📚 Year 13 OCR Chemistry Quick-Reference Formula & Theorem Handbook | Year 13 OCR 化学：公式定理速查手册
This handbook compiles the essential formulas, equations, and key constants required for the Year 13 OCR A Level Chemistry A (H432) specification. It covers physical chemistry, inorganic chemistry, and organic chemistry, serving as a rapid revision tool to cement quantitative relationships and conceptual links. Each entry is presented with clear notation using Unicode symbols, followed by paired explanations in English and Chinese.
本手册汇编了 Year 13 OCR A Level 化学 A (H432) 考试大纲所必需的核心公式、方程式和关键常数。内容覆盖物理化学、无机化学和有机化学，可作为快速复习工具，帮助你巩固定量关系和概念联系。每一条目均采用 Unicode 符号清晰标注，并配以中英文双语解释。
1. Mole Calculations & Ideal Gas Equation | 摩尔计算与理想气体方程
The amount of substance is the foundation of quantitative chemistry. The number of moles (n) relates mass (m), molar mass (M), and the Avogadro constant (NA). For gases, the ideal gas equation connects pressure, volume, temperature, and amount, provided the gas behaves ideally.
物质的量是定量化学的基石。摩尔数 (n) 关联质量 (m)、摩尔质量 (M) 和阿伏伽德罗常数 (NA)。对于气体，理想气体方程将压强、体积、温度与物质的量联系起来，前提是气体呈现理想行为。
n = m / M
Moles (mol) = mass (g) divided by molar mass (g mol⁻¹). This is used to convert between grams and moles for solids, liquids, and solutions.
摩尔数 (mol) = 质量 (g) / 摩尔质量 (g mol⁻¹)。用于固体、液体和溶液中克与摩尔之间的换算。
n = V (dm³) × c
Moles from solution: concentration (mol dm⁻³) multiplied by volume in dm³. If volume is in cm³, divide by 1000 first.
溶液中摩尔数：浓度 (mol dm⁻³) 乘以体积 (dm³)。若体积以 cm³ 为单位，需先除以 1000。
PV = nRT
The ideal gas equation: pressure (P) in Pa, volume (V) in m³, n in mol, R = 8.314 J mol⁻¹ K⁻¹, temperature (T) in kelvin. Remember to convert units: 1 atm = 101 325 Pa; 1 dm³ = 1 × 10⁻³ m³; °C to K by adding 273.15.
理想气体方程：压强 (P) 单位为 Pa，体积 (V) 单位为 m³，n 为摩尔数，R = 8.314 J mol⁻¹ K⁻¹，温度 (T) 单位为开尔文。务必换算单位：1 atm = 101 325 Pa；1 dm³ = 1×10⁻³ m³；°C 转 K 加 273.15。
2. Enthalpy Changes & Hess’s Law | 焓变与盖斯定律
Enthalpy change (ΔH) measures heat energy transferred at constant pressure. Standard conditions are 100 kPa and a stated temperature, usually 298 K. Hess’s Law states that the total enthalpy change for a reaction is independent of the route taken, allowing indirect determination of ΔH using known enthalpy changes of formation or combustion.
焓变 (ΔH) 衡量恒压下传递的热能。标准条件为 100 kPa 和指定温度（通常 298 K）。盖斯定律指出反应的总焓变与路径无关，因此可利用已知的生成焓或燃烧焓间接求算 ΔH。
q = mcΔT
Heat energy transferred: q (J) = mass of solution (g) × specific heat capacity (c, 4.18 J g⁻¹ K⁻¹ for water) × temperature change (ΔT in K or °C). This is the basis for calorimetry experiments.
传递的热量：q (J) = 溶液质量 (g) × 比热容 (c, 水的 c = 4.18 J g⁻¹ K⁻¹) × 温度变化 (ΔT, 单位 K 或 °C)。这是量热实验的基础。
ΔH = –q / n
Enthalpy change per mole: divide the heat energy by the limiting moles (n) and apply a negative sign for exothermic reactions (temperature rise) or positive for endothermic (temperature drop). Units are usually kJ mol⁻¹, so convert q from J to kJ by dividing by 1000.
