📚 Year 12 CIE Chemistry: Formula and Theorem Quick Reference Handbook | Year 12 CIE 化学：公式定理速查手册
This handbook collates the essential formulas, theorems and key concepts required for the Year 12 CIE AS-Level Chemistry course. Each section pairs a clear statement or formula with a concise explanation, helping you to recall and apply them quickly during revision.
本速查手册汇总了 Year 12 CIE AS 化学课程必须掌握的公式、定理和核心概念。每个部分都将公式或定义与简洁的说明配对，帮助你在复习时快速回忆并灵活运用。
1. The Mole and Amount of Substance | 摩尔与物质的量
tance. One mole contains exactly 6.022 × 10²³ elementary entities (Avogadro constant, Nₐ).
摩尔是物质的量的 SI 单位。1 摩尔物质恰好含有 6.022 × 10²³ 个基本单元（阿伏伽德罗常数 Nₐ）。
The number of moles n can be found from mass m and molar mass M: n = m / M es at room temperature and pressure (RTP: 20 °C, 1 atm), molar volume Vₘ ≈ 24.0 dm³ mol⁻¹; n = V(gas) / Vₘ.
物质的量 n 可通过质量 m 与摩尔质量 M 计算：n = m / M。在常温常压下 (RTP: 20 °C, 1 atm)，气体摩尔体积 Vₘ ≈ 24.0 dm³ mol⁻¹，因此 n = V(气体) / Vₘ。
For solutions, concentration c (mol dm⁻³) relates to moles and volume V (dm³): n = c × V. Always convert volumes to dm³ before calculation.
溶液中的物质的量由浓度 c (mol dm⁻³) 和体积 V (dm³) 决定：n = c × V。计算前务必将体积单位转换为 dm³。
2. Empirical and Molecular Formulae | 经验式与分子式
The empirical formula shows the simplest whole-number ratio of atoms in a compound. It is obtained from the mole ratios of the elements present.
经验式表示化合物中各元素原子的最简整数比，由各元素物质的量之比求得。
To find an empirical formula: convert the mass or percentage of each element to moles, divide by the smallest number of moles, then multiply to obtain whole numbers if necessary.
确定经验式的步骤：将各元素的质量或百分含量换算为物质的量，除以最小物质的量，必要时乘以整数以得到最简整数比。
The molecular formula is a multiple of the empirical formula: Molecular formula = n × Empirical formula, where n = Mᵣ(molecular) / Mᵣ(empirical).
分子式是经验式的整数倍：分子式 = n × 经验式，其中 n = 相对分子质量(分子) / 相对分子质量(经验式)。
3. Ideal Gas Equation and Gas Laws | 理想气体方程与气体定律
The ideal gas equation links pressure p (Pa), volume V (m³), amount n (mol), and temperature T (K): pV = nRT, where R = 8.31 J mol⁻¹ K⁻¹.
理想气体方程将压强 p (Pa)、体积 V (m³)、物质的量 n (mol) 和温度 T (K) 联系起来：pV = nRT，式中 R = 8.31 J mol⁻¹ K⁻¹。
Boyle’s law: at constant T, pV = constant. Charles’s law: at constant p, V ∝ T. Avogadro’s law: at constant T and p, V ∝ n. These are combined in the ideal gas equation.
玻义耳定律：恒温下 pV 为定值。查理定律：恒压下 V ∝ T。阿伏伽德罗定律：恒温恒压下 V ∝ n。三者均包含在理想气体方程中。
uation, always convert °C to K (T/K = t/°C + 273), cm³ or dm³ to m³, and kPa to Pa (×10³).
使用该方程时，务必将温度换算为开尔文 (T/K = t/°C + 273)，体积换算为 m³，压强换算为 Pa (kPa × 10³)。
4. Energy Changes and Calorimetry | 能量变化与量热法
The heat change q in a reaction can be measured by calorimetry: q = m c ΔT, where m is the mass of the substance heated (usually water), c the specific heat capacity (4.18 J g⁻¹ K⁻¹ for water), and ΔT the temperature change.
