📚 IB & CCEA Chemistry Formula Summary Handbook | IB与CCEA化学公式汇总手册
Whether you are navigating the IB Diploma Programme or the CCEA A-level specification, a solid grasp of the essential formulae is mission-critical. This handbook pulls together the most frequently used quantitative relationships in physical, inorganic and organic chemistry, organised by topic. Each entry presents the formula, defines every symbol, and explains when and why you would use it. Use it as a quick refresher, a pre-exam checklist or a scaffold for solving numerical problems.
无论你正在攻读IB文凭课程还是CCEA A-level大纲，牢固掌握核心公式都是至关重要的。本手册汇集了物理化学、无机化学和有机化学中最常用的定量关系，并按主题编排。每个条目都列出了公式、定义了每个符号，并解释何时以及为何使用它。你可以将其用作快速复习、考前清单或解决计算题的脚手架。
1. Mole Concept & Avogadro’s Constant | 摩尔概念与阿伏伽德罗常数
The mole is the chemist’s counting unit, linking the microscopic world of atoms to macroscopic masses we can measure. The amount of substance, n, in moles, is given by the mass of the sample divided by its molar mass. One mole of any substance contains exactly 6.02 × 1023 particles (Avogadro’s number, NA). Shorthand: the number of particles N = n × NA.
摩尔是化学家的计数单位，将原子的微观世界与我们可测量的宏观质量联系起来。物质的量 n（摩尔）等于样品质量除以其摩尔质量。一摩尔任何物质恰好包含 6.02 × 1023 个粒子（阿伏伽德罗常数 NA）。简写为：粒子数 N = n × NA。
n = m / M
N = n × NA (NA = 6.02 × 1023 mol⁻¹)
where n = amount (mol), m = mass (g), M = molar mass (g mol⁻¹).
其中 n = 物质的量 (mol)，m = 质量 (g)，M = 摩尔质量 (g mol⁻¹)。
2. Empirical & Molecular Formula | 经验式与分子式
Combustion analysis or percentage composition data lets you deduce the simplest whole-number ratio of atoms in a compound — the empirical formula. To convert it into the molecular formula, you need the relative molecular mass (Mr) of the compound. The multiplier = Mr / empirical formula mass.
通过燃烧分析或元素百分含量数据，可以推导出化合物中原子的最简整数比——经验式。要将其转换为分子式，需要知道化合物的相对分子质量 (Mr)。倍数因子 = Mr / 经验式质量。
Molecular formula = (Empirical formula) × n, where n = Mr / empirical mass
Always remember to convert percentage masses to moles by dividing by atomic mass, then divide by the smallest mole value to obtain the ratio.
务必记住：将各元素的质量百分数除以各自原子量化为摩尔数，再除以最小的摩尔值以获得最简比。
3. Molar Gas Volume & Ideal Gas Equation | 摩尔气体体积与理想气体状态方程
At standard temperature and pressure (STP: 0 °C, 100 kPa for IB; CCEA often uses 20 °C, 1 atm), one mole of an ideal gas occupies a fixed volume. More generally, the ideal gas law connects pressure, volume, temperature and amount. Choose R = 8.31 J K⁻¹ mol⁻¹ when using SI units (Pa, m³, K), or R = 0.0821 L atm K⁻¹ mol⁻¹ for non-SI data.
在标准状况下 (IB 使用 0 °C、100 kPa；CCEA 常使用 20 °C、1 atm)，一摩尔理想气体占有固定体积。更一般地，理想气体状态方程将压力、体积、温度和物质的量联系起来。使用 SI 单位 (Pa、m³、K) 时取 R = 8.31 J K⁻¹ mol⁻¹；若使用非 SI 数据，则取 R = 0.0821 L atm K⁻¹ mol⁻¹。
PV = nRT
Molar gas volume at STP ≈ 22.7 dm³ mol⁻¹ (IB) or 24.0 dm³ mol⁻¹ (CCEA, 20 °C)
Use V = n × Vm for simple stoichiometric gas calculations.
进行简单的气体计量计算时，可使用 V = n × Vm。
4. Concentration & Dilution | 浓度与稀释
Solution stoichiometry relies on the relationship between moles, concentration and volume. The key equations also govern serial dilutions and titrations. Always express volume in dm³ (or L) when using mol dm⁻³, and remember that 1 dm³ = 1000 cm³.
溶液计量学依赖于物质的量、浓度与体积之间的关系。这些关键方程也适用于连续稀释和滴定。当使用 mol dm⁻³ 时，务必用 dm³ (或 L) 表示体积，并记住 1 dm³ = 1000 cm³。
n = c × V (c in mol dm⁻³, V in dm³)
c₁V₁ = c₂V₂ (dilution)
In a titration, the unknown concentration is found using the stoichiometric ratio from the balanced equation, often expressed as (nA/nB) = (cAVA)/(cBVB).
