📚 CIE A-Level Chemistry Formula Handbook | CIE A-Level 化学：公式汇总手册
This is a comprehensive formula compendium for CIE A-Level Chemistry (9701). Every key equation you need for the exam is presented with clear symbols, units, and paired English–Chinese explanations. The handbook covers physical, inorganic, and quantitative chemistry, helping you master calculations in stoichiometry, thermodynamics, kinetics, equilibrium, electrochemistry, and more.
这是为 CIE A-Level 化学 (9701) 精心整理的一站式公式手册。手册包含了考试所需的每一个核心公式，并以清晰的符号、单位和中英双语解释呈现。内容涵盖物理化学、无机化学和定量化学，帮助你彻底掌握化学计量、热力学、动力学、平衡、电化学等领域的计算。
1. Mole & Stoichiometry | 摩尔与化学计量
Number of moles n = mass m (g) / molar mass M (g mol⁻¹). Used to convert between mass and amount of substance.
摩尔数 n = 质量 m (g) / 摩尔质量 M (g mol⁻¹)。用于质量与物质的量之间的换算。
For solutions: n = c × V, where c is concentration (mol dm⁻³) and V is volume in dm³. Always convert cm³ to dm³ by dividing by 1000.
对于溶液：n = c × V，其中 c 为物质的量浓度 (mol dm⁻³)，V 为体积 (dm³)。务必先将 cm³ 除以 1000 转换为 dm³。
Number of particles N = n × L, where L is the Avogadro constant (6.022 × 10²³ mol⁻¹). This connects the macroscopic amount to the number of atoms, molecules or ions.
粒子数 N = n × L，其中 L 为阿伏伽德罗常数 (6.022 × 10²³ mol⁻¹)。该公式将宏观物质的量与原子、分子或离子的数目联系起来。
Percentage yield = (actual yield / theoretical yield) × 100. Atom economy = (molar mass of desired product / sum of molar masses of all products) × 100.
产率 = (实际产量 / 理论产量) × 100。原子经济性 = (目标产物的摩尔质量 / 所有产物摩尔质量之和) × 100。
2. Gas Laws | 气体定律
Ideal gas equation: pV = nRT. p = pressure in Pa, V = volume in m³, n = moles, R = 8.31 J K⁻¹ mol⁻¹, T = temperature in K. This equation is used at low pressure and high temperature.
理想气体状态方程：pV = nRT。p 为压强 (Pa)，V 为体积 (m³)，n 为摩尔数，R = 8.31 J K⁻¹ mol⁻¹，T 为温度 (K)。该方程适用于低压高温条件。
Converting common pressure units: 1 atm = 101325 Pa, 1 bar = 10⁵ Pa. Volume: 1 dm³ = 10⁻³ m³. Temperature in Kelvin: T(K) = T(°C) + 273.
常见压强单位换算：1 atm = 101325 Pa，1 bar = 10⁵ Pa。体积：1 dm³ = 10⁻³ m³。开氏温度：T(K) = T(°C) + 273。
Molar volume of an ideal gas at RTP (20°C, 1 atm) is approximately 24.0 dm³ mol⁻¹; at STP (0°C, 1 atm) it is 22.4 dm³ mol⁻¹. These can be used for quick estimates.
在室温常压 (RTP, 20°C, 1 atm) 下，理想气体的摩尔体积约为 24.0 dm³ mol⁻¹；在标准状况 (STP, 0°C, 1 atm) 下为 22.4 dm³ mol⁻¹。可用于快速估算。
3. Enthalpy & Calorimetry | 焓与量热学
Heat change q = mcΔT, where m = mass of water/solution (g), c = specific heat capacity (usually 4.18 J g⁻¹ K⁻¹ for water), ΔT = temperature change (K or °C).
热量变化 q = mcΔT，其中 m 为水/溶液的质量 (g)，c 为比热容（水通常取 4.18 J g⁻¹ K⁻¹），ΔT 为温度变化 (K 或 °C)。
Enthalpy change per mole ΔH = –q / n (in kJ mol⁻¹ after converting J to kJ). The negative sign indicates that the heat measured is gained or lost by the surroundings.
