📚 Year 10 CIE Chemistry: Formulas & Theorems Quick Reference | Year 10 CIE 化学：公式定理速查手册
This handbook consolidates every essential formula, equation, and theorem you need for the Year 10 CIE Chemistry syllabus. Use it for rapid revision, problem-solving, and clarifying key quantitative relationships before exams.
本手册汇集了 Year 10 CIE 化学考纲所需的每条核心公式、方程式与定理。可用于快速复习、解题以及在考前理清关键定量关系。
1. Relative Atomic Mass and 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, taking isotopic abundances into account.
相对原子质量（Aᵣ）是一种元素原子的平均质量与一个碳-12原子质量的1/12的比值，考虑了同位素丰度。
Relative molecular mass (Mᵣ) is the sum of the relative atomic masses of all atoms in a molecular formula.
相对分子质量（Mᵣ）是分子式中所有原子相对原子质量的总和。
Mᵣ = Σ Aᵣ (of all atoms in the molecule)
Key concept: Aᵣ and Mᵣ are dimensionless (no units) because they are ratios.
关键概念： Aᵣ 和 Mᵣ 是无量纲量（无单位），因为它们表示比值。
Example: For CO₂, Aᵣ(C)=12, Aᵣ(O)=16. Therefore, Mᵣ = 12 + (2×16) = 44.
示例：对于 CO₂，Aᵣ(C)=12，Aᵣ(O)=16，故 Mᵣ = 12 + (2×16) = 44。
2. The Mole and Molar Mass | 摩尔与摩尔质量
ities (Avogadro constant, Nₐ). In chemistry, the mole is the unit for the amount of substance, symbol n, and its SI unit is mol.
一摩尔的物质恰好包含 6.02214076 × 10²³ 个基本单元（阿伏伽德罗常数，Nₐ）。在化学中，摩尔是物质的量的单位，符号为 n，SI单位是 mol。
Molar mass (M) is the mass of one mole of a substance. Its SI unit is g/mol. Numerically, M is equal to the relative formula mass (Mᵣ or Aᵣ) expressed in grams.
摩尔质量（M）是一摩尔物质的质量。SI 单位是 g/mol。数值上，M 等于以克为单位的相对式量（Mᵣ 或 Aᵣ）。
n = m / M
mol), m = mass (g), M = molar mass (g/mol). Always match mass units with molar mass units.
其中 n = 物质的量 (mol)，m = 质量 (g)，M = 摩尔质量 (g/mol)。始终保证质量单位与摩尔质量单位匹配。
3. Empirical Formula and Molecular Formula | 经验式与分子式
The empirical formula gives the simplest whole-number ratio of atoms of each element 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各元素原子的最简整数比。分子式表示一个分子中各元素原子的实际数目。
To find empirical formula from mass or percentage composition:
从质量或质量百分比求经验式的步骤：
- Convert mass (or % by mass) of each element to moles: n = mass / Aᵣ. | 将各元素质量（或质量百分比）换算为摩尔数：n = 质量 / Aᵣ。
- Divide each mole value by the smallest number of moles to obtain the simplest ratio. | 用最小的摩尔数除以各摩尔数，得到最简整数比。
- If necessary, multiply to clear fractions. | 如有需要，乘到整数。
Example: A compound has 40.0% C, 6.7% H, 53.3% = 6.7/1 = 6.7; O = 53.3/16 ≈ 3.33. Divide by 3.33 → C:H:O = 1:2:1, empirical formula CH₂O.
示例：某化合物含 C 40.0%、H 6.7%、O 53.3%（质量分数）。假设 100 g → 40 g C, 6.7 g H, 53.3 g O。摩尔数：C = 40/12 ≈ 3.33；H = 6.7/1 = 6.7；O = 53.3/16 ≈ 3.33。除以 3.33 → C:H:O = 1:2:1，经验式为 CH₂O。
ormula: Molecular formula = (Empirical formula)ₙ, where n = Mᵣ(molecular) / Mᵣ(empirical).
