📚 Year 13 Cambridge Chemistry: Formulae and Theorems Quick Reference | A2化学公式定理速查手册
This handbook provides a concise compilation of essential formulae and theorems for the Year 13 Cambridge Chemistry (A2) course. It is designed as a quick revision tool, covering physical, inorganic and organic chemistry. Use it to reinforce your understanding and boost your exam confidence.
本手册简明汇编了 Year 13 剑桥 A2 化学的核心公式与定理，涵盖物理化学、无机化学和有机化学。可作为考前速查工具，帮助巩固知识点，提升应试信心。
1. Ideal Gas Equation and Kinetic Theory | 理想气体方程与分子动理论
The ideal gas equation unites the macroscopic properties of a gas: pV = nRT, where p = pressure (Pa), V = volume (m³), n = amount (mol), R = 8.31 J mol⁻¹ K⁻¹, T = thermodynamic temperature (K). Real gases deviate from ideality at high pressure and low temperature.
理想气体状态方程：pV = nRT，式中 p 为压强(Pa)，V 为体积(m³)，n 为物质的量(mol)，R = 8.31 J mol⁻¹ K⁻¹，T 为热力学温度(K)。实际气体在高压低温下会偏离理想行为。
From the kinetic model, pV = 1/3 n M c_rms² and the average kinetic energy per mole of a monatomic gas is KE = (3/2) RT. The root mean square speed is given by c_rms = √(3RT/M), where M is molar mass in kg mol⁻¹.
根据分子动理论模型：pV = 1/3 n M c_rms²，单原子气体每摩尔平均动能 KE = (3/2) RT。均方根速率公式：c_rms = √(3RT/M)，M 为摩尔质量(kg mol⁻¹)。
2. Thermodynamic Functions: ΔH, ΔS and ΔG | 热力学函数：焓变、熵变与吉布斯自由能变
Enthalpy change ΔH = H(products) – H(reactants). Standard enthalpy changes are indicated by the symbol ° (e.g., ΔH°f, ΔH°c). Exothermic: ΔH < 0; endothermic: ΔH > 0.
焓变 ΔH = H(生成物) – H(反应物)。标准焓变用 ° 表示（如 ΔH°f, ΔH°c）。放热反应 ΔH < 0，吸热反应 ΔH > 0。
Entropy S measures the dispersal of energy. The Second Law states that for a spontaneous process, ΔS_total = ΔS_system + ΔS_surroundings > 0. ΔS_surroundings = –ΔH/T.
熵 S 衡量能量的分散程度。热力学第二定律指出，自发过程的总熵变 ΔS_total = ΔS_system + ΔS_surroundings > 0。环境熵变 ΔS_surroundings = –ΔH/T。
The Gibbs free energy change determines feasibility under constant temperature and pressure: ΔG = ΔH – TΔS. A reaction is feasible when ΔG < 0. At equilibrium, ΔG = 0. The standard free energy change is related to the equilibrium constant: ΔG° = –RT ln K.
吉布斯自由能变决定恒温恒压下反应的自发性：ΔG = ΔH – TΔS。当 ΔG < 0 时反应可行。平衡时 ΔG = 0。标准自由能变与平衡常数的关系为 ΔG° = –RT ln K。
3. Chemical Equilibrium: Kc and Kp | 化学平衡：Kc 与 Kp
For a reversible reaction aA + bB ⇌ cC + dD, the equilibrium constants are defined using equilibrium concentrations (Kc) or partial pressures (Kp):
对于可逆反应 aA + bB ⇌ cC + dD，平衡常数用平衡浓度 (Kc) 或分压 (Kp) 定义：
Kc = [C]ᶜ [D]ᵈ / [A]ᵃ [B]ᵇ Kp = p(C)ᶜ p(D)ᵈ / p(A)ᵃ p(B)ᵇ
The magnitude of Kc indicates the position of equilibrium. Kp and Kc are related by Kp = Kc (RT)^Δn, where Δn = (c+d) – (a+b) for gaseous species only.
Kc 的大小反映平衡位置。Kp 与 Kc 的关系为 Kp = Kc (RT)^Δn，其中 Δn = (c+d) – (a+b)，仅考虑气体物种。
4. Acid–Base Equilibria and pH Calculations | 酸碱平衡与 pH 计算
The ionic product of water at 298 K: Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶. pH is defined as pH = –log₁₀[H⁺]; similarly, pOH = –log₁₀[OH⁻] and pH + pOH = 14 at 298 K.
