📚 IB & CIE Chemistry: Last-Minute Revision Notes | IB CIE 化学：考前冲刺笔记
This set of concise revision notes covers the most frequently examined topics in both IB Chemistry (SL/HL) and CIE A Level Chemistry, with a focus on key definitions, essential formulas, and common pitfalls. Use it for quick recall right before your exam.
这套精简的考前冲刺笔记涵盖 IB 化学（SL/HL）与 CIE A Level 化学中最常考的主题，聚焦关键定义、必备公式和常见误区。考前快速浏览，帮助唤醒记忆。
1. Key Formulas & Constants | 关键公式与常数
Know your data booklet by heart: Avogadro constant L = 6.02 × 10²³ mol⁻¹, gas constant R = 8.31 J K⁻¹ mol⁻¹, Planck constant h = 6.63 × 10⁻³⁴ J s, speed of light c = 3.00 × 10⁸ m s⁻¹. Always write units in calculations.
熟练掌握数据手册中的常数：阿伏伽德罗常数 L = 6.02 × 10²³ mol⁻¹，气体常数 R = 8.31 J K⁻¹ mol⁻¹，普朗克常数 h = 6.63 × 10⁻³⁴ J s，光速 c = 3.00 × 10⁸ m s⁻¹。计算时务必带单位。
Essential formulas: n = m / M, PV = nRT, q = mcΔT, ΔH = q / n, rate = k[A]ᵐ[B]ⁿ, pH = –log[H⁺], Kc and Kp expressions. For electrochemistry, ΔG° = –nFE° and E°cell = E°cathode – E°anode.
必备公式：n = m / M，PV = nRT，q = mcΔT，ΔH = q / n，速率方程 rate = k[A]ᵐ[B]ⁿ，pH = –log[H⁺]，平衡常数 Kc 与 Kp 表达式。电化学中 ΔG° = –nFE°，E°cell = E°cathode – E°anode。
2. Atomic Structure & Periodicity | 原子结构与周期性
Recall: atomic number Z = number of protons. Isotopes have same Z but different neutron number. Relative atomic mass is the weighted average of isotopic masses on the ¹²C = 12 scale.
记住：原子序数 Z = 质子数。同位素质子数相同而中子数不同。相对原子质量是按 ¹²C=12 标度计算的同位素质量加权平均值。
Electron configuration: s, p, d, f blocks; orbital filling follows the Aufbau principle, Hund’s rule, and Pauli exclusion principle. For transition metals, note the special stability of half-filled and fully filled d subshells, e.g. Cr: [Ar] 3d⁵4s¹.
电子排布：s、p、d、f 分区；轨道填充遵循构造原理、洪特规则和泡利不相容原理。对过渡金属，注意半满和全满 d 亚层的特殊稳定性，如 Cr：[Ar] 3d⁵4s¹。
Periodic trends: atomic radius decreases across a period (increased nuclear charge) and increases down a group. Ionisation energy generally increases across a period, though there are drops between Be–B and N–O due to orbital changes. Electronegativity follows a similar pattern.
周期律：原子半径在同一周期自左向右减小（核电荷增大），同族向下增大。电离能通常同周期增大，但在 Be–B 和 N–O 之间因轨道变化而下降。电负性变化趋势类似。
3. Chemical Bonding & Structure | 化学键与结构
Ionic bonding: electrostatic attraction between oppositely charged ions, lattice structure, high melting point, brittle, conduct electricity when molten or aqueous. Covalent bonding: shared electron pairs; giant covalent (diamond, graphite, SiO₂) vs simple molecular (I₂, H₂O).
离子键：阴阳离子之间的静电引力，形成晶格结构，熔点高，脆，熔融态或水溶液导电。共价键：共用电子对；分为巨型共价（金刚石、石墨、SiO₂）和简单分子（I₂、H₂O）。
VSEPR theory predicts shape from number of electron domains: 2 → linear (180°), 3 → trigonal planar (120°), 4 → tetrahedral (109.5°), 5 → trigonal bipyramidal, 6 → octahedral. The presence of lone pairs reduces bond angles, e.g. NH₃ is pyramidal (~107°) and H₂O is bent (~104.5°).