分子式是经验式的整数倍：分子式 = (经验式)ₙ，其中 n = 分子 Mᵣ / 经验式 Mᵣ。
4. Reacting Masses and Stoichiometry | 反应质量与化学计量
Stoichiometry uses the mole ratios from a balanced chemical equation to calculate masses, volumes, or concentrations of reactants and products.
化学计量利用配平化学方程式中的摩尔比来计算反应物和产物的质量、体积或浓度。
Mass of desired substance = (moles of known) × (mole ratio) × (molar mass of desired)
rt given mass to moles → use mole ratio → convert to mass (or volume) of target substance.
步骤：写出配平方程式 → 将给定质量换算为摩尔数 → 应用摩尔比 → 换算为目标物质的质量（或体积）。
Crucial: the limiting reagent determines the theoretical yield when reactants are not in exact stoichiometric proportions.
关键：当反应物不按精确化学计量比投入时，限制试剂决定理论产量。
5. Concentration of Solutions | 溶液的浓度
Concentration measures the amount of solute dissolved in a given volume of solvent. The most common unit is mol/dm³ (molarity, symbol c).
浓度表示一定体积溶剂中溶解的溶质的量。最常用的单位是 mol/dm³（摩尔浓度，符号 c）。
c = n / V
), n = amount of solute (mol), V = volume of solution (dm³). Note: 1 dm³ = 1000 cm³ = 1 L.
其中 c = 浓度 (mol/dm³)，n = 溶质的物质的量 (mol)，V = 溶液体积 (dm³)。注意：1 dm³ = 1000 cm³ = 1 L。
n (g/dm³) to molar concentration: c (mol/dm³) = (mass concentration in g/dm³) / M (g/mol).
将质量浓度 (g/dm³) 转换为摩尔浓度：c (mol/dm³) = (以 g/dm³ 计的质量浓度) / M (g/mol)。
mula (conservation of moles): c₁V₁ = c₂V₂. Useful when water is added to a stock solution.
稀释公式（溶质物质的量守恒）：c₁V₁ = c₂V₂。在储备溶液中加水稀释时有用。
6. Molar Volume of Gases | 气体的摩尔体积
re (STP: 0 °C, 1 atm), molar volume is 22.4 dm³. CIE Year 10 typically uses RTP = 24 dm³/mol.
在室温常压条件下（RTP: 25 °C, 1 atm 或 101 kPa），一摩尔任何气体约占据 24 dm³。在标准温度与压力下（STP: 0 °C, 1 atm），摩尔体积为 22.4 dm³。CIE Year 10 通常采用 RTP = 24 dm³/mol。
Volume of gas (dm³) = n × 24 (at RTP)
This relationship holds for all ideal gases; it allows direct linking of gaseous volumes to moles and therefore to reacting masses.
这一关系适用于所有理想气体；可以将气体体积直接与摩尔数建立联系，进而与反应质量挂钩。
In reactions involving gases, Gay-Lussac's law applies: volumes of gaseous reactants and products, measured at the same temperature and pressure, are in simple whole-number ratios (equal to the mole ratios).
对于有气体参与的反应，适用盖-吕萨克定律：在同温同压下，气态反应物与产物的体积成简单整数比（等于摩尔比）。
7. Percent Yield and Atom Economy | 产率与原子经济
Percent yield shows the efficiency of a reaction by comparing the actual mass obtained to the theoretical maximum mass.
产率通过比较实际获得的质量与理论最大质量来反映反应效率。
% Yield = (actual yield / theoretical yield) × 100
Actual yield is measured experimentally. Theoretical yield is calculated from the limiting reagent. Yields are often less than 100% due to incomplete reaction, side reactions, or purification losses.