在滴定中，未知浓度可通过配平方程式中的计量比求出，常写为 (nA/nB) = (cAVA)/(cBVB)。
5. Enthalpy Changes & Hess’s Law | 焓变与盖斯定律
Enthalpy change, ΔH, is the heat transferred at constant pressure. Calorimetry experiments yield q = mcΔT, and the molar enthalpy change is ΔH = –q / n. Hess’s Law states that the total enthalpy change for a reaction is independent of the pathway; it can be calculated using standard enthalpies of formation or combustion.
焓变 ΔH 是恒压下的热传递量。量热实验给出 q = mcΔT，摩尔焓变为 ΔH = –q / n。盖斯定律表明，反应的总焓变与途径无关；可利用标准生成焓或标准燃烧焓来计算。
q = m c ΔT (c = specific heat capacity, J g⁻¹ K⁻¹)
ΔH = –q / n (exothermic: negative; endothermic: positive)
ΔH°reaction = Σ ΔH°f(products) – Σ ΔH°f(reactants)
ΔH°reaction = Σ ΔH°c(reactants) – Σ ΔH°c(products)
Always pay attention to the sign convention and to the physical state of reactants and products.
务必注意符号约定以及反应物和产物的物理状态。
6. Bond Enthalpies & Enthalpy of Reaction | 键焓与反应焓变
When a reaction involves only gases or can be approximated as bond-breaking and bond-making steps, the enthalpy change can be estimated as the difference between the energy required to break bonds and the energy released when new bonds form. Mean bond enthalpies are averaged over a range of compounds and are always endothermic for breaking.
当反应只涉及气体或可用断键和成键步骤近似时，反应焓变可估算为断键所需能量与成键释放能量之差。平均键焓是在一系列化合物中取的平均值，且断键总是吸热的。
ΔH ≈ Σ (bond enthalpies of bonds broken) – Σ (bond enthalpies of bonds formed)
This approach is less accurate than using formation enthalpies but gives useful insight, especially for combustion of organic molecules.
这种方法不如使用生成焓精确，但能提供有用的见解，尤其适用于有机分子燃烧。
7. Rate of Reaction & Rate Laws | 反应速率与速率方程
The rate of a chemical reaction is the change in concentration of a reactant or product per unit time. Elementary steps have rate laws that follow directly from stoichiometry, but overall rate laws must be determined experimentally. For a reaction aA + bB → products, the rate law often takes the form Rate = k [A]m[B]n, where m and n are the orders with respect to each reactant.
化学反应速率是反应物或产物浓度随单位时间的变化。基元反应的反应速率定律可直接从计量关系得出，但总反应的速率方程必须由实验确定。对于反应 aA + bB → 产物，速率方程常形如：速率 = k [A]m[B]n，其中 m 和 n 分别为对各反应物的反应级数。
Rate = k [A]m[B]n (overall order = m + n)
Rate = –(1/a) d[A]/dt = –(1/b) d[B]/dt = +(1/c) d[C]/dt
For first-order reactions, the integrated rate law and half-life are: ln[A] = ln[A]₀ – kt and t½ = ln 2 / k.
对于一级反应，积分速率方程和半衰期为：ln[A] = ln[A]₀ – kt，t½ = ln 2 / k。
8. Equilibrium Constant (Kc & Kp) | 平衡常数 (Kc 与 Kp)
For a reversible reaction at equilibrium, the concentrations (or partial pressures) of products and reactants are related by a constant. Kc uses molar concentrations; Kp uses partial pressures. The expression must be written with stoichiometric coefficients as exponents. Solids and pure liquids are omitted from the expression.
对于处于平衡状态的可逆反应，产物和反应物的浓度（或分压）之间由一个常数关联。Kc 依据摩尔浓度；Kp 依据分压。表达式中，计量系数须作为指数，且固体和纯液体不出现在表达式中。
For aA + bB ⇌ cC + dD: Kc = [C]c[D]d / ([A]a[B]b)
Kp = (PCc PDd) / (PAa PBb) where Pi = mole fraction × total pressure
Kp and Kc are related by Kp = Kc (RT)Δn, where Δn = moles of gaseous products – moles of gaseous reactants.