每摩尔焓变 ΔH = –q / n（单位 kJ mol⁻¹，需将 J 转换为 kJ）。负号表示测得的热量是环境获得或失去的热量。
For combustion, q = mcΔT for the water heated, then ΔHc = –q / n(fuel). For neutralisation, mix equal volumes of acid and alkali, measure ΔT, and use total mass.
对于燃烧焓，q = mcΔT 测得水吸收的热量，ΔHc = –q / n(燃料)。对于中和焓，混合等体积酸和碱，测量 ΔT，取溶液总质量。
4. Bond Energy & Hess’s Law | 键能与赫斯定律
Enthalpy change of reaction ΔHr ≈ ΣBE(bonds broken) – ΣBE(bonds formed). Bond energies are average values from gas-phase data.
反应焓变 ΔHr ≈ ΣBE(断裂键) – ΣBE(形成键)。键能是气态数据平均值。
Hess’s Law: The total enthalpy change for a reaction is independent of the route taken. ΔH₁ = ΔH₂ + ΔH₃. Draw enthalpy cycles, set the unknown route equal to the known route.
赫斯定律：反应的总焓变与途径无关。ΔH₁ = ΔH₂ + ΔH₃。画出焓变循环图，令未知路径等于已知路径。
Using standard enthalpy changes: ΔH°f = standard enthalpy of formation; ΔH°c = standard enthalpy of combustion. ΔHr = ΣΔH°f(products) – ΣΔH°f(reactants).
使用标准焓变：ΔH°f 为标准生成焓；ΔH°c 为标准燃烧焓。ΔHr = ΣΔH°f(产物) – ΣΔH°f(反应物)。
5. Entropy & Gibbs Free Energy | 熵与吉布斯自由能
Entropy change of the system ΔS°sys = ΣS°(products) – ΣS°(reactants). Units: J K⁻¹ mol⁻¹. Standard molar entropies S° are given in data booklets.
系统熵变 ΔS°sys = ΣS°(产物) – ΣS°(反应物)。单位：J K⁻¹ mol⁻¹。标准摩尔熵 S° 由数据手册提供。
Total entropy change ΔS°total = ΔS°sys + ΔS°surr, where ΔS°surr = –ΔH / T. A reaction is spontaneous (feasible) when ΔS°total > 0.
总熵变 ΔS°total = ΔS°sys + ΔS°surr，其中 ΔS°surr = –ΔH / T。当 ΔS°total > 0 时，反应可自发（可行）。
Gibbs free energy change ΔG = ΔH – TΔS. ΔG must be negative for a feasible reaction. T in Kelvin; ΔS in kJ K⁻¹ mol⁻¹ must match ΔH units.
吉布斯自由能变 ΔG = ΔH – TΔS。当 ΔG < 0 时反应可行。T 单位为 K；ΔS 单位需转化为 kJ K⁻¹ mol⁻¹ 以与 ΔH 匹配。
6. Equilibrium Constant | 平衡常数
For a reaction aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration: Kc = ([C]ᶜ [D]ᵈ) / ([A]ᵃ [B]ᵇ). Units vary with stoichiometry and are often omitted at A-Level.
对于反应 aA + bB ⇌ cC + dD，用浓度表示的平衡常数：Kc = ([C]ᶜ [D]ᵈ) / ([A]ᵃ [B]ᵇ)。单位因计量系数而异，A-Level 常省略单位。
In terms of pressure: Kp = (pCᶜ × pDᵈ) / (pAᵃ × pBᵇ), where pX is the partial pressure. pX = (mole fraction) × total pressure. Mole fraction = nX / nTotal.
用压强表示的平衡常数：Kp = (pCᶜ × pDᵈ) / (pAᵃ × pBᵇ)，pX 为气体分压。pX = 摩尔分数 × 总压。摩尔分数 = nX / nTotal。
Only gaseous and aqueous species appear in Kc/Kp expressions; solids and pure liquids are treated as having constant ‘concentration’ and are omitted.