实际产量由实验测量得到。理论产量根据限制试剂计算。由于反应不完全、副反应或纯化损失，产率常常低于 100%。
Atom economy evaluates how much of the starting materials end up in the desired product. It is particularly important in green chemistry.
原子经济性评价起始原料有多少最终进入目标产物，在绿色化学中尤其重要。
% Atom economy = (Mᵣ of desired product / Σ Mᵣ of all reactants) × 100
A reaction with high atom economy produces fewer waste by-products. Addition reactions typically have 100% atom economy; substitution reactions are lower.
高原子经济性的反应产生的废料更少。加成反应通常具有 100% 的原子经济性；取代反应则较低。
8. Acids, Bases and pH | 酸、碱与 pH
Arrhenius acids produce H⁺ ions in water; bases produce OH⁻ ions in water. A strong acid fully dissociates, a weak acid partially dissociates.
阿伦尼乌斯酸在水中产生 H⁺ 离子；碱在水中产生 OH⁻ 离子。强酸完全电离，弱酸部分电离。
Neutralisation: acid + base → salt + water. The ionic equation for any strong acid–strong base reaction is: H⁺(aq) + OH⁻(aq) → H₂O(l).
中和反应：酸 + 碱 → 盐 + 水。任何强酸与强碱反应的离子方程式为：H⁺(aq) + OH⁻(aq) → H₂O(l)。
ncentration: pH = -log₁₀[H⁺]. A change of one pH unit represents a tenfold change in [H⁺].
pH 是对氢离子浓度的对数度量：pH = -log₁₀[H⁺]。每变化一个 pH 单位，[H⁺] 改变十倍。
Acids react with metals, carbonates, and bases according to general equations:
酸与金属、碳酸盐及碱的反应通式：
- Metal + Acid → Salt + Hydrogen | 金属 + 酸 → 盐 + 氢气
- Metal carbonate + Acid → Salt + Water + Carbon dioxide | 金属碳酸盐 + 酸 → 盐 + 水 + 二氧化碳
- Metal oxide/hydroxide + Acid → Salt + Water | 金属氧化物/氢氧化物 + 酸 → 盐 + 水
9. Salts: Preparation and Solubility Rules | 盐的制备与溶解性规则
Salt preparation methods depend on the solubility of the salt and the reactants.
盐的制备方法取决于盐和反应物的溶解性。
| Method | Suitable for |
|---|---|
| Titration (react, then crystallise) | Soluble salts from an acid and a soluble base/carbonate (e.g., NaCl from NaOH + HCl) |
| Excess solid method | Soluble salts when one reactant is insoluble solid (e.g., CuSO₄ from CuO + H₂SO₄) |
| Precipitation | All insoluble salts (e.g., BaSO₄ by mixing solutions of BaCl₂ and Na₂SO₄) |
关键溶解性规则：所有钠盐、钾盐和铵盐可溶；所有硝酸盐可溶；大多数氯化物可溶，除了氯化银和氯化铅；大多数硫酸盐可溶，除了硫酸钡、硫酸钙和硫酸铅；大多数碳酸盐和氢氧化物不溶，除了第I族和铵的对应盐。
10. Rate of Reaction | 反应速率
The rate of a chemical reaction is defined as the change in concentration of a reactant or product per unit time. It can be followed by measuring volume of gas produced, change in mass, colour change, or precipitate formation.
化学反应速率定义为单位时间内反应物或产物浓度的变化。可通过测量气体产生体积、质量变化、颜色变化或沉淀生成来跟踪。
Average rate = Δ(quantity) / Δt
Rate depends on: concentration of reactants (increases collision frequency), temperature (increases both frequency and energy of collisions), surface area of solids (increases exposed reactant), and presence of a catalyst (lowers activation energy by providing an alternative pathway).
