📚 IGCSE CIE Chemistry Formula Handbook | IGCSE CIE 化学公式汇总手册
Mastering the key formulas in IGCSE CIE Chemistry is essential for solving numerical problems confidently in Paper 3 (Theory) and Paper 5 (Practical Test). This handbook brings together all the equations you need – clearly stated, with units and conditions explained. Use it alongside past papers to build speed and accuracy.
掌握 IGCSE CIE 化学的核心公式，对于在 Paper 3（理论卷）和 Paper 5（实验卷）中自信地解答计算题至关重要。本手册汇总了你需要的所有方程式，清晰说明单位和使用条件。结合历年真题使用，有助于提高解题速度和准确性。
1. The Mole and Molar Mass | 摩尔与摩尔质量
The mole is the central unit linking mass, particles and volume. The number of moles (n) can be found from the mass of a substance and its molar mass (Mr or Ar).
摩尔是连接质量、粒子数和体积的核心单位。物质的摩尔数（n）可以通过物质的质量与其摩尔质量（Ar 或 Mr）求得。
- n = m / M
- where n = amount of substance (mol), m = mass (g), M = molar mass (g/mol)
- n = 物质的量（mol），m = 质量（g），M = 摩尔质量（g/mol）
n = m / M
Molar mass Mr is the sum of relative atomic masses (Ar) from the Periodic Table. For elements, use Ar in g/mol. For compounds, add up all atoms present.
摩尔质量 Mr 是周期表中相对原子质量（Ar）的总和。单质使用 Ar（单位 g/mol）；对于化合物，将所有原子的相对原子质量相加即可。
This formula also rearranges to m = n × M and M = m / n. Always check that units match – mass in grams, not kilograms.
该公式还可变形为 m = n × M 以及 M = m / n。务必检查单位一致 – 质量用克（g），而非千克（kg）。
2. Molar Volume of Gases | 气体摩尔体积
At room temperature and pressure (r.t.p.), one mole of any gas occupies 24 dm³. This allows you to convert between volume and moles without needing the mass.
在室温常压（r.t.p.）下，1 mol 任何气体占据 24 dm³。利用这一关系，可以直接在体积和摩尔数之间转换，无需知道质量。
V (dm³) = n × 24
where V = volume of gas (dm³), n = number of moles. If volume is given in cm³, convert to dm³ by dividing by 1000.
其中 V = 气体体积（dm³），n = 摩尔数。若体积以 cm³ 给出，需除以 1000 换算为 dm³。
Note: r.t.p. is defined as 20 °C and 1 atmosphere pressure. At standard temperature and pressure (s.t.p., 0 °C, 1 atm), the molar volume is 22.4 dm³, but CIE IGCSE uses r.t.p. unless stated otherwise.
注意：r.t.p. 定义为 20 °C 和 1 大气压。在标准状况（s.t.p.，0 °C，1 atm）下，摩尔体积为 22.4 dm³，但 CIE IGCSE 除非特别说明，均使用 r.t.p.。
3. Concentration of Solutions | 溶液的浓度
Concentration tells you how much solute is dissolved in a given volume of solvent. In IGCSE, the most common units are mol/dm³ and g/dm³.
浓度表示在一定体积溶剂中溶质的溶解量。IGCSE 中最常用的单位是 mol/dm³ 和 g/dm³。
c (mol/dm³) = n / V
c = concentration (mol/dm³), n = moles of solute, V = volume of solution (dm³).
c = 浓度（mol/dm³），n = 溶质的摩尔数，V = 溶液体积（dm³）。
If concentration is given in g/dm³, use the relationship: c (g/dm³) = mass (g) / volume (dm³). To convert between the two: c (mol/dm³) = c (g/dm³) / Mr.
若浓度以 g/dm³ 给出，则使用：c (g/dm³) = 质量（g）/ 体积（dm³）。二者之间转换：c (mol/dm³) = c (g/dm³) / Mr。
Always remember to convert cm³ to dm³ (divide by 1000) before substituting into the formula. A common mistake is using cm³ directly.
在代入公式之前，务必记得将 cm³ 转换为 dm³（除以 1000）。一个常见错误是直接使用 cm³。
4. Percentage Yield | 百分比产率
Percentage yield compares the amount of product actually obtained in an experiment to the maximum theoretical amount predicted by stoichiometry.
百分比产率是将实验中实际获得的产品量与通过化学计量计算出的最大理论量进行比较。
% Yield = (actual yield / theoretical yield) × 100
Actual yield is the mass or moles of product collected (given in the question or obtained experimentally). Theoretical yield is calculated from the limiting reactant using mole ratios from the balanced equation.
实际产率是收集到的产物的质量或摩尔数（题目给出或实验测得）。理论产率是根据限制反应物，使用配平方程式中的摩尔比计算得出。
Yields are usually less than 100% due to incomplete reactions, side reactions, loss during purification, or reversible reactions. Understanding yield helps evaluate the efficiency of a process.