VSEPR 理论通过电子域数预测分子形状：2→直线形（180°），3→平面三角形（120°），4→四面体形（109.5°），5→三角双锥，6→八面体。孤对电子会减小键角，如 NH₃ 为三角锥形（~107°），H₂O 为 V 形（~104.5°）。
Hybridisation: sp (linear), sp² (trigonal planar), sp³ (tetrahedral). Delocalisation of π electrons explains resonance and conductivity in graphite and benzene.
杂化：sp（直线），sp²（平面三角），sp³（正四面体）。π 电子的离域可解释共振结构以及石墨和苯的导电性。
4. Stoichiometry & Mole Concepts | 化学计量与摩尔概念
One mole is the amount of substance containing 6.02 × 10²³ specified particles. Molar mass M (g mol⁻¹) is the mass of one mole. Always balance equations before calculating reacting masses.
1 摩尔物质含有 6.02 × 10²³ 个指定微粒。摩尔质量 M（g mol⁻¹）为 1 摩尔物质的质量。在计算反应质量之前必须配平化学方程式。
Limiting reactant: the reactant that is completely consumed first and determines the theoretical yield. Percentage yield = (actual yield / theoretical yield) × 100%. The atom economy = (molar mass of desired product / sum of molar masses of all products) × 100%.
限量反应物：最先被耗尽并决定理论产量的反应物。产率 =（实际产量 / 理论产量）× 100%。原子经济性 =（目标产物摩尔质量 / 所有产物摩尔质量之和）× 100%。
Solution calculations: c = n / V (mol dm⁻³), remember to convert cm³ to dm³ (÷1000). Dilution formula: c₁V₁ = c₂V₂. Back titration and gas volume calculations (molar volume = 22.7 dm³ mol⁻¹ at STP for IB, or 22.4 dm³ at 273 K/1 atm, 24 dm³ at 298 K for CIE) are common.
溶液计算：c = n / V（mol dm⁻³），注意将 cm³ 转换为 dm³（÷1000）。稀释公式：c₁V₁ = c₂V₂。返滴定和气体体积计算（IB 中 STP 下气体摩尔体积为 22.7 dm³ mol⁻¹，CIE 中 273 K/1 atm 为 22.4 dm³，298 K 下为 24 dm³）是常见考点。
5. Energetics & Thermochemistry | 能量学与热化学
Enthalpy change ΔH: negative for exothermic reactions, positive for endothermic. Calculate using q = mcΔT, then ΔH = –q / n. Always state the sign.
焓变 ΔH：放热反应为负值，吸热反应为正值。用 q = mcΔT 计算热量，再求 ΔH = –q / n。务必标明正负号。
Standard enthalpy changes: ΔH°f (formation), ΔH°c (combustion), ΔH°neut (neutralisation), ΔH°sol (solution). Hess’s Law: the enthalpy change for a reaction is independent of the pathway taken. Use enthalpy cycles to find unknown ΔH.
标准焓变：ΔH°f（生成焓）、ΔH°c（燃烧焓）、ΔH°neut（中和焓）、ΔH°sol（溶解焓）。盖斯定律：反应的焓变与途径无关。用焓变循环图求未知 ΔH。
Bond enthalpy: average value from a range of compounds. ΔH ≈ Σ(bonds broken) – Σ(bonds formed). Remember that bond breaking absorbs energy, bond making releases energy. Lattice enthalpy relates to the strength of ionic bonds; a more negative lattice enthalpy indicates a more stable compound.
