📚 Year 9 CAIE Chemistry: Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This quick reference handbook brings together the essential formulas, definitions, and fundamental theorems you need for Year 9 CAIE Chemistry. From relative atomic mass and the mole concept to solution concentration and pH, every topic is explained with clear paired English–Chinese explanations. Whether you are preparing for an end‑of‑topic test or building a solid foundation for IGCSE, this guide will help you recall key calculations and principles quickly and accurately.
这本速查手册汇集了Year 9 CAIE化学所需的核心公式、定义和基本定理。从相对原子质量和摩尔概念到溶液浓度和pH，每个主题都配有清晰的中英对照解释。无论你是在准备单元测验，还是在为IGCSE打下扎实基础，这份指南都能帮助你快速、准确地回顾关键计算和原理。
1. Atomic Structure & Relative Atomic Mass (Aᵣ) | 原子结构与相对原子质量
Atoms are made of protons, neutrons and electrons. The atomic number (Z) is the number of protons, and the mass number (A) is the total number of protons plus neutrons. Isotopes are atoms of the same element with different numbers of neutrons, hence different mass numbers.
原子由质子、中子和电子组成。原子序数(Z)是质子数，质量数(A)是质子数加中子数的总和。同位素是同一元素中中子数不同的原子，因此质量数不同。
Relative atomic mass, Aᵣ, is the average mass of all the isotopes of an element compared to 1/12 the mass of a carbon‑12 atom. The formula used to calculate Aᵣ from isotopic abundances is:
相对原子质量 Aᵣ 是指某元素所有同位素的平均质量与一个碳‑12原子质量的1/12相比较所得的数值。通过同位素丰度计算Aᵣ的公式为:
Aᵣ = (abundance%₁ × mass number₁ + abundance%₂ × mass number₂ + ...) / 100
For example, chlorine has two main isotopes: ⁷⁵Cl (75%) and ³⁷Cl (25%). Aᵣ(Cl) = (75 × 35 + 25 × 37) / 100 = 35.5.
例如，氯有两种主要同位素: ³⁵Cl (75%) 和 ³⁷Cl (25%)。Aᵣ(Cl) = (75 × 35 + 25 × 37) / 100 = 35.5。
2. Relative Molecular Mass (Mᵣ) & Formula Mass | 相对分子质量与化学式质量
The relative molecular mass, Mᵣ, is the sum of the relative atomic masses of all the atoms in a molecule. For ionic compounds we use the term relative formula mass, but the calculation method is identical.
相对分子质量 Mᵣ 是分子中所有原子的相对原子质量的总和。对于离子化合物，我们使用“相对化学式质量”这一术语，但计算方法完全相同。
Key rule: multiply the Aᵣ of each element by the number of atoms of that element shown in the formula, then add the results.
关键规则: 将每种元素的 Aᵣ 乘以该元素在化学式中的原子个数，然后相加。
Mᵣ(H₂O) = 2 × 1 + 16 = 18
Mᵣ(H₂O) = 2 × 1 + 16 = 18
Mᵣ(CO₂) = 12 + 2 × 16 = 44
Mᵣ(CO₂) = 12 + 2 × 16 = 44
Formula mass of CaCO₃ = 40 + 12 + 3 × 16 = 100
CaCO₃ 的化学式量 = 40 + 12 + 3 × 16 = 100
Always show your working clearly and remember that Mᵣ has no unit.
一定要清晰地写出计算过程，并记住 Mᵣ 没有单位。
3. The Mole Concept & Molar Mass (M) | 摩尔概念与摩尔质量
One mole of a substance contains 6.02 × 10²³ particles (Avogadro' Numerically, M is equal to the relative atomic mass (Aᵣ) or relative molecular mass (Mᵣ).
一摩尔物质含有 6.02 × 10²³ 个粒子（阿伏伽德罗常数）。摩尔质量 M 是一摩尔物质的质量，单位为 g/mol。数值上，M 等于相对原子质量 Aᵣ 或相对分子质量 Mᵣ。
The crucial formula linking mass, moles and molar mass is:
联系质量、摩尔数和摩尔质量的关键公式是:
n = m / M
where n = number of moles (mol), m = mass (g), M = molar mass (g/mol).
式中 n = 摩尔数 (mol)，m = 质量 (g)，M = 摩尔质量 (g/mol)。
formula: m = n × M and M = m / n. Always convert mass into grams before using the formula.
