📚 Year 13 AQA Chemistry: Formula & Theorem Quick Reference | AQA Year 13 化学：公式定理速查手册
This handbook compiles the most essential formulas, theorems, and constants required for Year 13 AQA Chemistry. It is designed for quick revision, linking theory to numerical application across physical, inorganic, and organic chemistry topics. Each section pairs explanation with the corresponding equations, ensuring you can recall and apply the correct relationships in the exam.
本手册汇编了 Year 13 AQA 化学中最关键的公式、定理和常数，用于快速复习，将理论与物理化学、无机化学和有机化学中的数值计算紧密结合起来。每一节都配有说明和对应的方程式，帮助你在考试中准确回忆并正确运用这些关系。
1. Fundamental Formulae & Constants | 基本公式与常数
The mole concept links mass, volume, and particle number. Key constants include the Avogadro constant, molar gas volume at RTP, and the ideal gas constant. These underpin stoichiometry and energy calculations throughout the A-level course.
摩尔概念将质量、体积和粒子数联系起来。关键常数包括阿伏伽德罗常数、常温常压下的摩尔气体体积和理想气体常数。它们是整个 A-level 课程中化学计量学和能量计算的基础。
Number of moles: n = m / M n = N / NA n = V(gas at RTP) / 24.0 dm³ mol⁻¹
物质的量： n = m / M n = N / NA n = V(气体，常温常压) / 24.0 dm³ mol⁻¹
Ideal Gas Equation: pV = nRT (p in Pa, V in m³, T in K, R = 8.31 J K⁻¹ mol⁻¹)
理想气体状态方程： pV = nRT (p 单位 Pa, V 单位 m³, T 单位 K, R = 8.31 J K⁻¹ mol⁻¹)
Key constants: NA = 6.022 × 10²³ mol⁻¹; molar gas volume at RTP = 24.0 dm³ mol⁻¹ (293 K, 101 kPa).
关键常数： NA = 6.022 × 10²³ mol⁻¹; 常温常压下摩尔气体体积 = 24.0 dm³ mol⁻¹ (293 K, 101 kPa)。
2. Rate Equations & Arrhenius Equation | 速率方程与阿伦尼乌斯方程
The rate equation expresses the dependence of reaction rate on reactant concentrations. The Arrhenius equation quantifies the temperature dependence of the rate constant, linking activation energy and the pre‑exponential factor.
速率方程表达了反应速率对反应物浓度的依赖关系。阿伦尼乌斯方程则定量描述了速率常数随温度的变化，将活化能与指前因子联系起来。
General rate equation: rate = k [A]ᵐ [B]ⁿ (m + n = overall order)
通用速率方程： 速率 = k [A]ᵐ [B]ⁿ (m + n = 总反应级数)
Arrhenius equation (linearised): ln k = –Ea/RT + ln A or k = A e–Ea/RT
阿伦尼乌斯方程（线性形式）： ln k = –Ea/RT + ln A 或 k = A e–Ea/RT
A graph of ln k against 1/T gives a straight line with gradient = –Ea/R and y‑intercept = ln A. The pre‑exponential factor A accounts for collision frequency and orientation.
以 ln k 对 1/T 作图得到一条直线，斜率 = –Ea/R，截距 = ln A。指前因子 A 考虑了碰撞频率和取向。
3. Chemical Equilibria: Kc & Kp | 化学平衡常数
Equilibrium constants express the ratio of product to reactant concentrations (or partial pressures) at equilibrium at a given temperature. Their magnitude indicates the position of equilibrium.
平衡常数表示在一定温度下，平衡时产物浓度（或分压）与反应物浓度（或分压）之比。其大小反映了平衡的位置。
Kc for a general reaction aA + bB ⇌ cC + dD:
对于一般反应 aA + bB ⇌ cC + dD 的 Kc：
Kc = [C]ᶜ [D]ᵈ / [A]ᵃ [B]ᵇ
Kp using partial pressures:
用分压表示的 Kp：
Kp = (pC)ᶜ (pD)ᵈ / (pA)ᵃ (pB)ᵇ
Partial pressure = mole fraction × total pressure. Temperature is the only factor that changes Kc or Kp; catalysts have no effect. If K >> 1 equilibrium lies to the right; if K << 1 it lies to the left.