键焓：取自多种化合物的平均值。ΔH ≈ Σ（断裂键的键焓）– Σ（形成键的键焓）。记住断键吸热，成键放热。晶格焓反映离子键强度；晶格焓越负，化合物越稳定。
6. Kinetics | 化学动力学
Rate of reaction = change in concentration / time. Factors affecting rate: concentration, pressure (for gases), temperature, surface area, and catalyst. Collision theory: particles must collide with correct orientation and energy ≥ Ea.
反应速率 = 浓度变化量 / 时间。影响速率的因素：浓度、压强（气体）、温度、表面积和催化剂。碰撞理论：粒子必须以正确取向且能量 ≥ 活化能 Ea 才能发生反应。
Maxwell-Boltzmann distribution: increasing temperature shifts the curve to the right and flattens it, greatly increasing the number of particles with E ≥ Ea. Catalysts provide an alternative pathway with lower Ea, increasing the proportion of successful collisions.
麦克斯韦–玻尔兹曼分布：升高温度使曲线右移并变平，能量超过 Ea 的粒子数大幅增加。催化剂提供更低 Ea 的替代途径，从而增大有效碰撞比例。
Rate equation: rate = k[A]ᵐ[B]ⁿ. Order of reaction (m, n) can only be determined experimentally. Units of k depend on overall order. For a first-order reaction, half-life is constant: t½ = ln2 / k.
速率方程：rate = k[A]ᵐ[B]ⁿ。反应级数（m、n）只能由实验确定。k 的单位取决于总级数。一级反应的半衰期恒定：t½ = ln2 / k。
7. Equilibrium | 化学平衡
Dynamic equilibrium: rate of forward reaction = rate of reverse reaction; macroscopic properties remain constant. Le Chatelier’s principle: if a system at equilibrium is disturbed, it shifts to oppose the change.
动态平衡：正反应速率 = 逆反应速率；宏观性质保持恒定。勒夏特列原理：如果改变平衡体系的条件，平衡将向减弱这种改变的方向移动。
Pressure increase shifts equilibrium towards side with fewer gas moles; temperature increase favours the endothermic direction; addition of catalyst speeds up both forward and reverse reactions equally – no shift in equilibrium position.
增大压强，平衡向气体分子数减少的方向移动；升高温度，平衡向吸热方向移动；加入催化剂同等程度加快正逆反应速率，平衡位置不移动。
Equilibrium constant Kc = [products]^{coefficients} / [reactants]^{coefficients}. For gases, use Kp with partial pressures. Kc and Kp are only affected by temperature. When Kc >> 1, products dominate; Kc << 1, reactants dominate.
平衡常数 Kc = [产物]^{系数} / [反应物]^{系数}。有气体参与时用 Kp 表示，以分压代替浓度。Kc 和 Kp 只受温度影响。Kc >> 1 时产物占优；Kc << 1 时反应物占优。
8. Acids & Bases | 酸与碱
Bronsted-Lowry acid: proton (H⁺) donor; base: proton acceptor. Conjugate acid-base pairs differ by one proton. Amphiprotic species can both donate and accept protons, e.g. H₂O, HCO₃⁻.
布朗斯特–劳里酸：质子（H⁺）给体；碱：质子受体。共轭酸碱对相差一个质子。两性物质既可给质子又可接受质子，如 H₂O、HCO₃⁻。
Strong acids and bases completely dissociate in water. Weak acids and bases partially dissociate, establishing an equilibrium. Ka = [H⁺][A⁻] / [HA]; pKa = –log Ka. The smaller the pKa, the stronger the acid.