仅气态与溶液态物种出现在 Kc/Kp 表达式中；固体和纯液体被视为“浓度”恒定，不写入表达式。
Le Chatelier’s principle predicts shifts to counteract changes. The effect of temperature on K: endothermic reaction – K increases with T; exothermic – K decreases with T.
勒夏特列原理可预测平衡移动。温度对 K 的影响：吸热反应——升温 K 增大；放热反应——升温 K 减小。
7. Rate Equations & Kinetics | 速率方程与动力学
Rate law: rate = k[A]ᵐ[B]ⁿ. m and n are orders of reaction with respect to A and B; they are experimentally determined, not from the stoichiometric coefficients.
速率方程：rate = k[A]ᵐ[B]ⁿ。m 和 n 分别为对 A、B 的反应级数，由实验确定，不可从化学计量系数推断。
Units of rate constant k: for overall order 0: mol dm⁻³ s⁻¹; order 1: s⁻¹; order 2: dm³ mol⁻¹ s⁻¹; order 3: dm⁶ mol⁻² s⁻¹.
速率常数 k 的单位：总级数为 0：mol dm⁻³ s⁻¹；1 级：s⁻¹；2 级：dm³ mol⁻¹ s⁻¹；3 级：dm⁶ mol⁻² s⁻¹。
Half-life for a first-order reaction: t½ = ln2 / k ≈ 0.693 / k. The half-life is constant and independent of initial concentration.
一级反应的半衰期：t½ = ln2 / k ≈ 0.693 / k。半衰期恒定，与初始浓度无关。
Arrhenius equation: k = Ae^(–Eₐ/RT) or ln k = –Eₐ/(RT) + ln A. A linear plot of ln k against 1/T yields a slope of –Eₐ/R.
阿伦尼乌斯方程：k = Ae^(–Eₐ/RT) 或 ln k = –Eₐ/(RT) + ln A。作 ln k – 1/T 图，斜率为 –Eₐ/R。
8. pH & Ionic Product of Water | pH 与水的离子积
pH = –log₁₀[H⁺], where [H⁺] is in mol dm⁻³. Similarly, pOH = –log₁₀[OH⁻]. At 25°C, pH + pOH = 14.
pH = –log₁₀[H⁺]，[H⁺] 单位为 mol dm⁻³。类似地，pOH = –log₁₀[OH⁻]。25°C 时，pH + pOH = 14。
Ionic product of water: Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25°C. Kw increases with temperature because auto-ionisation is endothermic.
水的离子积：Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ (25°C)。Kw 随温度升高而增大，因为水的自电离是吸热过程。
For a strong acid [H⁺] = cₐ (monoprotic); for a strong base [OH⁻] = c_b (monobasic). For weak acids: Ka = [H⁺][A⁻] / [HA]; [H⁺] = √(Ka × cₐ) for small dissociation.
强酸 [H⁺] = cₐ (一元酸)；强碱 [OH⁻] = c_b (一元碱)。弱酸：Ka = [H⁺][A⁻] / [HA]；电离度很小时 [H⁺] = √(Ka × cₐ)。
Buffer pH: Henderson–Hasselbalch equation for an acidic buffer: pH = pKa + log₁₀([salt]/[acid]). This is used when preparing buffers or calculating pH changes.
缓冲溶液 pH：酸性缓冲液的亨德森-哈塞尔巴尔赫方程：pH = pKa + log₁₀([盐]/[酸])。用于配制缓冲液或计算 pH 变化。
9. Electrochemistry | 电化学
Standard cell potential E°cell = E°(reduction at cathode) – E°(reduction at anode). A positive E°cell indicates a thermodynamically feasible reaction.
标准电池电动势 E°cell = E°(阴极还原) – E°(阳极还原)。E°cell 为正表示反应热力学可行。
Relationship linking Gibbs free energy and cell potential: ΔG° = –nFE°cell, where n is the number of moles of electrons transferred, and F is the Faraday constant (96 500 C mol⁻¹).