由于反应不完全、副反应、提纯过程中的损失或可逆反应，产率通常低于 100%。理解产率有助于评估过程的效率。
5. Atom Economy | 原子经济
Atom economy measures the proportion of reactant atoms that end up in the desired product. High atom economy means less waste and more sustainable chemistry.
原子经济衡量的是反应物原子最终进入目标产物的比例。高原子经济意味着废物更少，化学过程更可持续。
% Atom Economy = (Mr of desired product / sum of Mr of all products) × 100
Use the balanced equation to identify all products. The sum of Mr of all products equals the sum of Mr of all reactants (law of conservation of mass). You can also use total Mr of reactants if that is simpler.
利用配平方程式找出所有产物。所有产物的 Mr 之和等于所有反应物的 Mr 之和（质量守恒定律）。若更方便，也可使用所有反应物的总 Mr。
Atom economy is especially relevant when comparing different routes to make the same product. Addition reactions generally have 100% atom economy; substitution reactions typically have lower values.
在比较制备同一产品的不同路径时，原子经济尤为重要。加成反应通常具有 100% 的原子经济；取代反应通常数值较低。
6. Empirical and Molecular Formulae | 经验式与分子式
The empirical formula gives the simplest whole-number ratio of atoms in a compound. The molecular formula shows the actual number of atoms of each element in a molecule.
经验式给出化合物中原子最简整数比。分子式则显示分子中各元素原子的实际数目。
Step 1: Convert mass (or percentage composition by mass) of each element into moles using n = m ÷ Ar. Step 2: Divide all mole values by the smallest number of moles to get the simplest ratio. Step 3: If needed, multiply to get whole numbers.
步骤 1：利用 n = m ÷ Ar 将各元素的质量（或质量百分比）换算为摩尔数。步骤 2：将所有摩尔数除以最小摩尔数，得到最简比。步骤 3：如有必要，乘以系数得到整数。
To find the molecular formula, you need the relative molecular mass (Mr) of the compound. Divide Mr by the mass of the empirical formula unit to find the multiplying factor (n): Molecular formula = (empirical formula) × n.
要确定分子式，需知道该化合物的相对分子质量（Mr）。将 Mr 除以经验式单元的质量，得到倍数 n：分子式 = (经验式) × n。
7. Energy Changes and Calorimetry | 能量变化与量热法
Energy changes in reactions can be measured by temperature change in a known mass of water or solution. The specific heat capacity of water is assumed to be 4.2 J/(g °C).
反应中的能量变化可通过已知质量的水或溶液的温升来测定。水的比热容通常取 4.2 J/(g °C)。
Q = m × c × ΔT
Q = heat energy absorbed or released (J), m = mass of water/solution (g), c = specific heat capacity (usually 4.2 J/g°C), ΔT = temperature change (°C).
Q = 吸收或放出的热量（J），m = 水或溶液的质量（g），c = 比热容（通常 4.2 J/g°C），ΔT = 温度变化（°C）。
For exothermic reactions, ΔT is positive (temperature rises) and Q is considered negative for the reaction but calculated as positive heat given out. For endothermic, ΔT is negative.
放热反应中，ΔT 为正值（温度上升），对反应体系 Q 视为负值，但计算时取正的热量放出值。吸热反应中，ΔT 为负值。
ΔH = –Q / n
ΔH = molar enthalpy change (J/mol or kJ/mol), Q as above (J), n = moles of fuel burned or moles of limiting reactant. The negative sign is included for exothermic reactions to give a negative ΔH value.
ΔH = 摩尔焓变（J/mol 或 kJ/mol），Q 同上（J），n = 燃烧的燃料摩尔数或限制反应物的摩尔数。放热反应包含负号以得到负的 ΔH 值。
Remember to convert Q from J to kJ if required (1 kJ = 1000 J). Always state the sign of ΔH: negative for exothermic, positive for endothermic.
如有需要，记得将 Q 从 J 转换为 kJ（1 kJ = 1000 J）。务必注明 ΔH 的正负号：放热为负，吸热为正。
8. Rate of Reaction | 反应速率
The rate of a chemical reaction can be determined by measuring how quickly a reactant is consumed or a product is formed. Common measurements include change in mass, volume of gas evolved, or time for a colour change.
化学反应速率可通过测量反应物的消耗或产物的生成快慢来确定。常见测量包括质量变化、气体释放体积或颜色变化所需时间。
Rate = change in quantity / change in time
For gas production: Rate = volume of gas produced / time (cm³/s or cm³/min). For mass loss: Rate = mass lost / time (g/s). For disappearing cross experiments, an approximate rate = 1 / t, where t is the time taken.
对于气体生成：速率 = 产生气体的体积 / 时间（cm³/s 或 cm³/min）。对于质量减少：速率 = 质量损失 / 时间（g/s）。对于十字消失实验，近似速率 = 1 / t，其中 t 为所需时间。
The average rate over a time interval and the instantaneous rate (gradient of tangent on a graph) should both be understood. Collision theory connects rate to frequency of successful collisions.
