📚 GCSE AQA Chemistry: Formula Summary Handbook | GCSE AQA 化学：公式汇总手册
Welcome to your essential formula handbook for GCSE AQA Chemistry. This guide brings together every key equation required for the exams, covering quantitative chemistry, energy changes, rates of reaction, and more. Each formula is explained with clear units and typical applications, so you can master calculations and boost your confidence. Use it to revise systematically, practise worked examples, and check your understanding before the big day.
欢迎使用这本GCSE AQA化学必备公式手册。本指南汇集了考试所需的每一个关键方程式，涵盖定量化学、能量变化、反应速率等内容。每个公式都配有清楚的单位和典型应用说明，帮助你掌握计算并增强信心。你可以用它系统复习、练习例题，并在考试前检验自己的理解。
1. Relative Atomic Mass (Aᵣ) | 相对原子质量 (Aᵣ)
The relative atomic mass of an element is a weighted average mass of its isotopes compared to 1/12th the mass of carbon-12. It is used directly from the Periodic Table for calculations.
相对原子质量是元素各同位素质量的加权平均值，与¹²C原子质量的1/12相比较。计算时直接使用周期表中的数值。
Formula: Aᵣ = (sum of (isotope mass × % abundance)) / 100
公式：Aᵣ = (各同位素质量 × 丰度%)之和 / 100
Units: no unit (it is a relative value).
单位：无（相对值）。
- Used to calculate relative formula mass (Mᵣ) and moles.
- 用于计算相对式量 (Mᵣ) 和摩尔数。
2. Relative Formula Mass (Mᵣ) | 相对式量 (Mᵣ)
Relative formula mass is the sum of the relative atomic masses of all atoms in the formula of a compound. It is often just called ‘Mr’ and is used in mole calculations.
相对式量是化合物化学式中所有原子的相对原子质量之和。常简称为Mr，用于摩尔计算。
Formula: Mᵣ = Σ (Aᵣ of each element × number of atoms)
公式：Mᵣ = Σ (各元素Aᵣ × 原子个数)
Example: Mᵣ of H₂O = (2×1) + 16 = 18
示例：H₂O的Mᵣ = (2×1) + 16 = 18
3. The Mole and Avogadro Constant | 摩尔与阿伏伽德罗常数
The mole is the unit for amount of substance. One mole contains 6.02 × 10²³ particles (atoms, molecules, ions, or electrons). This value is the Avogadro constant.
摩尔是物质的量的单位。1摩尔含有6.02 × 10²³个粒子（原子、分子、离子或电子），这个数值即为阿伏伽德罗常数。
Formula to find number of particles: number of particles = moles × (6.02 × 10²³)
求粒子数的公式：粒子数 = 摩尔数 × (6.02 × 10²³)
This constant links the microscopic world to measurable masses.
这个常数将微观世界与可测量的质量联系起来。
4. Moles, Mass and Molar Mass | 摩尔、质量与摩尔质量
The most central formula in quantitative chemistry connects mass, moles and molar mass (which is numerically equal to Mᵣ in g/mol).
定量化学最核心的公式将质量、摩尔数与摩尔质量（数值上等于Mᵣ，单位g/mol）联系起来。
moles = mass (g) / Mᵣ (g/mol)
摩尔数 = 质量 (g) / Mᵣ (g/mol)
Rearrange as needed: mass = moles × Mᵣ
需要时可变换：质量 = 摩尔数 × Mᵣ
- Used to find reacting masses, limiting reagents, and percentage yield.
- 用于计算反应质量、限量试剂和产率百分比。
5. Conservation of Mass and Reacting Masses | 质量守恒与反应质量
In a chemical reaction, the total mass of reactants equals the total mass of products. Use the mole ratio from the balanced equation to calculate the mass of a substance required or produced.
化学反应中，反应物的总质量等于生成物的总质量。利用配平方程式中的摩尔比，可计算所需或生成的物质质量。
Steps: calculate moles of known substance → use mole ratio → find moles of unknown → convert to mass.
步骤：计算已知物质的摩尔数 → 使用摩尔比 → 求出未知物的摩尔数 → 转换为质量。
| Step | Action |
| 1 | Write balanced equation |
| 2 | Calculate moles of given substance (mass/Mᵣ) |
| 3 | Use mole ratio to find moles of target substance |
| 4 | Convert moles to mass (moles × Mᵣ) |
步骤：1. 写出配平方程式；2. 计算已知物质摩尔数 (质量/Mᵣ)；3. 利用摩尔比求目标物质摩尔数；4. 换算为质量 (摩尔数 × Mᵣ)。
6. Concentration of Solutions | 溶液的浓度
Concentration describes how much solute is dissolved in a given volume of solvent. In GCSE Chemistry, two main units are used: g/dm³ and mol/dm³.
浓度表示一定体积溶剂中溶解了多少溶质。GCSE化学主要使用两种单位：g/dm³和mol/dm³。
Concentration (g/dm³) = mass of solute (g) / volume of solution (dm³)
浓度 (g/dm³) = 溶质质量 (g) / 溶液体积 (dm³)
Remember: 1 dm³ = 1000 cm³. Always convert cm³ to dm³ by dividing by 1000.
