📚 Year 12 CAIE Chemistry: Formula & Theorem Quick Reference Handbook | Year 12 CAIE 化学：公式定理速查手册
This quick reference handbook brings together all the essential formulas, constants, and theorems you need to master the Year 12 CAIE Chemistry syllabus. Each entry is presented in a bilingual pair so you can revise confidently in both English and Chinese, with clear notation and worked definitions.
本速查手册汇集了 Year 12 CAIE 化学课程全部核心公式、常数和定理。每个条目均以中英双语对照呈现，辅以清晰的符号与定义，帮助你高效备考。
1. Mole Concept and Formulae | 摩尔概念与基本公式
The mole is the fundamental counting unit. The number of particles in one mole is Avogadro’s constant: 6.02 × 10²³ mol⁻¹. The mass of one mole of a substance is its molar mass M (g mol⁻¹).
摩尔是基本计数单位。1 mol 物质所含微粒数为阿伏伽德罗常数：6.02 × 10²³ mol⁻¹。1 mol 物质的质量即其摩尔质量 M（g mol⁻¹）。
Key formula: n = m / M, where n = amount in mol, m = mass in g, M = molar mass in g mol⁻¹.
核心公式：n = m / M，n 为物质的量（mol），m 为质量（g），M 为摩尔质量（g mol⁻¹）。
n = m / M
For gases at room temperature and pressure (r.t.p.): volume of 1 mol ≈ 24.0 dm³ (or 24 000 cm³). Therefore n = V(gas) / 24.0 (in dm³).
常温常压下气体：1 mol 气体体积约 24.0 dm³（或 24 000 cm³）。故 n = V(气体) / 24.0（使用 dm³）。
n = V (dm³) / 24.0
For solutions: n = c × V, where c = concentration in mol dm⁻³, V = volume in dm³.
溶液计算：n = c × V，c 为浓度（mol dm⁻³），V 为体积（dm³）。
n = c × V
2. The Ideal Gas Equation | 理想气体状态方程
The ideal gas law relates pressure, volume, temperature and amount. It is valid for calculations involving gases under typical conditions unless the gas is very close to liquefaction.
理想气体状态方程关联压强、体积、温度与物质的量，适用于一般条件下气体计算，除非气体接近液化。
pV = nRT
Where: p = pressure (Pa or N m⁻²), V = volume (m³), n = amount (mol), R = 8.31 J K⁻¹ mol⁻¹ (universal gas constant), T = temperature (K). Always convert °C to K by adding 273.
符号说明：p = 压强（Pa 或 N m⁻²），V = 体积（m³），n = 物质的量（mol），R = 8.31 J K⁻¹ mol⁻¹（摩尔气体常数），T = 温度（K）。摄氏温度须加 273 转换为开尔文。
Alternative units: If p is in kPa, V in dm³, then a convenient form is pV = nR’T with R’ = 8.31 × 10⁻³ kPa dm³ K⁻¹ mol⁻¹.
单位变体：若 p 用 kPa，V 用 dm³，则 R 变为 8.31 × 10⁻³ kPa dm³ K⁻¹ mol⁻¹，公式形式不变。
3. Concentration and Dilution | 浓度与稀释
Concentration can be expressed as mol dm⁻³ or g dm⁻³. The conversion involves molar mass.
浓度可用 mol dm⁻³ 或 g dm⁻³ 表示，两者通过摩尔质量转换。
c (mol dm⁻³) = c (g dm⁻³) / M
Dilution law: When a solution is diluted, the amount of solute remains constant: n₁ = n₂. Hence c₁V₁ = c₂V₂.
稀释定律：溶液稀释时溶质的物质的量不变：n₁ = n₂，因此 c₁V₁ = c₂V₂。
c₁V₁ = c₂V₂
Percentage purity and yield: % purity = (mass of pure substance / mass of impure sample) × 100. % yield = (actual yield / theoretical yield) × 100.
纯度与产率：纯度% = (纯物质质量 / 不纯样品质量) × 100；产率% = (实际产量 / 理论产量) × 100。
4. Enthalpy Changes | 焓变
The heat energy change in a reaction at constant pressure is measured by enthalpy change ΔH. A negative ΔH indicates an exothermic reaction; a positive ΔH, endothermic.
恒压下反应的热量变化用焓变 ΔH 衡量。ΔH 为负表示放热，正表示吸热。
In solution calorimetry: q = mcΔT, where q = heat energy (J), m = mass of solution (g), c = specific heat capacity (usually 4.18 J g⁻¹ K⁻¹ for water), ΔT = temperature change (K or °C). Then ΔH = -q / n (exothermic as negative).