你可以变形这个公式: m = n × M 以及 M = m / n。在使用公式前一定要将质量单位换算成克。
| Quantity (物理量) | Symbol (符号) | Unit (单位) |
|---|---|---|
| Mass (质量) | m | g |
| Moles (摩尔数) | n | mol |
| Molar mass (摩尔质量) | M | g/mol |
4. Molar Gas Volume & Avogadro's Law | 气体摩尔体积与阿伏伽德罗定律
Avogadro's law states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. At room temperature and pressure (r.t.p., 20 °C and 1 atm), one mole of any gas occupies 24 dm³ (24 000 cm³).
阿伏伽德罗定律指出，在相同温度和压力下，相同体积的任何气体都含有相同数量的分子。在常温常压下 (r.t.p., 20 °C 和 1 atm)，一摩尔任何气体所占体积为 24 dm³ (24 000 cm³)。
The formula for gas volume is:
气体体积计算公式为:
V = n × Vₘ
he units of volume match: if Vₘ is in dm³, V is in dm³; if using cm³, Vₘ = 24 000 cm³/mol.
式中 V 是体积，n 是摩尔数，Vₘ 是气体摩尔体积（常温常压下为 24 dm³/mol）。注意体积单位要一致: 如果 Vₘ 用 dm³，V 也用 dm³；如果使用 cm³，Vₘ = 24 000 cm³/mol。
Example: What volume does 0.5 mol of CO₂ occupy at r.t.p.? V = 0.5 × 24 = 12 dm³.
例题: 0.5 mol CO₂ 在常温常压下占多大体积？V = 0.5 × 24 = 12 dm³。
5. Concentration of Solutions | 溶液浓度
Concentration tells us how much solute is dissolved in a certain volume of solvent. The most common concentration unit in CAIE Chemistry is mol/dm³ (molarity).
浓度表示一定体积溶剂中溶解了多少溶质。CAIE化学中最常用的浓度单位是 mol/dm³ (摩尔浓度)。
The formula is:
公式为:
c = n / V
here c = concentration (mol/dm³), n = moles of solute (mol), V = volume of solution (dm³).
式中 c = 浓度 (mol/dm³)，n = 溶质的摩尔数 (mol)，V = 溶液的体积 (dm³)。
) = concentration (mol/dm³) × M. Often you need to convert cm³ to dm³ by dividing by 1000.
你也可以用 g/dm³ 表示浓度，换算关系为: 浓度 (g/dm³) = 浓度 (mol/dm³) × M。经常需要将 cm³ 转换为 dm³，只需除以 1000。
Dilution: when water is added, the number of moles of solute stays the same. This gives the dilution formula:
稀释: 加水时溶质的摩尔数保持不变。由此得到稀释公式:
c₁V₁ = c₂V₂
where c₁, V₁ are the initial concentration and volume, and c₂, V₂ are the final concentration and volume.
式中 c₁、V₁ 是初始浓度和体积，c₂、V₂ 是最终浓度和体积。
6. Percentage Composition & Purity | 百分组成与纯度
Percentage composition by mass gives the mass of each element present in a compound as a percentage of the total mass. The formula is:
质量百分组成是指化合物中每种元素的质量占化合物总质量的百分比。公式为:
% element = (total mass of the element in 1 mole of compound / Mᵣ of compound) × 100%
For example, the percentage of oxygen in H₂O is (mass of O / Mᵣ H₂O) × 100% = (16 / 18) × 100% = 88.9%.
例如，水中氧元素的百分含量为 (氧的质量 / 水的 Mᵣ) × 100% = (16 / 18) × 100% = 88.9%。
Purity of a sample is often expressed as a percentage. It is the mass of the pure substance divided by the total mass of the impure sample, multiplied by 100%.
样品纯度通常用百分比表示。它是纯物质的质量除以不纯样品的总质量，再乘以 100%。
% purity = (mass of pure substance / mass of sample) × 100%
This formula is very useful when calculating the actual amount of reactant taking part in a reaction.
这个公式在计算参与反应的实际反应物数量时非常有用。
7. Law of Conservation of Mass & Balancing Equations | 质量守恒定律与化学方程式配平
The law of conservation of mass states that matter cannot be created or destroyed in a chemical reaction. Therefore, the total mass of the reactants must equal the total mass of the products.