Kp 与 Kc 的关系为 Kp = Kc (RT)Δn，其中 Δn = 气态产物的摩尔数 – 气态反应物的摩尔数。
9. Acid-Base Equilibria: pH, pOH, Ka, Kb, Kw | 酸碱平衡：pH、pOH、Ka、Kb、Kw
The strength of an acid or base is quantified by its dissociation constant. The water autoprotolysis constant, Kw, links [H⁺] and [OH⁻] at a given temperature. The pH scale is logarithmic: a change of one pH unit represents a tenfold change in [H⁺]. The relationships pKa + pKb = pKw = 14.00 at 298 K are fundamental.
酸或碱的强度由其解离常数定量描述。水的自解离常数 Kw 在给定温度下将 [H⁺] 与 [OH⁻] 关联。pH 标度为对数标度：pH 值改变 1，[H⁺] 改变 10 倍。关系式 pKa + pKb = pKw = 14.00（298 K 时）是基本公式。
pH = –log₁₀[H⁺] pOH = –log₁₀[OH⁻] pH + pOH = 14
Ka = [H⁺][A⁻] / [HA] Kb = [BH⁺][OH⁻] / [B]
Kw = [H⁺][OH⁻] = 1.00 × 10⁻¹⁴ at 298 K
For a weak acid, [H⁺] ≈ √(Ka Cacid) provided the approximation C/Ka > 100 is valid.
对于弱酸，若近似条件 C/Ka > 100 成立，则 [H⁺] ≈ √(Ka Cacid)。
10. Buffers & Henderson-Hasselbalch Equation | 缓冲溶液与亨德森-哈塞尔巴尔赫方程
A buffer resists changes in pH when small amounts of acid or base are added. It consists of a weak acid and its conjugate base (or a weak base and its conjugate acid). The Henderson-Hasselbalch equation provides a direct link between pH, pKa and the ratio of conjugate base to acid concentrations.
缓冲溶液能在加入少量酸或碱时抵抗 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-哈塞尔巴尔赫方程将 pH、pKa 以及共轭碱与酸的浓度比直接联系起来。
pH = pKa + log₁₀([A⁻] / [HA])
Buffers are most effective when the ratio [A⁻]/[HA] is close to 1, i.e. pH ≈ pKa. The buffer capacity depends on the absolute concentrations of the components.
当 [A⁻]/[HA] 比值接近 1，即 pH ≈ pKa 时，缓冲效果最佳。缓冲容量取决于组分浓度的绝对值。
11. Electrochemistry: Cell Potential & Nernst Equation | 电化学：电池电势与能斯特方程
The electromotive force (EMF) of a galvanic cell under standard conditions is calculated from standard reduction potentials. Under non-standard conditions, the Nernst equation adjusts the cell potential for concentration (or pressure) effects. The relationship between Gibbs free energy and cell potential, ΔG° = –nFE°, allows you to determine thermodynamic feasibility.
原电池在标准条件下的电动势 (EMF) 可由标准还原电势计算。在非标准条件下，能斯特方程根据浓度（或压力）对电池电势进行修正。吉布斯自由能与电池电势之间的关系 ΔG° = –nFE° 可用于判断热力学可行性。
E°cell = E°cathode – E°anode
Ecell = E°cell – (RT / nF) ln Q (Nernst equation at 298 K: E = E° – (0.0592 / n) log Q)
ΔG = –nFEcell ΔG° = –nFE°cell
where n = number of moles of electrons transferred, F = 96 500 C mol⁻¹, and Q is the reaction quotient.
其中 n = 转移电子的摩尔数，F = 96 500 C mol⁻¹，Q 为反应商。
12. Entropy & Gibbs Free Energy | 熵与吉布斯自由能
Spontaneous change is governed by the Gibbs free energy, which combines the system’s enthalpy and entropy changes at constant temperature. A negative ΔG indicates a thermodynamically favourable process. The equation ΔG = ΔG° + RT ln Q links the reaction quotient to the driving force.
自发变化由吉布斯自由能决定，它综合了恒温下体系的焓变与熵变。ΔG 为负表示过程在热力学上有利。方程 ΔG = ΔG° + RT ln Q 将反应商与驱动力关联起来。
ΔG = ΔH – TΔS
ΔG° = ΔH° – TΔS° and ΔG° = –RT ln K
ΔG = ΔG° + RT ln Q
At equilibrium, ΔG = 0 and Q = K, giving ln K = –ΔH°/RT + ΔS°/R (van’t Hoff equation in linear form). This allows determination of ΔH° and ΔS° from a plot of ln K vs 1/T.
平衡时 ΔG = 0，Q = K，得 ln K = –ΔH°/RT + ΔS°/R（范特霍夫方程的线性形式）。由此可通过 ln K 对 1/T 作图求得 ΔH° 和 ΔS°。
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