反应的热效应 q 可通过量热法测量：q = m c ΔT，其中 m 为被加热物质（通常为水）的质量，c 为比热容（水为 4.18 J g⁻¹ K⁻¹），ΔT 为温度变化。
Molar enthalpy change ΔH is the heat absorbed or released per mole of reactant: ΔH = – q / n (sign convention: negative for exothermic, positive for endothermic). Ensure n is the moles of the limiting reactant specified.
摩尔焓变 ΔH 是每摩尔反应物吸收或释放的热量：ΔH = – q / n（符号规定：放热为负，吸热为正）。注意 n 是指定限制反应物的物质的量。
5. Hess’s Law and Enthalpy Cycles | 赫斯定律与焓变循环
Hess’s law states that the total enthalpy change for a reaction is independent of the route taken, depending only on the initial and final states.
赫斯定律指出：一个反应的总焓变与反应途径无关，只取决于始态和终态。
The standard enthalpy change of formation (ΔH°f) is the enthalpy change when one mole of a compound is formed from its elements in their standard states. The standard enthalpy change of combustion (ΔH°c) is the enthalpy change when one mole of a substance is completely burned in oxygen under standard conditions.
标准生成焓 (ΔH°f) 是在标准状态下，由稳定单质生成 1 mol 化合物时的焓变。标准燃烧焓 (ΔH°c) 是 1 mol 物质在标准状态下完全燃烧的焓变。
Using formation data: ΔH° = Σ ΔH°f(products) − Σ ΔH°f(reactants). Using combustion data: ΔH° = Σ ΔH°c(reactants) − Σ ΔH°c(products). Always balance the equation and use the stoichiometric coefficients.
利用生成焓计算：ΔH° = Σ ΔH°f(生成物) − Σ ΔH°f(反应物)。利用燃烧焓计算：ΔH° = Σ ΔH°c(反应物) − Σ ΔH°c(生成物)。务必配平方程并乘以相应的化学计量数。
6. Rate of Reaction and Rate Equations | 反应速率与速率方程
The rate of a reaction is the change in concentration of a reactant or product per unit time. It can be expressed as rate = k[A]ᵐ[B]ⁿ, where k is the rate constant, and m, n are the orders with respect to A and B.
反应速率为单位时间内反应物或生成物浓度的变化。速率方程可表示为 速率 = k[A]ᵐ[B]ⁿ，k 为速率常数，m 和 n 分别为对 A 和 B 的反应级数。
The overall order is m + n. Orders must be determined experimentally; they are not simply the stoichiometric coefficients. Zero order: rate independent of [A]; first order: rate ∝ [A]; second order: rate ∝ [A]².
总反应级数为 m+n。反应级数必须通过实验测定，不能直接从化学计量数推出。零级反应：速率与 [A] 无关；一级反应：速率 ∝ [A]；二级反应：速率 ∝ [A]²。
For a first-order reaction, the half-life is constant: t₁/₂ = ln 2 / k. The integrated rate law is ln[A]ₜ = ln[A]₀ – kt.
一级反应的半衰期为常数：t₁/₂ = ln 2 / k。其积分速率方程为 ln[A]ₜ = ln[A]₀ – kt。
7. Chemical Equilibrium and Le Chatelier’s Principle | 化学平衡与勒夏特列原理
At dynamic equilibrium, the rates of the forward and reverse reactions are equal; concentrations of reactants and products remain constant. The equilibrium constant Kc for aA + bB ⇌ cC + dD is Kc = ([C]ᶜ[D]ᵈ) / ([A]ᵃ[B]ᵇ), using equilibrium concentrations.