每摩尔焓变：将热量除以限制性物质的摩尔数 (n)，放热反应（温度升高）加负号，吸热（温度下降）加正号。单位通常为 kJ mol⁻¹，需将 q 从 J 转换为 kJ（除以 1000）。
ΔHreaction = ΣΔHf°(products) – ΣΔHf°(reactants)
Using standard enthalpies of formation: sum of ΔHf° of products minus sum of ΔHf° of reactants. Similarly, for combustion data: ΔHreaction = ΣΔHc°(reactants) – ΣΔHc°(products). Watch the direction of subtraction.
利用标准生成焓：ΔH反应 = ΣΔHf°(生成物) – ΣΔHf°(反应物)。若使用燃烧焓数据：ΔH反应 = ΣΔHc°(反应物) – ΣΔHc°(生成物)。注意相减方向。
3. Rate Equations & The Arrhenius Equation | 速率方程与阿伦尼乌斯方程
The rate of a reaction depends on concentration of reactants, temperature, and the presence of a catalyst. The rate equation links rate to concentration raised to powers (orders), determined experimentally. The Arrhenius equation quantifies the effect of temperature on the rate constant k.
反应速率取决于反应物浓度、温度和催化剂的存在。速率方程将速率与浓度的若干次幂（反应级数）联系起来，级数由实验确定。阿伦尼乌斯方程定量描述了温度对速率常数 k 的影响。
rate = k [A]m [B]n
Rate equation: k is the rate constant; m and n are orders with respect to A and B (0, 1, 2, etc.). Overall order = m + n. Units of k depend on overall order: for zero order, mol dm⁻³ s⁻¹; first order, s⁻¹; second order, dm³ mol⁻¹ s⁻¹; third order, dm⁶ mol⁻² s⁻¹.
速率方程：k 为速率常数；m 和 n 分别为对 A 和 B 的反应级数（0, 1, 2 等）。总级数 = m + n。k 的单位取决于总级数：零级为 mol dm⁻³ s⁻¹；一级为 s⁻¹；二级为 dm³ mol⁻¹ s⁻¹；三级为 dm⁶ mol⁻² s⁻¹。
k = A e–Ea / RT
Arrhenius equation: A is the pre-exponential factor, Ea the activation energy (J mol⁻¹), R the gas constant (8.314 J mol⁻¹ K⁻¹), T the temperature (K). The exponential term e–Ea/RT represents the fraction of molecules with energy ≥ Ea.
阿伦尼乌斯方程：A 为指前因子，Ea 为活化能 (J mol⁻¹)，R 为气体常数 (8.314 J mol⁻¹ K⁻¹)，T 为温度 (K)。指数项 e–Ea/RT 代表能量不低于 Ea 的分子分数。
ln k = –Ea / R (1/T) + ln A
Linear form: a graph of ln k against 1/T yields a straight line with gradient = –Ea/R. This is used in the OCR PAG12 investigation to determine activation energy.
线性形式：以 ln k 对 1/T 作图得直线，斜率 = –Ea/R。OCR PAG12 探究中利用此式测定活化能。
4. Equilibrium Constants Kc & Kp | 平衡常数 Kc 与 Kp
Dynamic equilibrium occurs when the forward and reverse rates are equal. The equilibrium constant expresses the relationship between concentrations (Kc) or partial pressures (Kp) at a given temperature. Its magnitude indicates the position of equilibrium.
动态平衡指正逆反应速率相等的状态。平衡常数表达在给定温度下浓度 (Kc) 或分压 (Kp) 之间的关系，其大小指示平衡位置。
Kc = [C]c[D]d / [A]a[B]b
For the reaction aA + bB ⇌ cC + dD, square brackets denote equilibrium concentrations (mol dm⁻³). Solids and pure liquids are omitted because their concentrations are constant.