强酸和强碱在水中完全解离。弱酸和弱碱部分解离，建立平衡。Ka = [H⁺][A⁻] / [HA]；pKa = –log Ka。pKa 越小，酸性越强。
pH = –log[H⁺]; [H⁺] = 10⁻^{pH}. For strong acids, [H⁺] = initial acid concentration (monoprotic). Buffer solutions resist pH change and consist of a weak acid and its conjugate base or a weak base and its conjugate acid. Henderson-Hasselbalch: pH = pKa + log([A⁻]/[HA]).
pH = –log[H⁺]；[H⁺] = 10⁻^{pH}。对于一元强酸，[H⁺] 等于酸的初始浓度。缓冲溶液能抵抗 pH 变化，由弱酸及其共轭碱或弱碱及其共轭酸组成。亨德森–哈塞尔巴尔赫方程：pH = pKa + log([A⁻]/[HA])。
9. Redox Processes | 氧化还原过程
Oxidation is loss of electrons, increase in oxidation number; reduction is gain of electrons, decrease in oxidation number. OIL RIG. Oxidising agent is reduced; reducing agent is oxidised.
氧化：失去电子，氧化数升高；还原：得到电子，氧化数降低。OIL RIG 助记。氧化剂本身被还原，还原剂本身被氧化。
Assign oxidation numbers using rules: free element = 0, oxygen usually –2, hydrogen usually +1, sum of oxidation numbers in a neutral compound = 0, in a polyatomic ion equals the charge.
氧化数规则：单质为 0，氧通常为 –2，氢通常为 +1，中性化合物中氧化数和为 0，多原子离子中等于离子电荷。
Balancing redox half-equations: add H₂O to balance O, H⁺ to balance H, then electrons to balance charge. In basic solution, add OH⁻ to neutralise H⁺. Combine half-equations ensuring electron loss = electron gain.
配平氧化还原半反应：加 H₂O 配平 O，加 H⁺ 配平 H，再加电子配平电荷。在碱性溶液中，加入 OH⁻ 中和 H⁺。合并半反应时确保电子得失相等。
Electrochemical cell: anode is where oxidation occurs (negative in galvanic cell); cathode is where reduction occurs (positive). Standard electrode potentials E° are measured under standard conditions. A spontaneous reaction has positive E°cell. Electrolysis uses electrical energy to drive non-spontaneous reactions; cathode is negative (reduction), anode is positive (oxidation).
电化学电池：阳极发生氧化（原电池中为负极）；阴极发生还原（正极）。标准电极电势 E° 在标准条件下测量。自发反应的 E°cell 为正。电解则利用电能驱动非自发反应；电解池中阴极为负极（还原），阳极为正极（氧化）。
10. Organic Chemistry Essentials | 有机化学精要
Homologous series: same functional group, same general formula, gradation in physical properties. Functional groups to know: alkane, alkene, halogenoalkane, alcohol, aldehyde, ketone, carboxylic acid, ester, amine, amide, nitrile, arene.
同系物：相同官能团、相同通式，物理性质递变。必须掌握的官能团：烷烃、烯烃、卤代烷、醇、醛、酮、羧酸、酯、胺、酰胺、腈、芳烃。
Nomenclature: longest carbon chain, lowest number locants for substituents and functional groups. Prefixes di-, tri- used for multiple identical substituents. Carbonyl compounds: aldehydes end in –al, ketones in –one; carboxylic acids end in –oic acid.
命名法：最长碳链为母体，取代基和官能团取最小位次。多个相同取代基用二、三等前缀。羰基化合物：醛以 –al 结尾，酮以 –one 结尾；羧酸以 –oic acid 结尾。
Key reaction types: substitution (alkanes with halogens in UV light), addition (alkenes with H₂, Br₂, HBr, H₂O – electrophilic addition), oxidation (primary alcohol → aldehyde → carboxylic acid; secondary alcohol → ketone), reduction (carbonyl → alcohol with NaBH₄ or LiAlH₄). Nucleophilic substitution for halogenoalkanes (SN1 and SN2).