注意：1 dm³ = 1000 cm³。务必通过除以1000将cm³转化为dm³。
For molar concentration: concentration (mol/dm³) = moles of solute / volume (dm³)
摩尔浓度：浓度 (mol/dm³) = 溶质的摩尔数 / 体积 (dm³)
7. Titration Calculations | 滴定计算
Titrations use known concentrations and volumes to find an unknown concentration. The key relationship uses the mole ratio from the balanced equation.
滴定利用已知浓度和体积来求未知浓度。关键关系是利用配平方程式中的摩尔比。
Formula: moles of known solution = concentration × volume (in dm³)
公式：已知溶液的摩尔数 = 浓度 × 体积 (dm³)
Then use the ratio: if ratio is 1:1, moles of unknown = moles of known; if 2:1, multiply or divide accordingly. Finally calculate unknown concentration = moles / volume.
然后利用比例：若比为1:1，未知物摩尔数 = 已知物摩尔数；若为2:1，相应乘除。最后计算未知浓度 = 摩尔数 / 体积。
Always convert average titre volume to dm³ (÷1000).
始终将平均滴定体积换算为dm³ (÷1000)。
8. Atom Economy | 原子经济性
Atom economy measures the efficiency of a reaction in converting reactants into the desired product. High atom economy reduces waste and is a principle of Green Chemistry.
原子经济性衡量反应将反应物转化为目标产物的效率。高原子经济性可减少废物，是绿色化学的一项原则。
Atom economy (%) = (Mᵣ of desired product / Σ Mᵣ of all reactants) × 100
原子经济性 (%) = (所需产物的Mᵣ / 所有反应物的Mᵣ之和) × 100
By adding up the Mᵣ of all reactants (as per the balanced equation), you can compare reactions to choose the more sustainable one.
通过加总所有反应物的Mᵣ（按配平方程式），可以比较不同反应，选择更可持续的反应。
9. Percentage Yield | 产率百分比
Percentage yield compares the actual mass of product obtained from an experiment to the theoretical mass calculated from the balanced equation. It is never above 100% due to practical losses.
产率百分比将实验实际获得的产物质量与根据配平方程式计算的理论质量进行比较。由于实际损失，产率绝不会超过100%。
Percentage yield = (actual mass / theoretical mass) × 100
产率百分比 = (实际质量 / 理论质量) × 100
- Reasons for less than 100%: incomplete reaction, side reactions, product lost during purification.
- 低于100%的原因：反应不完全、副反应、纯化过程中产物损失。
10. Energy Changes: Bond Energies | 能量变化：键能
Using bond energies, you can calculate the overall heat energy change (ΔH) for a reaction. Energy is absorbed to break bonds and released when bonds form.
利用键能可以计算反应的总热能量变化 (ΔH)。断键需要吸收能量，成键时释放能量。
ΔH = total energy absorbed for bond breaking − total energy released for bond forming
ΔH = 断裂键吸收的总能量 − 形成键释放的总能量
If ΔH is negative, the reaction is exothermic; if positive, it is endothermic. Use the bond energies (kJ/mol) provided in the exam.
若ΔH为负，反应放热；若为正，反应吸热。使用考题给出的键能数据 (kJ/mol)。
11. Rate of Reaction | 反应速率
The rate of reaction tells us how quickly reactants are used up or products are made. It can be expressed in terms of mass loss, volume of gas produced, or change in concentration over time.
反应速率表示反应物消耗或产物生成的快慢。可用质量减少、产生气体的体积或浓度随时间的变化来表示。
Two common formulae:
两个常用公式：
mean rate = quantity of reactant used or product formed / time
平均速率 = 反应物消耗量或产物生成量 / 时间
If measuring gas volume: mean rate = change in volume (cm³) / time (s). Units: cm³/s.
若测量气体体积：平均速率 = 体积变化 (cm³) / 时间 (s)。单位：cm³/s。
If using mass loss: mean rate = mass lost (g) / time (s). Units: g/s.
若采用质量减少：平均速率 = 损失的质量 (g) / 时间 (s)。单位：g/s。
For a graph, the rate at a specific point is the gradient (slope) of the tangent at that point.
从图上，某时刻的瞬时速率是该点切线的斜率。
12. Ideal Gas Equation (Triple/HT) | 理想气体方程 (仅限Triple/高等级)
At higher tier and Triple Science, you may be asked to use the relationship between volume and moles of a gas at room temperature and pressure (rtp).
在高等级和Triple Science中，可能要求使用室温常压下气体体积与摩尔数的关系。
At rtp (20 °C, 1 atm), one mole of any gas occupies 24 dm³ (24000 cm³).
在室温常压下 (20 °C, 1 atm)，1摩尔任何气体体积为24 dm³ (24000 cm³)。
Volume (dm³) = moles × 24
气体体积 (dm³) = 摩尔数 × 24
Rearrange: moles = volume (dm³) / 24. Always ensure volume is in dm³.
变换：摩尔数 = 体积 (dm³) / 24。务必保证体积单位是dm³。
- This molar volume rule applies only to gases at rtp.
- 此摩尔体积法则仅适用于室温常压下的气体。
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