📚 Formula & Theorem Quick Reference Handbook | 公式定理速查手册
Welcome to your Year 9 CIE Chemistry quick reference – a compact guide to the essential formulas, equations, and key principles you need to master. Whether you are revising for a topic test or preparing for the checkpoint, having these relationships at your fingertips will help you solve numerical problems and explain chemical behaviour with confidence. Keep this handbook handy, and make sure you practise applying each formula in context.
欢迎使用你的 Year 9 CIE 化学速查手册——这是一份涵盖核心公式、方程和关键原理的精简指南。无论你是在为主题测试复习，还是为 checkpoint 考试做准备，能随时查阅这些关系式都将帮助你自信地解决计算题并解释化学行为。请将本手册放在手边，并确保在具体情境中练习应用每条公式。
1. Relative Atomic Mass & Relative Molecular Mass | 相对原子质量与相对分子质量
The relative atomic mass (Aᵣ) of an element is the average mass of its atoms compared to 1/12th the mass of a carbon‑12 atom. For a compound, the relative molecular mass (Mᵣ) is the sum of the Aᵣ values of all atoms in the formula.
一种元素的相对原子质量 (Aᵣ) 是其原子的平均质量与碳‑12 原子质量的 1/12 之比。对于一种化合物，相对分子质量 (Mᵣ) 是化学式中所有原子的 Aᵣ 值之和。
Example: Water, H₂O: Mᵣ = (2 × 1) + 16 = 18
示例：水，H₂O：Mᵣ = (2 × 1) + 16 = 18
2. The Mole & Molar Mass | 摩尔与摩尔质量
One mole of any substance contains 6.02 × 10²³ particles (Avogadro’s constant). The molar mass (g/mol) is the mass of one mole of a substance, numerically equal to its Aᵣ or Mᵣ.
任何物质的一摩尔都含有 6.02 × 10²³ 个微粒（阿伏伽德罗常数）。摩尔质量（g/mol）是一摩尔物质的质量，数值上等于其 Aᵣ 或 Mᵣ。
n = m ÷ M
物质的量 = 质量 ÷ 摩尔质量
Where: n = amount in mol, m = mass in g, M = molar mass in g/mol. Always show the units when using this triangle.
其中：n = 物质的量（mol），m = 质量（g），M = 摩尔质量（g/mol）。使用此关系时请务必标注单位。
3. Percentage Composition & Empirical Formula | 百分含量与经验式
Percentage by mass of an element in a compound = (total mass of the element in one mole ÷ Mᵣ) × 100%. The empirical formula is the simplest whole‑number ratio of atoms in a compound, found from masses or percentage data.
化合物中某元素的质量百分数 =（一摩尔中该元素的总质量 ÷ 相对分子质量）× 100%。经验式是化合物中原子最简整数比，可通过质量或百分含量数据求得。
Steps to find empirical formula: 1) divide each mass (or %) by the element’s Aᵣ; 2) divide each result by the smallest number obtained; 3) write the whole‑number ratio.
求经验式的步骤： 1) 将各质量（或百分数）除以该元素的 Aᵣ；2) 将每个结果除以所得最小值；3) 写出整数比。
4. Concentration of Solutions | 溶液的浓度
The concentration of a solution tells us how much solute is dissolved in a given volume of solvent. The standard unit is mol/dm³, but g/dm³ is also used.
溶液的浓度表示在一定体积溶剂中溶解了多少溶质。标准单位是 mol/dm³，但也使用 g/dm³。
c = n ÷ V (in mol/dm³)
c = m ÷ V (in g/dm³)
Where V is the volume in dm³. Remember: 1 dm³ = 1000 cm³. Always convert volumes to dm³ before calculation.
其中 V 是以 dm³ 为单位的体积。请记住：1 dm³ = 1000 cm³。计算前务必将体积换算为 dm³。
5. Molar Gas Volume | 气体摩尔体积
At room temperature and pressure (r.t.p., typically 20 °C and 1 atm), one mole of any gas occupies 24 dm³. This gives a simple relationship between moles and gas volume.
在室温和常压下（r.t.p.，通常为 20 °C 和 1 atm），一摩尔任何气体的体积为 24 dm³。这提供了物质的量与气体体积之间的简单关系。
n = V(gas) ÷ 24 (at r.t.p.)
Use this to find the volume of gas produced in a reaction, or to calculate the amount of gas from a measured volume.
利用此关系可求出反应生成的气体体积，或通过测量体积计算气体的物质的量。
6. Density & Particle Theory | 密度与粒子理论
Density links the mass of a substance to its volume. For solids and liquids it is typically given in g/cm³; for gases, g/dm³.
密度将物质的质量与其体积联系起来。对固体和液体，单位通常为 g/cm³；对气体则为 g/dm³。
ρ = m ÷ V
Changes of state can be explained by the spacing and motion of particles. Solids have closely packed, vibrating particles; liquids have particles that can slide past each other; gases have widely spaced particles moving rapidly.