对于反应 aA + bB ⇌ cC + dD，方括号表示平衡浓度 (mol dm⁻³)。固体和纯液体因其浓度恒定而不写入表达式。
Kp = (PC)c(PD)d / (PA)a(PB)b
Kp uses partial pressures (e.g., in Pa, atm, or kPa). Partial pressure of a gas = mole fraction × total pressure. Kp has units unless Δn = 0, where Δn = (c+d) – (a+b) for gaseous species only.
Kp 使用分压（单位如 Pa, atm 或 kPa）。某气体的分压 = 摩尔分数 × 总压。除非 Δn = 0，Kp 有单位，Δn 只针对气体物种，(c+d) – (a+b)。
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. Only temperature alters the value of Kc or Kp.
勒夏特列原理： 若平衡体系受到浓度、压力或温度的改变，平衡将向削弱改变的方向移动。只有温度会改变 Kc 或 Kp 的数值。
5. pH, Ka, Kw & pKa | pH、Ka、Kw 与 pKa
The acidity of aqueous solutions is governed by the concentration of hydrogen ions. The ionic product of water, Kw, is fundamental; at 298 K, Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶. For weak acids, the acid dissociation constant Ka indicates the extent of dissociation.
水溶液的酸度由氢离子浓度决定。水的离子积 Kw 是基础；在 298 K 时，Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶。对于弱酸，酸解离常数 Ka 表示解离程度。
pH = –log₁₀ [H⁺]
Definition of pH. [H⁺] must be in mol dm⁻³. For strong monoprotic acids, [H⁺] equals the acid concentration. To find [H⁺] from pH: [H⁺] = 10–pH.
pH 的定义。[H⁺] 必须以 mol dm⁻³ 为单位。对于强一元酸，[H⁺] 等于酸的浓度。从 pH 求 [H⁺]： [H⁺] = 10–pH。
Kw = [H⁺][OH⁻]
At 298 K, Kw = 1.0 × 10⁻¹⁴. In pure water, [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³, giving pH 7. In alkaline solutions, [OH⁻] > [H⁺]; pOH = –log₁₀[OH⁻], and pH + pOH = 14 at 298 K.
298 K 下，Kw = 1.0 × 10⁻¹⁴。纯水中 [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³，pH 为 7。碱性溶液中 [OH⁻] > [H⁺]；pOH = –log₁₀[OH⁻]，且 298 K 时 pH + pOH = 14。
Ka = [H⁺][A⁻] / [HA]
For a weak acid HA ⇌ H⁺ + A⁻. The approximation [H⁺] = √(Ka × [HA]initial) is valid when dissociation is less than 5% and Ka is small. The pKa = –log₁₀ Ka; the smaller the pKa, the stronger the acid.
对于弱酸 HA ⇌ H⁺ + A⁻。当解离度小于 5% 且 Ka 较小时，可使用近似 [H⁺] = √(Ka × [HA]初始)。pKa = –log₁₀ Ka；pKa 越小，酸性越强。
6. Buffer Solutions & Henderson–Hasselbalch | 缓冲溶液与亨德森-哈塞尔巴赫方程
A buffer solution resists changes in pH upon addition of small amounts of acid or base. It consists of a weak acid and its conjugate base (or a weak base and its conjugate acid). The Henderson–Hasselbalch equation is a logarithmic rearrangement of the Ka expression and is highly useful for buffer calculations.
缓冲溶液能抵抗因加入少量酸或碱而引起的 pH 变化。它由弱酸及其共轭碱（或弱碱及其共轭酸）组成。亨德森-哈塞尔巴赫方程是 Ka 表达式的对数重组形式，对缓冲计算极为有用。
pH = pKa + log₁₀ ([A⁻] / [HA])
Henderson–Hasselbalch equation for an acidic buffer. Here [A⁻] is the concentration of the conjugate base (salt) and [HA] the concentration of the weak acid. This equation assumes that the volumes are the same, so mole ratio can be used directly.