关键反应类型：取代（烷烃与卤素在紫外光下），加成（烯烃与 H₂、Br₂、HBr、H₂O——亲电加成），氧化（伯醇→醛→羧酸；仲醇→酮），还原（羰基→醇，使用 NaBH₄ 或 LiAlH₄）。卤代烷的亲核取代（SN1 和 SN2 机理）。
Benzene: undergoes electrophilic substitution (nitration, alkylation) rather than addition due to delocalised π system. Isomerism: structural isomers (chain, position, functional group) and stereoisomers (E/Z geometric and optical isomers). Optical isomerism requires a chiral carbon with four different groups.
苯：由于离域 π 电子体系，发生亲电取代（硝化、烷基化）而非加成。同分异构：构造异构（碳链、位置、官能团）和立体异构（E/Z 几何异构和光学异构）。光学异构需要含四个不同基团的手性碳原子。
11. Measurement & Data Processing | 测量与数据处理
Uncertainty: analogue instruments ± half the smallest division; digital instruments ± the smallest division. Combine uncertainties: when adding or subtracting, add absolute uncertainties; when multiplying or dividing, add percentage uncertainties.
不确定度：模拟仪器为最小分度值的一半；数字仪器为最小分度值。不确定度合成：加减运算将绝对不确定度相加；乘除运算将百分比不确定度相加。
Significant figures: give your answer to the same number of significant figures as the least precise measurement used. In pH, the number of decimal places corresponds to significant figures of [H⁺]. Graph plotting: draw a best-fit line, use gradient for rate calculations, and show data points clearly.
有效数字：结果的有效数字位数应与所用最不精确测量的位数相同。pH 的小数位数对应 [H⁺] 的有效数字位数。作图：画出最佳拟合线，用斜率计算速率，数据点清晰标示。
Spectroscopy: IR identifies functional groups (characteristic absorption ranges, e.g. O–H broad ~3200–3600 cm⁻¹, C=O sharp ~1700 cm⁻¹). Mass spectrometry gives molecular ion peak (M⁺) and fragmentation pattern. NMR: number of peaks indicates number of different proton environments; area ratio gives relative number of protons; splitting follows n+1 rule.
光谱学：红外光谱识别官能团（特征吸收范围，如 O–H 宽峰 3200–3600 cm⁻¹，C=O 尖峰 ~1700 cm⁻¹）。质谱给出分子离子峰 (M⁺) 和碎片峰。核磁共振：峰的数量反映不同质子环境的数目；峰面积比给出各环境质子数的相对比例；裂分遵循 n+1 规则。
12. Exam Tips & Common Pitfalls | 考试技巧与常见误区
Always write state symbols (s), (l), (g), (aq) in equations unless told otherwise. Use the data booklet for formulas rather than memorising all constants. In IB, Paper 1 requires quick MCQ strategy; Paper 2 demands extended response clarity. CIE papers often test definitions precisely – use exact wording.
化学方程式中务必标注状态符号 (s)、(l)、(g)、(aq)，除非题目另有说明。善用数据手册中的公式，无需强记所有常数。IB 卷一需快速解答选择题；卷二需清晰的扩展回答。CIE 试卷常考定义的准确表述——使用教材原话。
Do not confuse ‘precision’ with ‘accuracy’; repeat readings improve precision but not accuracy. For organic mechanisms, curly arrows start from a bond or lone pair and point towards the electron-deficient species. Show dipoles when appropriate.
不要混淆”精密度”与”准确度”；重复读数提高精密度但不影响准确度。有机反应机理中，弯箭头从化学键或孤对电子出发，指向缺电子物种。必要时标明偶极。
Double-check units: cm³ to dm³, °C to K (+273), kJ mol⁻¹ vs J mol⁻¹. When calculating Kc, divide by volume to obtain concentration before substituting. In redox, connect the direction of electron flow to the sign of E°cell.
检查单位：cm³ 转换为 dm³，°C 转换为 K (+273)，kJ mol⁻¹ 与 J mol⁻¹ 的区分。计算 Kc 时，先除以体积得到浓度再代入。氧化还原中，将电子流动方向与 E°cell 的正负联系起来。
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