质量守恒定律指出，在化学反应中物质既不能凭空产生也不能凭空消失。因此，反应物的总质量一定等于生成物的总质量。
This law is the foundation of balancing chemical equations. The number of atoms of each element must be the same on both sides of the arrow.
这一定律是配平化学方程式的基础。箭头两边每一种元素的原子数目必须相等。
Balancing steps: (1) Write the correct formulas for all reactants and products. (2) Count the atoms of each element on both sides. (3) Add coefficients (numbers in front of the formulas) to balance the atoms one element at a time. (4) Check that all coefficients are in the lowest whole‑number ratio.
配平步骤: (1) 写出所有反应物和生成物的正确化学式。(2) 数一数两边每种元素的原子数。(3) 通过添加系数（化学式前面的数字）逐一配平各元素的原子。(4) 检查所有系数是否为最简整数比。
e total mass of reactants (16 + 64 = 80) equals the total mass of products (44 + 36 = 80).
示例: CH₄ + 2O₂ → CO₂ + 2H₂O。反应物总质量 (16 + 64 = 80) 等于生成物总质量 (44 + 36 = 80)。
Using balanced equations, we can calculate reacting masses and moles—this is called stoichiometry. The mole ratio from the equation is the key to all calculations.
利用配平后的方程式，我们可以计算反应物和生成物的质量与摩尔数，这叫做化学计量学。方程式给出的摩尔比是所有计算的关键。
8. Law of Definite Proportions | 定比定律
The law of definite proportions (also called the law of constant composition) states that a given chemical compound always contains its component elements in a fixed mass ratio, regardless of its source or how it was prepared.
定比定律（又称定组成定律）指出，一种给定的化合物总是以固定的质量比包含其组成元素，无论其来源或制备方法如何。
For example, pure water always has a hydrogen‑to‑ = 2:16). This means every 9 g of water contains exactly 1 g of hydrogen and 8 g of oxygen.
例如，纯水中氢与氧的质量比始终是 1 : 8 (H:O = 2:16)。这意味着每9克水恰含1克氢和8克氧。
This law helps us identify and confirm the purity of a compound and distinguishes compounds from mixtures.
这条定律帮助我们识别并确认化合物的纯度，并将化合物与混合物区分开来。
9. The Reactivity Series & Displacement | 金属活动性顺序与置换反应
The reactivity series is a list of metals arranged in order of decreasing reactivity. A common mnemonic: Potassium, Sodium, Calcium, Magnesium, Aluminium, (Carbon), Zinc, Iron, (Hydrogen), Copper, Silver, Gold.
金属活动性顺序是按金属活泼性由强到弱排成的表。常用的记忆顺序: 钾、钠、钙、镁、铝、(碳)、锌、铁、(氢)、铜、银、金。
A more reactive metal can displace a less reactive metal from its compound in an aqueous solution or molten state. The general equation is:
较活泼的金属可以将较不活泼的金属从其化合物的水溶液或熔融盐中置换出来。通式为:
al + less reactive metal’s compound → less reactive metal + more reactive metal’s compound
+ ZnSO₄(aq). Zinc displaces copper because zinc is above copper in the reactivity series.
示例: Zn(s) + CuSO₄(aq) → Cu(s) + ZnSO₄(aq)。锌将铜置换出来，因为锌在活动性顺序中位于铜之上。
This principle is used to extract metals and predict whether a reaction will occur. A theoretical rule: if element A is above element B in the series, A displaces B.
这一原理用于提炼金属和预测反应是否会发生。理论规则: 若元素A在顺序表中位于元素B之上，则A能将B置换出来。
10. pH Scale & Neutralisation Formula | pH标度与中和公式
The pH scale measures how acidic or basic a solution is. It ranges from 0 (strongly acidic) to 14 (strongly alkaline), with 7 being neutral. The mathematical definition is:
pH标度用来衡量溶液的酸碱性。范围从0（强酸性）到14（强碱性），7为中性。其数学定义为:
pH = -log₁₀[H⁺]
where [H⁺] is the concentration of hydrogen ions in mol/dm³. A change of one pH unit means a tenfold change in [H⁺].