吉布斯自由能与电池电动势的关系：ΔG° = –nFE°cell，n 为转移电子摩尔数，F 为法拉第常数 (96 500 C mol⁻¹)。
Quantitative electrolysis: Q = I × t, where Q is charge (C), I is current (A), t is time (s). Moles of electrons n(e⁻) = Q / F. Mass deposited m = (Q × M) / (n × F).
定量电解：Q = I × t，Q 为电荷量 (C)，I 为电流 (A)，t 为时间 (s)。电子摩尔数 n(e⁻) = Q / F。析出质量 m = (Q × M) / (n × F)。
Nernst equation (for non-standard conditions): E = E° – (RT/nF) lnQ, or at 25°C: E = E° – (0.0592/n) logQ. Q is the reaction quotient.
能斯特方程（非标准条件）：E = E° – (RT/nF) lnQ，25°C 时简化为 E = E° – (0.0592/n) logQ。Q 为反应商。
10. Quantitative Organic Chemistry | 定量有机化学
Percentage by mass of an element in a compound = (number of atoms × Ar / Mr of compound) × 100. Used in elemental analysis.
化合物中某元素的质量分数 = (原子个数 × Ar / 化合物的 Mr) × 100。用于元素分析。
Empirical formula from mass composition: convert % to mass → divide by Ar → divide by smallest → obtain simplest whole-number ratio. Molecular formula requires molar mass.
由质量组成确定经验式：% → 质量 → 除以 Ar → 除以最小比值 → 最简整数比。分子式需要摩尔质量。
For organic reactions, calculate theoretical mass of product using stoichiometric ratios, then apply percentage yield and atom economy as in Section 1.
对于有机反应，利用化学计量比计算产物的理论质量，再套用第1节中的产率和原子经济性公式。
11. Partition Coefficient & Solvent Extraction | 分配系数与溶剂萃取
Partition coefficient Kpc = [solute in organic phase] / [solute in aqueous phase] at equilibrium. Typically the organic solvent is on top.
分配系数 Kpc = [有机相溶质] / [水相溶质] (平衡时)。通常有机溶剂位于上层。
For successive extractions, the mass remaining in the aqueous phase after n extractions: m_n = m₀ × (V_aq / (V_aq + Kpc × V_org))ⁿ. Multiple small-volume extractions are more efficient than a single large one.
多重萃取后水相中剩余溶质质量：m_n = m₀ × (V_aq / (V_aq + Kpc × V_org))ⁿ。多次小体积萃取比单次大体积萃取效率更高。
12. Suggested Formula Sheet & Exam Tips | 公式速查表与应试技巧
| Topic | Essential Formula | Quick Check |
|---|---|---|
| Moles | n = m/M; n = cV | Units: g, mol dm⁻³, dm³ |
| Gas | pV = nRT | R = 8.31 J K⁻¹ mol⁻¹ |
| Energy | q = mcΔT; ΔH = –q/n | c = 4.18 J g⁻¹ K⁻¹ |
| Hess | ΔHr = ΣΔHf(p) – ΣΔHf(r) | Draw a cycle |
| Entropy/Gibbs | ΔG = ΔH – TΔS | ΔG < 0 for feasible |
| Kc / Kp | Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ | Omit solids/liquids |
| Rate | rate = k[A]ᵐ[B]ⁿ | Determine orders experimentally |
| pH | pH = –log[H⁺]; Kw = [H⁺][OH⁻] | Kw = 1e-14 at 25°C |
| Cell potential | E°cell = E°cathode – E°anode | ΔG° = –nFE° |
| Electrolysis | Q = It; n(e⁻) = Q/F | F = 96 500 C mol⁻¹ |
Always check units and significant figures. When using equations, write the formula first, substitute numbers with units, and then calculate. A clear method gains partial credit even if the final answer is wrong.
答题时务必检查单位与有效数字。使用公式时，先写表达式，再代入带有单位的数字，最后计算。清晰的解题步骤即使最终答案错误也能获得部分分数。
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