溶液量热法：q = mcΔT，q 为热量（J），m 为溶液质量（g），c 为比热容（水一般取 4.18 J g⁻¹ K⁻¹），ΔT 为温度变化。则 ΔH = -q / n（放热为负值）。
q = mcΔT ΔH = -q / n
Standard enthalpy definitions: ΔH°f (formation), ΔH°c (combustion), ΔH°neut (neutralisation) all refer to 1 mol under standard conditions (100 kPa, 298 K, 1 mol dm⁻³ for solutions).
标准焓定义：ΔH°f（生成焓）、ΔH°c（燃烧焓）、ΔH°neut（中和焓）均指在标准条件下（100 kPa，298 K，溶液 1 mol dm⁻³）每摩尔反应对应的焓变。
5. Hess’s Law | 赫斯定律
Hess’s Law states that the total enthalpy change for a reaction is independent of the route taken, provided the initial and final conditions are the same. It allows the use of enthalpy cycles.
赫斯定律指出，化学反应的总焓变与途径无关，只取决于初末状态。这允许我们使用焓循环图计算未知焓变。
Using formation enthalpies: ΔH°r = Σ ΔH°f (products) – Σ ΔH°f (reactants)
利用生成焓：ΔH°r = Σ ΔH°f (产物) – Σ ΔH°f (反应物)
Using combustion enthalpies: ΔH°r = Σ ΔH°c (reactants) – Σ ΔH°c (products)
利用燃烧焓：ΔH°r = Σ ΔH°c (反应物) – Σ ΔH°c (产物)
Be careful to multiply each ΔH by the stoichiometric coefficient from the balanced equation.
注意将每个 ΔH 乘以配平方程式中对应的化学计量数。
6. Chemical Equilibrium and Kc | 化学平衡与 Kc
For a reversible reaction aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration is:
对可逆反应 aA + bB ⇌ cC + dD，基于浓度的平衡常数 Kc 为：
Kc = [C]ᶜ [D]ᵈ / [A]ᵃ [B]ᵇ
Only aqueous and gaseous species appear in Kc expression; solids and pure liquids are omitted. The value of Kc changes only with temperature.
只有溶液和气体组分出现在 Kc 表达式中；固体和纯液体省略。Kc 数值仅随温度变化。
Le Chatelier’s principle: If a system at equilibrium is subjected to change, the equilibrium shifts to oppose the change.
勒夏特列原理：平衡体系受到外界改变时，平衡向减弱该改变的方向移动。
Effect on Kc: Temperature increases endothermic direction and thus changes Kc; pressure or concentration changes do not alter Kc (they shift position of equilibrium).
对 Kc 的影响：升温使平衡向吸热方向移动，Kc 变化；压强或浓度变化不改变 Kc（只改变平衡位置）。
7. Rate of Reaction | 反应速率
Rate refers to the change in concentration of a reactant or product per unit time. Rate can be followed by measuring volume of gas evolved, mass loss, colour change, pH change etc.
速率指反应物或产物浓度在单位时间内的变化。可通过测量气体体积、质量损失、颜色变化、pH 变化等跟踪速率。
Rate = -Δ[reactant] / Δt = Δ[product] / Δt
Rate equation: For a reaction A + B → products, experimentally determined rate = k [A]ᵐ[B]ⁿ. m and n are orders of reaction, not necessarily stoichiometric coefficients. k is the rate constant, whose units depend on overall order.
速率方程：对于 A + B → 产物，实验测得的速率方程：速率 = k [A]ᵐ[B]ⁿ。m 和 n 是反应级数，不一定等于化学计量数。k 为速率常数，单位取决于总级数。
Collision theory: Reactions occur when particles collide with sufficient energy (≥ activation energy Ea) and correct orientation.
碰撞理论：当粒子以足够能量（不小于活化能 Ea）和正确取向碰撞时，反应才会发生。
8. Atomic Structure and Related Calculations | 原子结构与相关计算
Atoms consist of protons, neutrons and electrons. The atomic number Z equals the number of protons; the mass number A equals protons + neutrons. Isotopes have the same Z but different A.
原子由质子、中子和电子构成。原子序数 Z = 质子数；质量数 A = 质子数 + 中子数。同位素的 Z 相同但 A 不同。
Relative atomic mass Aᵣ: Aᵣ = Σ (isotopic mass × fractional abundance) / 1.
相对原子质量 Aᵣ：Aᵣ = Σ（各同位素质量 × 丰度分数）。
Empirical and molecular formula: Empirical formula gives the simplest whole number ratio; molecular formula = n × empirical formula. n = molecular mass / empirical formula mass.