应理解一段时间间隔内的平均速率以及瞬时速率（图上切线的斜率）。碰撞理论将速率与有效碰撞的频率联系起来。
9. Titration Calculations | 滴定计算
Titration is used to find the concentration of an unknown solution by reacting it with a standard solution of known concentration. The key formula is based on the mole ratio from the balanced equation.
滴定法通过已知浓度的标准溶液与未知溶液反应，来测定未知溶液的浓度。关键公式建立于配平方程式的摩尔比之上。
nₐ / nₐᵣ = (cₐ × Vₐ) / (cₐᵣ × Vₐᵣ)
Where nₐ and nₐᵣ are the mole ratios of acid and base from the equation, c = concentration (mol/dm³), V = volume. For a 1:1 reaction like HCl + NaOH, simply: c₁V₁ = c₂V₂.
其中 nₐ 和 nₐᵣ 是方程式中酸和碱的摩尔比，c = 浓度（mol/dm³），V = 体积。对于 1:1 反应如 HCl + NaOH，简化为：c₁V₁ = c₂V₂。
Always ensure volumes are in dm³ if concentration is in mol/dm³. Use the average titre volume from concordant results (within 0.2 cm³) to ensure accuracy.
若浓度以 mol/dm³ 表示，务必确保体积单位是 dm³。使用来自一致结果（偏差在 0.2 cm³ 以内）的平均滴定体积以保证准确性。
10. Electrolysis Calculations | 电解计算
Electrolysis calculations link the quantity of electricity passed to the mass of substance deposited or liberated at an electrode. The key quantitative relationship involves charge and moles of electrons.
电解计算将通过的电量与电极上沉积或析出的物质质量联系起来。定量关系的关键涉及电荷和电子的摩尔数。
Q = I × t
Q = charge (coulombs, C), I = current (amperes, A), t = time (seconds, s). Then, 1 mole of electrons carries 96 500 C (1 Faraday). Use electrode half-equations to find moles of electrons → moles of product.
Q = 电荷量（库仑，C），I = 电流（安培，A），t = 时间（秒，s）。然后，1 mol 电子携带 96 500 C 电量（1 法拉第）。利用电极半反应式找出电子摩尔数 → 产物的摩尔数。
For example, in Cu²⁺ + 2e⁻ → Cu, depositing 1 mol of Cu requires 2 mol of electrons (2 × 96 500 C). Then m = n × M gives the mass deposited.
例如，在 Cu²⁺ + 2e⁻ → Cu 中，沉积 1 mol Cu 需要 2 mol 电子（2 × 96 500 C）。然后通过 m = n × M 计算沉积的质量。
At IGCSE, calculations usually involve the mass of a metal deposited or volume of a gas collected. Remember: for gases at r.t.p., volume = moles × 24 dm³.
在 IGCSE 阶段，计算通常涉及金属沉积质量或收集的气体体积。记住：对于处于 r.t.p. 的气体，体积 = 摩尔数 × 24 dm³。
11. Excess and Limiting Reactants | 过量与限制反应物
In many reactions, one reactant is used up completely while the other remains in excess. The limiting reactant determines the amount of products formed.
在许多反应中，一种反应物会完全消耗，而另一种有剩余。限制反应物决定了生成产物的量。
To identify the limiting reactant, calculate the moles of each reactant. Then use the balanced equation to see which one gives the smallest amount of product. The other reactant is in excess.
要识别限制反应物，先计算各反应物的摩尔数。然后通过配平方程式判断哪种反应物会得到最少的产物。该反应物即为限制反应物，另一种则过量。
Excess reactants are often used to ensure complete reaction of a more expensive reactant, or to speed up a reaction. Calculations of theoretical yield must be based on the limiting reactant.
过量的反应物常用于确保更昂贵的反应物完全反应，或加速反应进程。理论产率的计算必须基于限制反应物进行。
12. Quick Reference Formula Table | 公式速查表
Keep this table handy when revising or practising questions. It summarises all the central formulas with their units.
复习或练习题目时，请将此表格放在手边。它汇总了所有核心公式及其单位。
| Formula 公式 | Description 描述 |
|---|---|
| n = m / M | Moles from mass and molar mass 由质量和摩尔质量求摩尔数 |
| V = n × 24 dm³ | Volume of gas at r.t.p. 室温常压下气体体积 |
| c = n / V | Concentration (mol/dm³) 浓度（mol/dm³） |
| % Yield | (actual / theoretical) × 100 实际产量/理论产量 × 100 |
| % Atom Economy | (Mr desired / total Mr products) × 100 |
| Q = m c ΔT | Heat energy change 热量变化 |
| ΔH = –Q / n | Molar enthalpy change 摩尔焓变 |
| Rate = Δ quantity / Δ t | Reaction rate 反应速率 |
| c₁V₁ / n₁ = c₂V₂ / n₂ | Titration mole ratio 滴定摩尔比 |
| Q = I × t | Charge in electrolysis 电解电量 |
Using these formulas systematically and showing full working will help you avoid common errors. Always check that the equation is balanced before starting any stoichiometry calculation.
系统地使用这些公式并展示完整的解题步骤，有助于避免常见错误。在进行任何化学计量计算之前，务必检查方程式是否已配平。
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