298 K 时水的离子积：Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶。pH 定义为 pH = –log₁₀[H⁺]，同理 pOH = –log₁₀[OH⁻]，且 pH + pOH = 14。
For a weak acid HA: Ka = [H⁺][A⁻] / [HA] and pKa = –log₁₀ Ka. The approximation [H⁺] = √(Ka × [HA]) works when dissociation is very small. For a weak base B: Kb = [BH⁺][OH⁻] / [B].
弱酸 HA：Ka = [H⁺][A⁻] / [HA]，pKa = –log₁₀ Ka。解离度很小时可用近似公式 [H⁺] = √(Ka × [HA])。弱碱 B：Kb = [BH⁺][OH⁻] / [B]。
5. Buffers and Henderson–Hasselbalch Equation | 缓冲溶液与亨德森-哈塞尔巴尔赫方程
A buffer solution resists changes in pH upon addition of small amounts of acid or base. It contains a weak acid and its conjugate base (or a weak base and its conjugate acid). The pH of an acidic buffer is given by:
缓冲溶液能抵抗少量外加酸或碱引起的 pH 变化。其由弱酸及其共轭碱（或弱碱及其共轭酸）组成。酸性缓冲液的 pH 由下式计算：
pH = pKa + log₁₀([A⁻] / [HA])
This is the Henderson–Hasselbalch equation. For a basic buffer, an analogous expression using pKb applies. Buffer capacity is highest when [A⁻] = [HA], i.e., pH = pKa.
此为亨德森-哈塞尔巴尔赫方程。碱性缓冲液可使用类似的 pKb 表达式。当 [A⁻] = [HA] 即 pH = pKa 时，缓冲容量最大。
6. Solubility Equilibria: Ksp and the Common Ion Effect | 溶解平衡：溶度积与同离子效应
For a sparingly soluble salt MₐXₐ (where X is an anion), the solubility product is Ksp = [M⁺]ᵐ [X⁻]ˣ, defined for a saturated solution at a given temperature. Ksp can be used to predict precipitation: precipitation occurs when the ionic product (IP) > Ksp.
对于难溶盐 MₐXₐ，溶度积定义为饱和溶液中 Ksp = [M⁺]ᵐ [X⁻]ˣ。可用于判断沉淀：当离子积 IP > Ksp 时产生沉淀。
The common ion effect reduces solubility; for instance, adding NaCl to a saturated AgCl solution shifts the equilibrium AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq) to the left, decreasing [Ag⁺].
同离子效应降低溶解度；例如在饱和 AgCl 溶液中加入 NaCl，平衡 AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq) 向左移动，[Ag⁺] 减小。
7. Electrochemistry: Standard Electrode Potentials and Nernst Equation | 电化学：标准电极电势与能斯特方程
The standard cell potential E°cell = E°(right) – E°(left) or E°(cathode) – E°(anode) under standard conditions (298 K, 1 mol dm⁻³, 100 kPa). A positive E°cell indicates a feasible reaction. ΔG° = –nFE°cell, where F = 96 500 C mol⁻¹.
标准电池电动势 E°cell = E°(右) – E°(左) 或 E°(阴极) – E°(阳极)，在标准条件 (298 K, 1 mol dm⁻³, 100 kPa) 下测定。E°cell > 0 表示反应可行。ΔG° = –nFE°cell，F = 96 500 C mol⁻¹。
Under non-standard conditions, the Nernst equation allows calculation of electrode potentials:
E = E° – (RT / nF) ln Q
At 298 K, this simplifies to E = E° – (0.0592 / n) log₁₀ Q (in volts). The reaction quotient Q takes the same form as Kc but using actual concentrations/pressures.
非标准条件下，通过能斯特方程计算电极电势：E = E° – (RT / nF) ln Q。298 K 时可简化为 E = E° – (0.0592 / n) log₁₀ Q (V)。反应商 Q 形式与平衡常数相同，但采用实际浓度/分压。
8. Rate Laws, Order of Reaction and Arrhenius Equation | 速率定律、反应级数与阿伦尼乌斯方程
For a reaction A + B → products, the rate law is rate = k [A]ᵐ [B]ⁿ, where m and n are partial orders determined experimentally. The overall order is m + n. Units of k depend on the overall order: for zero order, mol dm⁻³ s⁻¹; first order, s⁻¹; second order, dm³ mol⁻¹ s⁻¹.
反应 A + B → 产物，速率方程为 rate = k [A]ᵐ [B]ⁿ，m 和 n 为实验测定的分级数，总级数为 m + n。k
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