物态的变化可用微粒的间距和运动来解释。固体中微粒紧密排列并振动；液体中微粒可以相互滑过；气体中微粒间距很大并快速运动。
7. Rate of Reaction | 反应速率
The rate of a chemical reaction can be measured by the change in amount of a reactant or product per unit time. Common units are g/s, cm³/s, or mol/s.
化学反应的速率可通过单位时间内反应物或产物的量的变化来测量。常见单位有 g/s、cm³/s 或 mol/s。
Average rate = Δquantity ÷ Δtime
Factors affecting rate include temperature, concentration, surface area, and catalysts. Collision theory states that for a reaction to occur, particles must collide with energy greater than or equal to the activation energy and with the correct orientation.
影响速率的因素包括温度、浓度、表面积和催化剂。碰撞理论指出，要发生反应，微粒必须以大于或等于活化能的能量并以正确方向碰撞。
8. Energy Changes: Exothermic & Endothermic | 能量变化：放热与吸热
In an exothermic reaction, energy is released to the surroundings, usually as heat, causing a temperature rise. In an endothermic reaction, energy is absorbed from the surroundings, causing a temperature drop.
在放热反应中，能量释放到周围环境中（通常以热的形式），导致温度升高。在吸热反应中，能量从周围环境中吸收，导致温度降低。
Bond breaking is always endothermic; bond making is always exothermic. The overall enthalpy change ΔH can be negative (exothermic) or positive (endothermic).
断键总是吸热的；成键总是放热的。总焓变 ΔH 可以为负值（放热）或正值（吸热）。
A simple calorimetry experiment uses the formula: q = m × c × ΔT, where q = heat energy (J), m = mass of water (g), c = specific heat capacity (4.2 J/g°C), ΔT = temperature change.
简单的量热实验使用公式：q = m × c × ΔT，其中 q = 热能（J），m = 水的质量（g），c = 比热容（4.2 J/g°C），ΔT = 温度变化。
9. Writing & Balancing Chemical Equations | 书写与配平化学方程式
A chemical equation represents a reaction using symbols and formulas. The law of conservation of mass states that atoms are neither created nor destroyed, so the total mass of reactants equals the total mass of products.
化学方程式使用符号和化学式来表示反应。质量守恒定律指出，原子既不能被创造也不能被消灭，因此反应物的总质量等于生成物的总质量。
Steps: 1) Write the correct formula for each reactant and product; 2) Count the number of atoms of each element on both sides; 3) Add coefficients (big numbers) in front of formulas to balance the atoms; 4) Never change the formulas themselves.
步骤： 1) 写出每种反应物和生成物的正确化学式；2) 数出两边每种元素的原子个数；3) 在化学式前添加系数（大数字）使原子个数相等；4) 绝对不要改变化学式本身。
State symbols are used to show the physical state: (s) solid, (l) liquid, (g) gas, (aq) aqueous (dissolved in water).
状态符号用于表示物质的物理状态：(s) 固体，(l) 液体，(g) 气体，(aq) 水溶液（溶于水）。
10. pH Scale & Neutralisation | pH 标度与中和反应
The pH scale ranges from 0 to 14, indicating how acidic or alkaline a solution is. pH < 7 is acidic; pH = 7 is neutral; pH > 7 is alkaline. The scale is logarithmic, so each unit change represents a tenfold change in hydrogen ion concentration.
pH 标度范围为 0 到 14，表示溶液的酸碱程度。pH < 7 为酸性；pH = 7 为中性；pH > 7 为碱性。标度为对数尺度，每变化一个单位表示氢离子浓度改变十倍。
Neutralisation is a reaction between an acid and a base (or alkali) to produce a salt and water:
中和反应是酸与碱（或碱性物质）反应生成盐和水：
acid + base → salt + water
For example: HCl + NaOH → NaCl + H₂O. The ionic equation for neutralisation is: H⁺ + OH⁻ → H₂O.
例如：HCl + NaOH → NaCl + H₂O。中和反应的离子方程式为：H⁺ + OH⁻ → H₂O。
11. Electrolysis: Key Principles | 电解：关键原理
Electrolysis is the decomposition of an ionic compound when molten or in aqueous solution by the passage of an electric current. The substance being broken down is the electrolyte.
电解是指熔融或水溶液中的离子化合物在电流通过时发生分解的过程。被分解的物质称为电解质。
Positive ions (cations) move to the cathode (negative electrode) and gain electrons (reduction). Negative ions (anions) move to the anode (positive electrode) and lose electrons (oxidation). Use OIL RIG: Oxidation Is Loss of electrons, Reduction Is Gain of electrons.
阳离子（正离子）移向阴极（负极）并得到电子（还原）。阴离子（负离子）移向阳极（正极）并失去电子（氧化）。可使用记忆口诀 OIL RIG：氧化是失电子，还原是得电子。
For aqueous solutions, the products depend on the relative reactivity of the ions and the concentration. Hydrogen may form at the cathode if the metal is more reactive than hydrogen; oxygen or a halogen may form at the anode.
对于水溶液，产物取决于离子的相对活性和浓度。如果金属比氢更活泼，阴极可能生成氢气；阳极可能生成氧气或卤素。
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