在动态平衡中，正逆反应速率相等，各物质浓度保持恒定。对于反应 aA + bB ⇌ cC + dD，平衡常数 Kc = ([C]ᶜ[D]ᵈ) / ([A]ᵃ[B]ᵇ)，浓度为平衡浓度。
Kc depends only on temperature. If Kc >> 1, equilibrium lies to the right; if Kc << 1, it lies to the left. Solids and pure liquids are omitted from the Kc expression.
Kc 只与温度有关。若 Kc >> 1，平衡偏向产物；若 Kc << 1，平衡偏向反应物。固体和纯液体不写入 Kc 表达式。
Le Chatelier’s principle: if a system at equilibrium is subjected to a change in concentration, pressure or temperature, the equilibrium shifts to oppose the change.
勒夏特列原理：如果改变平衡体系的浓度、压强或温度，平衡将向减弱这种改变的方向移动。
Increasing concentration of a reactant shifts equilibrium to the products. | 增加反应物浓度，平衡向生成物方向移动。
For gaseous reactions, increasing pressure favours the side with fewer gas molecules. | 对于气体反应，增大压强，平衡向气体分子数较少的方向移动。
Increasing temperature favours the endothermic direction; adding a catalyst has no effect on equilibrium position, only speeds up attainment of equilibrium. | 升高温度，平衡向吸热方向移动；加入催化剂不改变平衡位置，只加快到达平衡的速率。
8. Acids, Bases, and pH Calculations | 酸、碱与 pH 计算
A Brønsted–Lowry acid is a proton donor; a base is a proton acceptor. The pH scale is defined as pH = –log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration in mol dm⁻³. Similarly, pOH = –log₁₀[OH⁻].
根据布朗斯特–劳里理论，酸是质子给予体，碱是质子接受体。pH 定义为 pH = –log₁₀[H⁺]，[H⁺] 为氢离子浓度 (mol dm⁻³)。类似地，pOH = –log₁₀[OH⁻]。
The ionic product of water Kw at 25 °C is 1.0 × 10⁻¹⁴ mol² dm⁻⁶: Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴. This gives the relationship pH + pOH = 14 at 25 °C.
25 °C 时水的离子积 Kw 为 1.0 × 10⁻¹⁴ mol² dm⁻⁶: Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴。由此可得 pH + pOH = 14 (25 °C)。
s, [OH⁻] equals the base concentration. Dilution effects are calculated using C₁V₁ = C₂V₂.
对于强一元酸，[H⁺] 等于酸的浓度（忽略水的微弱电离）。对于强碱，[OH⁻] 等于碱的浓度。稀释效果通过 C₁V₁ = C₂V₂ 计算。
9. Redox and Oxidation Numbers | 氧化还原与氧化数
Oxidation is loss of electrons; reduction is gain of electrons (OIL RIG). The oxidation number (state) is a formalism that helps track electron transfer.
氧化是失去电子，还原是得到电子 (OIL RIG)。氧化数是一种形式电荷，用来追踪电子转移。
Rules for assigning oxidation numbers: free elements have oxidation number 0; for simple ions it equals the charge; in compounds, H is usually +1, O is usually –2; the sum of oxidation numbers in a neutral compound is 0, in a polyatomic ion it equals the ion charge.
氧化数确定规则：游离态元素氧化数为 0；单原子离子的氧化数等于其电荷；化合物中 H 通常为 +1，O 通常为 –2；中性分子中各元素氧化数之和为 0，多原子离子中等于离子电荷。
In a redox reaction, one species is oxidised (increase in oxidation number) and another is reduced (decrease in oxidation number). The total increase in oxidation numbers equals the total decrease.
氧化还原反应中，一种物质被氧化（氧化数升高），另一种被还原（氧化数降低）。氧化数升高总数等于降低总数。
10. Atomic Structure and Electron Arrangement | 原子结构与电子排布
ng discrete energy levels (shells) around the nucleus. Mass number A = protons + neutrons.
