.
微粒数 = 摩尔数 × 6.02 × 10²³。摩尔将微观世界与我们可以称量的质量联系了起来。
4. Mass–Mole Calculations | 质量‑摩尔计算
The amount of a substance n (mol) is calculated from its mass m (g) and its molar mass M (g/mol). Molar mass equals Aᵣ or Mᵣ expressed in grams per mole.
物质的量 n (mol) 由其质量 m (g) 和摩尔质量 M (g/mol) 计算得出。摩尔质量在数值上等于 Aᵣ 或 Mᵣ，单位为 g/mol。
n = m / M → m = n × M
Example: What mass of NaOH is in 0.500 mol? M(NaOH) = 23 + 16 + 1 = 40 g/mol, so m = 0.500 × 40 = 20.0 g.
示例：0.500 mol NaOH 的质量是多少？M(NaOH) = 23 + 16 + 1 = 40 g/mol，所以 m = 0.500 × 40 = 20.0 g。
5. Empirical & Molecular Formulae | 实验式与分子式
The empirical formula gives the simplest whole‑number ratio of atoms in a compound. The molecular formula tells you the actual number of each atom in a molecule.
实验式给出化合物中各原子的最简整数比。分子式则给出一个分子中每种原子的实际数目。
Steps for empirical formula: (1) convert mass or % ltiply the empirical formula by n, where n = (Mᵣ of compound) / (Mᵣ of empirical formula).
推导实验式的步骤：(1) 把质量或百分数换算为摩尔，(2) 除以最小的摩尔值，(3) 写出整数比。求分子式时，用 n 乘以实验式，其中 n = (化合物的 Mᵣ) / (实验式的 Mᵣ)。
6. Reacting Masses (Stoichiometry) | 反应质量（化学计量学）
ss calculations always follow this route: mass → moles → use mole ratio → mass of unknown.
配平后的化学方程式给出了反应物与生成物的摩尔比。反应质量计算始终遵循以下思路：质量 → 摩尔 → 利用摩尔比 → 未知物质量。
Example: 2Mg + O₂ → 2MgO. How many grams of MgO form from 48.0 g of Mg? mol. Ratio Mg:MgO = 2:2 = 1:1, so n(MgO)=2.0 mol. M(MgO)=40 g/mol, mass = 2.0×40 = 80.0 g.
示例：2Mg + O₂ → 2MgO。 48.0 g 镁能生成多少克 MgO？M(Mg)=24，n(Mg)=48/24=2.0 mol。 Mg:MgO = 2:2 = 1:1，因此 n(MgO)=2.0 mol，M(MgO)=40 g/mol，质量 = 2.0×40 = 80.0 g。
7. Concentration of Solutions | 溶液浓度
Concentration in mol/dm³ tells you how many moles of solute are dissolved in 1 dm³ of solution. It is the most common unit in titration calculations.
以 mol/dm³ 为单位的浓度表示 1 dm³ 溶液中溶解了多少摩尔溶质。这是滴定计算中最常用的单位。
c = n / V (c: mol/dm³, n: mol, V: dm³)
c = n / V (c: mol/dm³, n: mol, V: dm³)
centration: mass concentration (g/dm³) = c (mol/dm³) × Mᵣ. Remember that 1 dm³ = 1000 cm³.
你还可能见到质量浓度：质量浓度 (g/dm³) = c (mol/dm³) × Mᵣ。记住 1 dm³ = 1000 cm³。
8. Molar Volume of Gases (r.t.p.) | 气体摩尔体积（常温常压）
At room temperature and pressure (r.t.p., 20 °C and 1 atm), one mole of any gas occupies 24 dm³. This simplifies calculating gas volumes from moles.
在常温常压 (r.t.p., 20 °C 和 1 atm) 下，1 摩尔任何气体占据 24 dm³ 的体积。这使得通过摩尔计算气体体积变得很简单。
Volume (dm³) = n × 24 or n = Volume / 24
Example: How many moles of CO₂ are in 48 dm³ at r.t.p.? n = 48/24 = 2.0 mol.
示例：48 dm³ 的 CO₂ 在 r.t.p. 下有多少摩尔？ n = 48/24 = 2.0 mol。
9. Percentage Yield | 产率
The percentage yield compares the mass of product actually obtained to the theoretical maximum mass calculated from stoichiometry. It measures the efficiency of a reaction.
产率将实际获得的产品质量与根据化学计量计算的理论最大质量进行比较，用以衡量反应的效率。
% yield = (actual yield / theoretical yield) × 100%
产率 = (实际产量 / 理论产量) × 100%
A yield lower than 100% is common due to incomplete reactions, side reactions or product lost during purification.
由于反应不完全、发生副反应或产品在提纯过程中损失，产率通常低于 100%。
10. Atom Economy | 原子经济性
Atom economy tells you what fraction of the total mass of reactants ends up in the desired product. It is especially important when evaluating the ‘greenness’ of a synthesis.
原子经济性表示总反应物质量中有多少进入了目标产物。它对于评估合成路线的“绿色”程度格外重要。
Atom economy = (Mᵣ of desired product / Σ Mᵣ of all reactants) × 100%
原子经济性 = (目标产物的 Mᵣ / 所有反应物 Mᵣ 之和) × 100%
A higher atom economy means less waste and a more sustainable process. Addition reactions usually give 100% atom economy.
原子经济性越高，意味着废弃物越少且工艺更具可持续性。加成反应的原子经济性通常可达 100%。
11. Energy Changes: q = mcΔT | 能量变化：q = mcΔT
When a reaction is carried out in solution, the heat energy absorbed or released can be measured using a simple calorimeter. The fundamental equation links heat energy, mass, specific heat capacity and temperature change.
当反应在溶液中进行时，吸收或放出的热能可以用简易量热计测量。基本公式将热能、质量、比热容和温度变化联系起来。
q = m × c × ΔT
- q = heat energy (J)
- m = mass of solution (g, often the mass of water)
- c = specific heat capacity (typically 4.2 J/g°C for water)
- ΔT = temperature change (°C)
q = m × c × ΔT
- q = 热能 (J)
- m = 溶液质量 (g，通常是水的质量)
- c = 比热容 (水约为 4.2 J/g°C)
- ΔT = 温度变化 (°C)
To find the enthalpy change per mole, divide q by the number of moles that reacted: ΔH = –q / n (negative for exothermic).
要获得每摩尔的焓变，用 q 除以反应的摩尔数：ΔH = –q / n (放热反应 ΔH 为负)。
12. Rate of Reaction | 反应速率
The average rate of a reaction describes how quickly a reactant is consumed or a product is made. It is defined as the change in amount per unit time.
平均反应速率描述了反应物消耗或产物生成的快慢，其定义为每单位时间内物质的量的变化。
Average rate = Δ quantity / Δ time
平均速率 = Δ 量 / Δ 时间
reaction, rate ≈ 1/time taken for a cross to disappear (an arbitrary but useful measure).
该“量”可以是质量 (g)、气体体积 (cm³) 或浓度 (mol/dm³)。对于生成气体的反应，速率 = 气体体积 / 时间。对于生成沉淀的反应，可用“十字消失时间”的倒数来近似表示速率（一种人为定义但很有用的量度）。
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