酸性缓冲溶液的亨德森-哈塞尔巴赫方程。[A⁻] 为共轭碱（盐）的浓度，[HA] 为弱酸浓度。此方程假设体积相同，因此可直接使用摩尔比。
Preparation of buffers: Mix a weak acid with its salt (e.g., CH₃COOH / CH₃COONa) or partially neutralise a weak acid with a strong base. The pH of an alkaline buffer can be derived from the Kb of the weak base and its conjugate acid.
缓冲液的配制： 将弱酸与其盐混合（例如 CH₃COOH / CH₃COONa）或用强碱部分中和弱酸。碱性缓冲液的 pH 可从弱碱的 Kb 及其共轭酸导出。
Buffer action: Added H⁺ reacts with A⁻ to form HA; added OH⁻ reacts with HA to form A⁻ and water. The ratio [A⁻]/[HA] changes slightly, but the pH shift is minimal as long as the buffer capacity is not exceeded.
缓冲作用： 加入的 H⁺ 与 A⁻ 反应生成 HA；加入的 OH⁻ 与 HA 反应生成 A⁻ 和水。比值 [A⁻]/[HA] 略有变化，但只要不超过缓冲容量，pH 变化极小。
7. Redox & Electrochemical Cells | 氧化还原与电化学电池
Electrochemical cells convert chemical energy into electrical energy. The cell potential (Ecell) is the difference between the reduction potentials of the two half-cells under standard conditions. The standard hydrogen electrode (SHE) is the reference with an assigned potential of 0.00 V.
电化学电池将化学能转化为电能。电池电动势 (Ecell) 是标准条件下两个半电池还原电势之差。标准氢电极 (SHE) 作为参比，其电势规定为 0.00 V。
E°cell = E°reduction (right) – E°oxidation (left)
Standard cell potential. Write the cell with the more positive E° on the right (reduction occurs). A positive E°cell indicates a feasible reaction. Under non-standard conditions, the Nernst equation is used.
标准电池电动势。把 E° 较正的半电池写在右侧（发生还原）。E°cell 为正，表明反应可行。非标准条件下需使用能斯特方程。
ΔG° = –n F E°cell
Relation between Gibbs free energy and cell potential. n = number of moles of electrons transferred, F = Faraday constant = 96 500 C mol⁻¹. For a feasible reaction, ΔG° < 0, so E°cell > 0.
吉布斯自由能与电池电动势的关系。n = 转移电子摩尔数，F = 法拉第常数 = 96 500 C mol⁻¹。反应可行时 ΔG° < 0，故 E°cell > 0。
Rechargeable cells and fuel cells: In a hydrogen-oxygen fuel cell, the overall reaction is 2H₂ + O₂ → 2H₂O. The half-equations are: anode (oxidation) H₂ + 2OH⁻ → 2H₂O + 2e⁻; cathode (reduction) O₂ + 2H₂O + 4e⁻ → 4OH⁻. The electrolyte is alkaline.
可充电电池与燃料电池： 氢氧燃料电池的总反应为 2H₂ + O₂ → 2H₂O。半反应式为：阳极（氧化）H₂ + 2OH⁻ → 2H₂O + 2e⁻；阴极（还原）O₂ + 2H₂O + 4e⁻ → 4OH⁻。电解质为碱性。
8. Born–Haber Cycles & Lattice Enthalpy | 玻恩-哈伯循环与晶格焓
The Born–Haber cycle is an application of Hess’s Law to ionic compounds, relating lattice enthalpy, enthalpy of formation, ionisation energies, electron affinities, and enthalpies of atomisation. Lattice enthalpy (ΔLEH) is the enthalpy change when one mole of solid ionic compound is formed from its gaseous ions.
玻恩-哈伯循环是盖斯定律在离子化合物中的应用，它关联晶格焓、生成焓、电离能、电子亲和能和原子化焓。晶格焓 (ΔLEH) 指由气态离子形成一摩尔固体离子化合物时的焓变。
ΔfH° = Σ (atomisation, IE, EA) + ΔLEH
For NaCl(s) from Na(s) and ½Cl₂(g): ΔfH°(NaCl) = ΔatH°(Na) + IE₁(Na) + ½ΔatH°(Cl₂) + EA(Cl) + ΔLEH(NaCl). Lattice enthalpy is exothermic (negative). The theoretical value from the perfect ionic model often differs from the experimental Born–Haber value; the difference indicates covalent character.