分压 = 摩尔分数 × 总压。温度是唯一能改变 Kc 或 Kp 的因素，催化剂无影响。若 K ≫ 1，平衡偏向右侧；若 K ≪ 1，平衡偏向左侧。
4. Acid–Base Equilibria | 酸碱平衡
Brønsted–Lowry acids donate protons; bases accept protons. For weak acids and bases, the dissociation constant quantifies the extent of ionisation. The ionic product of water, Kw, links H⁺ and OH⁻ concentrations.
根据 Brønsted–Lowry 理论，酸是质子的给予体，碱是质子的接受体。对于弱酸和弱碱，解离常数可以衡量电离程度。水的离子积 Kw 将 H⁺ 和 OH⁻ 的浓度联系起来。
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ (at 298 K)
pH = –log₁₀[H⁺] [H⁺] = 10–pH
Weak acid dissociation constant: Ka = [H⁺][A⁻] / [HA] pKa = –log Ka
弱酸解离常数： Ka = [H⁺][A⁻] / [HA] pKa = –log Ka
For a buffer solution, the Henderson–Hasselbalch approximation is often used: pH ≈ pKa + log([A⁻]/[HA]). A buffer resists pH changes when small amounts of acid or base are added; it consists of a weak acid and its conjugate base in similar concentrations.
缓冲溶液常用 Henderson–Hasselbalch 近似公式：pH ≈ pKa + log([A⁻]/[HA])。当加入少量酸或碱时，缓冲溶液能够抵抗 pH 的变化；它由浓度相近的弱酸及其共轭碱组成。
5. Thermodynamics: Gibbs Free Energy & Entropy | 热力学：吉布斯自由能与熵
Feasibility of a reaction is determined by the Gibbs free‑energy change. Entropy measures disorder, and the total entropy change must be positive for a spontaneous process.
反应的可行性由吉布斯自由能变决定。熵衡量体系的混乱程度，对于自发过程，总熵变必须为正值。
ΔG = ΔH – TΔS
ΔG < 0 for a feasible (spontaneous) reaction. ΔG = 0 at equilibrium. The relationship between ΔG and the equilibrium constant is:
反应的可行性（自发）要求 ΔG < 0。平衡时 ΔG = 0。ΔG 与平衡常数的关系为：
ΔG° = –RT ln K
Entropy change of the surroundings: ΔSsurr = –ΔH/T. Total entropy change: ΔStotal = ΔSsys + ΔSsurr. A reaction is thermodynamically feasible when ΔStotal > 0.
环境熵变：ΔSsurr = –ΔH/T。总熵变：ΔStotal = ΔSsys + ΔSsurr。当 ΔStotal > 0 时，反应在热力学上可行。
Also, ΔG° = –nFE°cell links thermodynamics to electrochemistry (F = 96 500 C mol⁻¹).
此外，ΔG° = –nFE°cell 将热力学与电化学联系起来（F = 96 500 C mol⁻¹）。
6. Electrode Potentials & Electrochemical Cells | 电极电位与电化学电池
The cell potential is the difference in tendency of two half‑cells to gain electrons. Standard conditions (298 K, 100 kPa, 1.0 mol dm⁻³ solutions) must be used to compare electrode potentials.
电池电动势是两种半电池得电子趋势的差异。比较电极电位时必须使用标准条件（298 K, 100 kPa, 1.0 mol dm⁻³ 溶液）。
Ecell = Eright – Eleft (when written as a cell diagram: left || right).
Ecell = Eright – Eleft （以电池图示表示时：左 || 右）。
A positive Ecell indicates a thermodynamically feasible reaction. The electrode with the more positive reduction potential undergoes reduction. For electrolysis, the same principles apply, but an external voltage greater than the cell potential must be supplied to reverse a spontaneous reaction.
Ecell 为正说明反应在热力学上可行。标准还原电位更正的电极发生还原反应。电解时也遵循同样的原理，但必须施加大于电池电动势的外加电压才能逆转自发反应。
For quantitative electrolysis: Q = It and the number of moles of electrons n(e⁻) = Q / F, where F = 96 500 C mol⁻¹. Mass of substance deposited or evolved is calculated via n = m/M and stoichiometry.