原子由包含质子 (原子序数 Z) 和中子的原子核以及核外占据分立能级（电子层）的电子组成。质量数 A = 质子数 + 中子数。
Electron shells: 1st shell holds up to 2 electrons, 2nd shell up to 8, 3rd shell up to 18 (but filled as 8 for period 3 elements). Subshells: s (max 2), p (max 6), d (max 10). The order of filling follows the Aufbau principle: 1s, 2s, 2p, 3s, 3p, 4s, 3d...
电子层容量：第一层最多 2 个电子，第二层最多 8 个，第三层最多 18 个（但第三周期元素只填充至 8）。亚层：s (最多 2), p (最多 6), d (最多 10)。填充顺序遵循构造原理：1s, 2s, 2p, 3s, 3p, 4s, 3d……
The electronic configuration of an element is written as, e.g., O: 1s² 2s² 2p⁴. Ions lose electrons from the outermost shell first (for transition metals, from 4s before 3d).
元素的电子排布写作，例如 O: 1s² 2s² 2p⁴。离子形成时优先失去最外层电子（对过渡金属，先失 4s 再失 3d）。
11. Periodic Trends and Group Properties | 元素周期律与族性质
Atomic radius decreases across a period (increasing nuclear charge, same shielding) and increases down a group (extra shells, more shielding).
原子半径在同周期从左到右递减（核电荷增大，屏蔽相近）；同族由上至下递增（电子层增加，屏蔽增强）。
First ionisation energy generally increases across a period and decreases down a group. Small drops occur between Be and B, and N and O, due to subshell energy and electron pairing repulsion.
第一电离能通常在同周期递增，同族递减。Be 与 B 之间、N 与 O 之间出现小幅下降，源于亚层能级和电子配对排斥。
Group 1 (alkali metals) react vigorously with water to give hydroxides and hydrogen; reactivity increases down the group. Group 17 (halogens) become less reactive down the group; a halogen higher up can displace a lower halide from its salt.
第 1 族（碱金属）与水剧烈反应生成氢氧化物和氢气；反应活性向下递增。第 17 族（卤素）向下反应活性递减；较上方的卤素可从盐中置换较下方的卤离子。
12. Organic Chemistry: Key Functional Groups and Reactions | 有机化学：重要官能团与反应
Hydrocarbons: alkanes (C–C, C– tution. Alkenes contain a C=C bond, general formula CₙH₂ₙ, undergo electrophilic addition.
烃类：烷烃（含 C–C, C–H）通式为 CₙH₂ₙ₊₂，发生自由基取代反应。烯烃含 C=C 双键，通式为 CₙH₂ₙ，发生亲电加成反应。
Halogenoalkanes (R–X) undergo nucleophilic substitution (Sₙ1 / Sₙ2) and elimination. Alcohols (R–OH) can be oxidised to aldehydes, ketones or carboxylic acids depending on the class and oxidising agent.
卤代烷 (R–X) 可发生亲核取代 (Sₙ1/Sₙ2) 和消除反应。醇 (R–OH) 可根据醇的类型和氧化剂被氧化为醛、酮或羧酸。
Carboxylic acids (R–COOH) are weak acids; they react with alcohols to form esters (R–COOR') in the presence of an acid catalyst (esterification). Carbonyl compounds (aldehydes and ketones) undergo nucleophilic addition.
羧酸 (R–COOH) 是弱酸；在酸催化下与醇反应生成酯 (R–COOR')，即酯化反应。醛、酮等羰基化合物发生亲核加成反应。
| Homologous Series | Functional Group | General Formula |
| Alkane | C–C, C–H | CₙH₂ₙ₊₂ |
| Alkene | C=C | CₙH₂ₙ |
| Halogenoalkane | R–X (X = F, Cl, Br, I) | CₙH₂ₙ₊₁X |
| Alcohol | –OH | CₙH₂ₙ₊₁OH |
| Aldehyde | –CHO | CₙH₂ₙO |
| Ketone | >C=O | CₙH₂ₙO |
| Carboxylic acid | –COOH | CₙH₂ₙO₂ |
| Ester | –COOR' | CₙH₂ₙO₂ |
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