速率取决于：反应物浓度（增加碰撞频率）、温度（既增加碰撞频率又增加能量）、固体表面积（增加反应物暴露程度）、催化剂的存在（通过提供替代路径降低活化能）。
Interpretation of Maxwell-Boltzmann distribution: temperature increase shifts the curve to the right, increasing the proportion of particles with energy greater than activation energy (Eₐ). Catalysts lower Eₐ, thus a larger fraction of particles can react.
麦克斯韦-玻尔兹曼分布解释：升高温度使曲线右移，增加能量超过活化能（Eₐ）的粒子比例。催化剂降低 Eₐ，使能反应的粒子比例增大。
11. Electrolysis and Quantitative Electrolysis | 电解与定量电解
Electrolysis uses direct current to drive a non-spontaneous chemical reaction. Key components: anode (positive electrode) attracts anions and oxidation occurs; cathode (negative electrode) attracts cations and reduction occurs.
电解利用直流电驱动非自发化学反应。关键组成：阳极（正极）吸引阴离子，发生氧化；阴极（负极）吸引阳离子，发生还原。
In molten ionic compounds, the ions are free to move. In aqueous solutions, the products depend on the reactivity of the ions and the concentration of solution. At the cathode, the less reactive element is discharged first; at the anode, the halide ions are discharged in preference to OH⁻ unless the halide concentration is low.
在熔融离子化合物中，离子可自由移动。在水溶液中，产物取决于离子反应活性和溶液浓度。阴极处，较不活泼的元素先放电；阳极处，卤离子优先于 OH⁻ 放电，除非卤离子浓度很低。
Faraday's first law of electrolysis: The mass of substance discharged at an electrode is directly proportional to the quantity of electricity (charge) passed.
法拉第电解第一定律：电极上析出的物质质量与通过的电荷量成正比。
Q = I × t
where Q = charge (coulombs, C), I = current (amperes, A), t = time (seconds, s).
其中 Q = 电荷量 (C)，I = 电流 (A)，t = 时间 (s)。
To calculate mass deposited:
n(e⁻) = Q / F, n(metal) = n(e⁻) / z, mass = n(metal) × Aᵣ
per ion (e.g., for Cu²⁺ + 2e⁻ → Cu, z=2). Combine to form: mass = (I × t × Aᵣ) / (z × F).
其中 F = 法拉第常数 ≈ 96 500 C/mol，z = 每个离子所需的电子数（例如，Cu²⁺ + 2e⁻ → Cu，z=2）。合并得：质量 = (I × t × Aᵣ) / (z × F)。
12. Energetics: Enthalpy Changes | 能量学：焓变
Enthalpy change (ΔH) is the heat energy transferred in a reaction at constant pressure. Exothermic reactions release heat (ΔH negative); endothermic reactions absorb heat (ΔH positive).
焓变（ΔH）是恒压条件下反应中传递的热能。放热反应释放热量（ΔH 为负）；吸热反应吸收热量（ΔH 为正）。
Experimental measurement of enthalpy change uses the equation:
Q = m c ΔT
thalpy change per mole is then ΔH = -Q / n (negative sign indicates heat released to surroundings in exothermic reactions).
其中 Q = 热量 (J)，m = 溶液/水的质量 (g)，c = 比热容（水通常取 4.18 J/g·°C），ΔT = 温度变化 (°C)。则每摩尔焓变 ΔH = -Q / n（负号表示放热反应中热量释放给环境）。
d energies of bonds broken) - Σ (bond energies of bonds formed). Bond breaking is endothermic; bond making is exothermic.
键能计算：ΔH ≈ Σ（断裂键的键能总和） - Σ（生成键的键能总和）。断键吸热；成键放热。
Energy level diagrams and reaction profiles show the relative enthalpy of reactants and products. The activation energy (Eₐ) is the minimum energy needed for a reaction to occur. A catalyst provides an alternative pathway with a lower Eₐ.
能级图和反应历程图显示反应物与产物的相对焓值。活化能（Eₐ）是反应发生所需的最低能量。催化剂提供具有较低 Eₐ 的替代路径。
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