定量电解：Q = It，电子物质的量 n(e⁻) = Q / F，其中 F = 96 500 C mol⁻¹。沉积或析出物质的质量通过 n = m/M 和化学计量比计算。
7. Born–Haber Cycles & Energetics | 波恩–哈伯循环与能量学
Born–Haber cycles apply Hess’s law to ionic compound formation, linking atomisation energies, ionisation energies, electron affinities, and lattice enthalpy. The lattice enthalpy is the enthalpy change when one mole of an ionic solid is formed from its gaseous ions.
波恩–哈伯循环将 Hess 定律应用于离子化合物的形成过程，将原子化能、电离能、电子亲和能和晶格焓联系起来。晶格焓是指由气态离子形成 1 mol 离子固体时的焓变。
ΔfH°(salt) = Σ (atomisation enthalpies) + Σ (ionisation energies) + Σ (electron affinities) + ΔLEH°
Lattice enthalpy is exothermic and its magnitude depends on ionic charge and ionic radius: the greater the charge and the smaller the ion, the more negative the lattice enthalpy. This explains trends in thermal stability and melting points.
晶格焓为放热过程，其数值取决于离子电荷和离子半径：电荷越高、离子越小，晶格焓越负。这可以解释热稳定性和熔点的变化趋势。
Enthalpy of solution = –lattice enthalpy + hydration enthalpies. If the sum is negative, the salt is likely to dissolve. If positive, solubility is low.
溶解焓 = –晶格焓 + 水合焓。如果总焓变为负，盐类可能易溶；若为正，则溶解度较低。
8. Acid–Base Titrations & Indicators | 酸碱滴定与指示剂
The shape of a pH titration curve depends on the strengths of the acid and base. The vertical section contains the equivalence point, where moles of acid = moles of base. Indicators are chosen so that their pKa lies within the steep pH change of the titration.
pH 滴定曲线的形状取决于酸和碱的强弱。垂直段包含化学计量点，此时酸的物质的量与碱的物质的量相等。选择指示剂时，应使其 pKa 值落入滴定 pH 突跃范围之内。
| Titration type | pH jump range | Suitable indicator (pKa) |
|---|---|---|
| Strong acid – strong base | ~3 to ~11 | Phenolphthalein (9.3) or methyl orange (3.5) |
| Weak acid – strong base | ~7 to ~11 | Phenolphthalein |
| Strong acid – weak base | ~3 to ~7 | Methyl orange |
For a weak acid – weak base titration, the pH change is gradual; no single indicator gives a sharp colour change, so it is not recommended.
对于弱酸 – 弱碱滴定，pH 变化平缓，没有任何单一指示剂能产生敏锐的颜色变化，因此不建议使用指示剂法。
9. Key Organic Reaction Conditions (Quick Reference) | 关键有机反应条件速查
Memorising the reagents, conditions, and mechanisms for organic transformations is vital. Below is a concise summary of frequently tested reactions in Year 13 AQA Chemistry.
熟记有机反应的试剂、条件和机理至关重要。以下简要归纳了 Year 13 AQA 化学中常考的反应。
| Reaction | Reagents & Conditions | Key points |
|---|---|---|
| Benzene nitration | Conc. HNO₃ / conc. H₂SO₄, 55 °C | Electrophilic substitution; NO₂⁺ electrophile |
| Friedel–Crafts acylation | RCOCl, AlCl₃ catalyst, anhydrous | Introduces acyl group; prevents poly-substitution |
| Reduction of nitrobenzene | Sn / conc. HCl, reflux, then NaOH | Produces phenylamine |
| Aldehyde → carboxylic acid | K₂Cr₂O₇ / H₂SO₄, reflux | Full oxidation; colour change orange → green |
| Esterification | Alcohol + carboxylic acid, conc. H₂SO₄ catalyst, heat | Equilibrium; use excess reactant to improve yield |
| Acyl chloride + amine | Room temperature, anhydrous | Produces N‑substituted amide + HCl |
| Polymerisation (addition) | High pressure, heat, radical initiator | Monomer must have C=C bond |
Always consider safety, use of fume cupboards for toxic gases, and correct temperature control to avoid side‑reactions.
务必注意安全，使用通风橱处理有毒气体，并严格控制温度以避免副反应。
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