以 Na(s) 和 ½Cl₂(g) 生成 NaCl(s) 为例：ΔfH°(NaCl) = ΔatH°(Na) + IE₁(Na) + ½ΔatH°(Cl₂) + EA(Cl) + ΔLEH(NaCl)。晶格焓为负值（放热）。由纯离子模型计算的理论值常与实验玻恩-哈伯值存在差异，该差异表明化合物具有共价特性。
Enthalpy of solution and hydration: ΔsolH = –ΔLEH + ΣΔhydH (cations + anions). If hydration enthalpy outweighs lattice enthalpy, dissolution is exothermic.
溶解焓与水合焓： ΔsolH = –ΔLEH + ΣΔhydH（阳离子 + 阴离子）。若水合焓超过晶格焓，溶解过程放热。
9. Entropy & Gibbs Free Energy | 熵与吉布斯自由能
Entropy (S) is a measure of disorder. The Second Law states that the total entropy of the universe increases for a spontaneous process. Gibbs free energy (G) combines enthalpy and entropy to predict feasibility at constant temperature and pressure.
熵 (S) 是体系无序度的量度。热力学第二定律指出，自发过程的总熵增加。吉布斯自由能 (G) 结合焓和熵，可在恒温恒压下预测反应的可行性。
ΔS° = ΣS°(products) – ΣS°(reactants)
Standard entropy change. Units are J K⁻¹ mol⁻¹. Note that entropy values for gases are much larger than for liquids or solids. An increase in the number of gas molecules usually corresponds to a positive ΔS°.
标准熵变。单位为 J K⁻¹ mol⁻¹。注意气体的熵值远大于液体或固体。气体分子数增加通常对应正的 ΔS°。
ΔG = ΔH – TΔS
Gibbs free energy equation. ΔG must be negative for a reaction to be feasible. Temperature (T) must be in kelvin. When ΔH and ΔS have opposite signs, feasibility is temperature-independent; when they have the same sign, temperature determines the sign of ΔG.
吉布斯自由能方程。要使反应可行，ΔG 必须为负。温度 (T) 必须以开尔文为单位。若 ΔH 和 ΔS 符号相反，可行性不受温度影响；若符号相同，则温度将决定 ΔG 的正负。
Calculating the temperature at which a reaction becomes feasible: Set ΔG = 0, then T = ΔH / ΔS. Remember to convert ΔH to J mol⁻¹ to match ΔS units.
计算反应刚刚可行的温度： 令 ΔG = 0，则 T = ΔH / ΔS。注意将 ΔH 转换为 J mol⁻¹ 以与 ΔS 单位匹配。
10. Organic Synthesis & Isomerism | 有机合成与异构现象
Year 13 OCR organic chemistry builds on the functional group interconversions from Year 12, adding aromatic chemistry, carbonyl compounds, carboxylic acids, amines, polymers, and biological molecules. A solid grasp of structural, stereoisomerism (E/Z and optical), and key reaction mechanisms is essential.
Year 13 OCR 有机化学建立在 Year 12 官能团转化的基础之上，增加了芳香化学、羰基化合物、羧酸、胺、聚合物和生物分子等内容。牢固掌握结构异构、立体异构 (E/Z 和旋光异构) 以及关键反应机理至关重要。
Optical isomerism: A carbon atom bonded to four different groups is a chiral centre. Two non-superimposable mirror images (enantiomers) rotate plane-polarised light equally but in opposite directions. A racemic mixture contains equal amounts of both enantiomers and is optically inactive.