实验式与分子式：实验式给出最简整数比；分子式 = n × 实验式，n = 分子质量 / 实验式质量。
Ionisation energy trends: Across a period, 1st ionisation energy generally increases due to increased nuclear charge and similar shielding. Down a group, it decreases due to increased distance and shielding.
电离能趋势：同周期从左到右，第一电离能总体增大（核电荷增大、屏蔽相似）；同族从上到下减小（距离增大、屏蔽增强）。
9. Acid-Base Calculations | 酸碱计算
Brønsted–Lowry acid is a proton donor; base is a proton acceptor. In aqueous solution at 298 K, [H⁺][OH⁻] = Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶.
布朗斯特–劳里酸是质子给体，碱是质子受体。298 K 水溶液中：[H⁺][OH⁻] = Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶。
pH = -log₁₀ [H⁺]
Strong acid/ base treatment: For a monoprotic strong acid, [H⁺] = initial concentration. For a strong base, [OH⁻] = initial concentration, then [H⁺] = Kw / [OH⁻], and pH = 14 + log₁₀ [OH⁻].
强酸强碱处理：对于一元强酸，[H⁺] = 初始浓度。强碱：[OH⁻] = 初始浓度，则 [H⁺] = Kw / [OH⁻]，且 pH = 14 + log₁₀ [OH⁻]。
Dilution of strong acids: Each tenfold dilution increases pH by 1 (within reasonable concentration range).
强酸稀释：每稀释 10 倍，pH 升高 1（需考虑浓度范围，极稀时水的自电离不可忽略）。
10. Electrochemistry | 电化学
Redox reactions involve electron transfer. The relative tendency of a species to be reduced is given by its standard electrode potential E°.
氧化还原反应涉及电子转移。物质被还原的相对趋势由标准电极电势 E° 表示。
E°cell = E°(right) – E°(left)
Or equivalently: E°cell = E°(cathode) – E°(anode). A positive E°cell indicates a feasible reaction.
或等价地：E°cell = E°(正极) – E°(负极)。E°cell 为正则反应可行。
Standard conditions: 298 K, 1.0 mol dm⁻³ ion concentration, 100 kPa gas pressure. Platinum electrode used when no solid metal is present.
标准条件：298 K，离子浓度 1.0 mol dm⁻³，气体压强 100 kPa。若无固体金属，使用铂电极。
11. Redox and Equation Balancing | 氧化还原与方程式配平
Oxidation is loss of electrons, reduction is gain (OIL RIG). Oxidation number changes help balance half-equations.
氧化是失去电子，还原是得到电子（OIL RIG）。通过氧化数变化配平半反应。
Steps for half-equations in acidic medium: Balance atoms except O and H; add H₂O to balance O; add H⁺ to balance H; add electrons to balance charge.
酸性条件下半反应配平步骤：先配平除 O、H 外的原子；加 H₂O 配平 O；加 H⁺ 配平 H；加电子配平电荷。
Combining half-equations: Multiply each half-reaction so that electrons equal, then add and cancel electrons.
合并半反应：对各半反应乘以适当倍数使电子数相等，相加消去电子。
12. Important Constants and Conversion Factors | 重要常数与换算因子
- Avogadro’s constant: 6.02 × 10²³ mol⁻¹
- Molar gas constant R: 8.31 J K⁻¹ mol⁻¹
- Standard molar volume (r.t.p.): 24.0 dm³ mol⁻¹ (or 24 000 cm³ mol⁻¹)
- Specific heat capacity of water: 4.18 J g⁻¹ K⁻¹
- Ionic product of water Kw: 1.0 × 10⁻¹⁴ mol² dm⁻⁶ (at 298 K)
- 1 dm³ = 1000 cm³ = 1 L
- 1 m³ = 1000 dm³
- 1 atm = 101 325 Pa = 101.325 kPa
- 0 °C = 273 K
- 阿伏伽德罗常数：6.02 × 10²³ mol⁻¹
- 摩尔气体常数 R：8.31 J K⁻¹ mol⁻¹
- 标准摩尔体积（常温常压）：24.0 dm³ mol⁻¹（或 24 000 cm³ mol⁻¹）
- 水的比热容：4.18 J g⁻¹ K⁻¹
- 水的离子积 Kw：1.0 × 10⁻¹⁴ mol² dm⁻⁶（298 K）
- 1 dm³ = 1000 cm³ = 1 L
- 1 m³ = 1000 dm³
- 1 atm = 101 325 Pa = 101.325 kPa
- 0 °C = 273 K
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