式中 [H⁺] 为氢离子浓度，单位 mol/dm³。pH值每变化1个单位，[H⁺] 就改变10倍。
Neutralisation is the reaction between an acid and a base to produce salt and water. The general ionic equation for neutralisation is:
中和反应是酸与碱反应生成盐和水的过程。中和反应的通式离子方程式为:
H⁺(aq) + OH⁻(aq) → H₂O(l)
When an acid reacts with a metal carbonate, a salt, water and carbon dioxide are formed:
当酸与金属碳酸盐反应时，生成盐、水和二氧化碳:
acid + metal carbonate → salt + water + CO₂
Titration calculations often use the formula cₐVₐ / a = cbV tric coefficients of acid and base from the balanced equation. This is an extension of the mole ratio concept.
滴定计算常用公式 cₐVₐ / a = cbV_b / b，式中 a 和 b 分别为配平方程式中酸和碱的化学计量系数。这是摩尔比概念的延伸。
11. Electrolysis Basics & Faraday's Rule (Qualitative) | 电解基础与法拉第规则（定性）
Electrolysis is the breakdown of an ionic compound, when molten or in solution, by passing an electric current. Positive ions (cations) move to the cathode, negative ions (anions) move to the anode.
电解是指让电流通过熔融态或溶液中的离子化合物，使其分解的过程。阳离子移向阴极，阴离子移向阳极。
Faraday's first law (simplified): The mass of substance produced at an electrode is directly proportional to the quantity of electricity passed. The quantity of electricity, Q, is measured in coulombs and is given by:
法拉第第一定律（简化表述）: 电极上生成物质的质量与通过的电量成正比。电量 Q 的单位为库仑，计算公式为:
Q = I × t
where I = current (A), t = time (s). In Year 9, we often compare products qualitatively— electrolysis of brine, chlorine gas is produced at the anode and hydrogen at the cathode.
式中 I = 电流 (A)，t = 时间 (s)。在Year 9阶段，我们通常对产物进行定性比较——例如，电解盐水时阳极生成氯气，阴极生成氢气。
The reactivity of metals influences the order of discharge at the cathode: the less reactive the metal, the easier it is reduced. In aqueous solutions, hydrogen is often produced if the metal is above hydrogen in the reactivity series.
金属的活动性影响阴极放电顺序: 金属越不活泼，越容易被还原。在水溶液中，若金属在活动性顺序中位于氢之上，则往往生成氢气。
12. Key Reminders & Exam Tips | 重点提醒与考试技巧
Always write down the formula you are using before substituting numbers. This shows the examiner your reasoning. State the units in your final answer and check that they make sense.
务必先写出所使用的公式，再代入数字。这样可以向考官展示你的推导过程。在最终答案中写明单位，并检查单位是否合理。
When dealing with gas calculations, state whether you are using r.t.p. or standard conditions. Convert volumes to dm³ if you are using molar gas volume 24 dm³/mol; use 24 000 cm³/mol if you are keeping cm³.
进行气体计算时，要说明用的是常温常压还是标准状况。如果使用气体摩尔体积 24 dm³/mol，则需将体积换算成 dm³；如果保留 cm³，则使用 24 000 cm³/mol。
Balancing equations is a skill that improves with practice. Start with elements that appear in only one reactant and one product. Leave oxygen and hydrogen until last. After balancing, count all atoms again.
配平方程式是一项熟能生巧的技能。从只出现在一种反应物和一种生成物中的元素开始配平。最后再处理氧和氢。配平之后再数一次所有原子数目。
Remember that Avogadro' of particles in one mole of substance. Use it when you are asked about the number of atoms, ions or molecules.
记住阿伏伽德罗常数 (6.02 × 10²³) 是一摩尔物质中所含的粒子数。当题目问及原子、离子或分子数目时使用它。
Finally, when a calculation seems tricky, break it down into three steps: (1) find the moles of a known substance, (2) use the mole ratio from the equation to find moles of the unknown, (3) convert moles to the required quantity (mass, volume or concentration). This 'mole bridge' approach solves almost every stoichiometry problem.
最后，如果计算看起来很棘手，就把它分解为三个步骤: (1) 计算已知物质的摩尔数，(2) 利用方程式的摩尔比求出未知物的摩尔数，(3) 将摩尔数转化成所需的物理量（质量、体积或浓度）。这种“摩尔桥”方法能解决几乎所有的化学计量问题。
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