旋光异构： 连有四个不同基团的碳原子为手性中心。两个不能重叠的镜像（对映体）使平面偏振光发生等量但方向相反的旋转。外消旋混合物含有等量的两种对映体，无旋光性。
Benzene and electrophilic substitution: Benzene has a delocalised π-system. It undergoes nitration (HNO₃/H₂SO₄), halogenation (X₂/AlX₃), Friedel–Crafts alkylation (RCl/AlCl₃) and acylation (RCOCl/AlCl₃). The general mechanism involves generation of the electrophile, attack by benzene π-electrons, formation of a Wheland intermediate, and loss of H⁺ to restore aromaticity.
苯与亲电取代： 苯具有离域 π 体系。它可发生硝化 (HNO₃/H₂SO₄)、卤代 (X₂/AlX₃)、傅-克烷基化 (RCl/AlCl₃) 和酰基化 (RCOCl/AlCl₃)。通用机理包括亲电试剂的生成、苯 π 电子的进攻、韦兰德中间体的形成以及失去 H⁺ 恢复芳香性。
Carbonyl compounds and nucleophilic addition: Aldehydes and ketones undergo nucleophilic addition with HCN (to form hydroxynitriles) and with 2,4-DNPH (to identify the carbonyl group as an orange precipitate). Reduction with NaBH₄ gives primary or secondary alcohols.
羰基化合物与亲核加成： 醛和酮与 HCN 发生亲核加成（生成羟腈），并与 2,4-二硝基苯肼反应生成橙色沉淀以鉴定羰基。用 NaBH₄ 还原可得到伯醇或仲醇。
Polymerisation: Addition polymers are formed from alkenes; condensation polymers such as polyesters and polyamides form with the elimination of a small molecule (water or HCl). Nylon-6,6, Kevlar, and polypeptides are key examples. Hydrolysis of polyesters and polyamides can be acid- or base-catalysed.
聚合反应： 加成聚合物由烯烃形成；缩合聚合物如聚酯和聚酰胺在形成时脱去小分子（水或 HCl）。尼龙-6,6、凯夫拉尔和多肽是重要例子。聚酯和聚酰胺可在酸或碱催化下水解。
11. Spectroscopy & Structure Determination | 光谱与结构解析
Structure determination in OCR Year 13 integrates mass spectrometry, infrared (IR) spectroscopy, and ¹³C and ¹H NMR spectroscopy. Together, these techniques provide molecular mass, functional groups, and detailed carbon/hydrogen environments.
OCR Year 13 的结构解析综合了质谱、红外光谱以及碳谱和氢谱核磁共振。这些技术共同提供分子质量、官能团以及详细的碳/氢环境信息。
IR absorption: C=O ~1700 cm⁻¹; O–H ~2500–3300 cm⁻¹ (broad); C–O ~1000–1300 cm⁻¹
Key infrared absorptions: a strong sharp peak near 1700 cm⁻¹ indicates C=O; a broad peak between 2500–3300 cm⁻¹ is characteristic of O–H in carboxylic acids; alcohols give a broad O–H around 3200–3600 cm⁻¹.
关键红外吸收：1700 cm⁻¹ 附近强尖峰指示 C=O；2500–3300 cm⁻¹ 范围内的宽峰是羧酸中 O–H 的特征；醇的 O–H 在 3200–3600 cm⁻¹ 呈宽峰。
¹³C NMR: Number of peaks = number of non-equivalent carbon environments. Chemical shifts (δ): 0–50 ppm for saturated C; 50–90 ppm for C–O (alcohols, ethers); 90–160 ppm for alkene/aromatic C; 160–185 ppm for ester/acid C; 190–220 ppm for aldehyde/ketone C=O. The solvent used is CDCl₃ or CCl₄, and TMS is the reference (δ = 0).
¹³C 核磁共振： 峰的数量 = 不等价碳环境的数目。化学位移 (δ)：饱和碳为 0–50 ppm；与氧相连的碳 (醇、醚) 为 50–90 ppm；烯烃/芳香碳为 90–160 ppm；酯/酸碳为 160–185 ppm；醛/酮羰基碳为 190–220 ppm。所用溶剂为 CDCl₃ 或 CCl
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