📚 Year 12 Cambridge Chemistry: Formula & Theorem Quick Reference Handbook | 剑桥AS化学：公式定理速查手册
This quick reference handbook compiles all the essential formulas, equations, and theorems required for Year 12 Cambridge AS Chemistry. It is designed to help you rapidly locate key quantitative relationships and conceptual principles when solving problems or revising for examinations. Keep it handy and refer to it often.
本速查手册汇总了剑桥 Year 12 AS 化学所需的全部重要公式、方程式和定理，帮助你在解题或备考复习时快速定位关键的定量关系与概念原理。请随时查阅，反复练习。
1. The Mole & Avogadro’s Constant | 摩尔与阿伏伽德罗常数
The mole is the SI unit for amount of substance. One mole contains exactly 6.02214076 × 10²³ elementary entities (Avogadro constant, NA). The number of moles n can be found from the number of particles N using n = N / NA.
摩尔是物质的量的 SI 单位。1 摩尔含有正好 6.02214076 × 10²³ 个基本单元（阿伏伽德罗常数，NA）。物质的量 n 可通过粒子数 N 求得：n = N / NA。
The molar mass M (g mol⁻¹) links mass m (g) and amount n (mol): n = m / M. This is the central formula for all stoichiometric calculations.
摩尔质量 M（g mol⁻¹）将质量 m（g）与物质的量 n（mol）联系起来：n = m / M。这是所有化学计量计算的核心公式。
2. Empirical & Molecular Formulae | 实验式与分子式
The empirical formula gives the simplest whole-number ratio of atoms in a compound. To find it, convert the percentage composition or mass of each element to moles (n = m / M), then divide all mole values by the smallest mole number to obtain the ratio.
实验式表示化合物中各原子最简整数比。要求实验式，先把各元素的质量分数或质量换算成物质的量（n = m / M），再将所有摩尔数除以最小值得到比例。
The molecular formula is a whole-number multiple of the empirical formula. The multiplier is determined by: Molecular formula mass / Empirical formula mass = n, where n must be an integer.
分子式是实验式的整数倍。倍数由下式求得：分子式相对质量 / 实验式相对质量 = n，n 必须为整数。
3. Ideal Gas Equation | 理想气体方程
The ideal gas equation relates pressure (p), volume (V), amount (n) and temperature (T): pV = nRT. Where p is in pascals (Pa), V in m³, n in mol, T in kelvin (K), and R is the molar gas constant, 8.31 J K⁻¹ mol⁻¹.
理想气体方程将压强(p)、体积(V)、物质的量(n)和温度(T)关联：pV = nRT。其中 p 单位为帕斯卡(Pa)，V 为立方米(m³)，n 为摩尔(mol)，T 为开尔文(K)，R 为摩尔气体常数 8.31 J K⁻¹ mol⁻¹。
You can also rearrange to find molar volume or convert to g dm⁻³ using m/M = n. Always convert units: 1 dm³ = 1 × 10⁻³ m³, 1 kPa = 1000 Pa, °C to K by adding 273.15.
可重组公式求摩尔体积，或通过 m/M = n 换算为 g dm⁻³。务必统一单位：1 dm³ = 1 × 10⁻³ m³，1 kPa = 1000 Pa，℃ 转 K 加 273.15。
4. Concentration & Dilution | 浓度与稀释
Concentration c (mol dm⁻³) is defined as c = n / V, where n is amount of solute (mol) and V is volume of solution (dm³). This is fundamental for solution stoichiometry.
浓度 c（mol dm⁻³）定义为 c = n / V，n 为溶质的物质的量(mol)，V 为溶液体积(dm³)。这是溶液计量的基础。
For dilution, the number of moles of solute remains the same: c₁V₁ = c₂V₂. The initial concentration and volume equal the final concentration and volume after dilution.
稀释时溶质的物质的量不变：c₁V₁ = c₂V₂。初始浓度与体积的乘积等于稀释后的终浓度与终体积的乘积。
5. Enthalpy Changes | 焓变
The enthalpy change ΔH for a reaction can be calculated from experimental data using q = mcΔT, where q is heat energy (J), m mass of solution (g), c specific heat capacity (usually 4.18 J g⁻¹ K⁻¹ for water), and ΔT temperature change (K or °C). Then ΔH = –q / n (exothermic → negative sign).
反应的焓变 ΔH 可通过实验数据利用 q = mcΔT 计算，q 为热量(J)，m 为溶液质量(g)，c 为比热容（通常水为 4.18 J g⁻¹ K⁻¹），ΔT 为温度变化(K 或 ℃)。然后 ΔH = –q / n（放热为负号）。
Standard enthalpy changes (ΔH°) are often quoted under standard conditions: 100 kPa and a stated temperature, usually 298 K. Typical definitions include ΔH°c (combustion) and ΔH°f (formation).
标准焓变(ΔH°)通常指定标准条件：100 kPa，规定温度常为 298 K。典型定义包括标准燃烧焓 ΔH°c 和标准生成焓 ΔH°f。
6. Hess’s Law | 盖斯定律
Hess’s Law states that the total enthalpy change for a chemical reaction is independent of the route taken, provided the initial and final conditions are the same. This allows calculation of unknown ΔH values using known enthalpy changes of related reactions.
盖斯定律指出，化学反应的总焓变与途径无关，只取决于初态与终态。因此可利用已知相关反应的焓变计算未知 ΔH。
A common application: ΔH°r = Σ ΔH°f(products) – Σ ΔH°f(reactants). Similarly, for combustion data: ΔH°r = Σ ΔH°c(reactants) – Σ ΔH°c(products).
常见应用：ΔH°r = Σ ΔH°f(生成物) – Σ ΔH°f(反应物)。同样，使用燃烧焓数据时：ΔH°r = Σ ΔH°c(反应物) – Σ ΔH°c(生成物)。
7. Bond Enthalpies | 键焓
Mean bond enthalpy is the average energy needed to break one mole of a given covalent bond in the gaseous state. For a reaction: ΔH ≈ Σ (bond enthalpies of bonds broken) – Σ (bond enthalpies of bonds formed). This gives an estimate because mean bond enthalpies are averages over different environments.
平均键焓是指在气态下断裂 1 摩尔某种共价键所需的平均能量。对于反应：ΔH ≈ Σ (断裂键的键焓) – Σ (形成键的键焓)。由于平均键焓是不同环境的平均值，因此该方法只是估计值。
Always draw out the molecules to count all bonds broken in reactants and all bonds formed in products. Endothermic steps (bond breaking) have positive values, exothermic (bond making) have negative contributions.
务必画出分子结构，分别统计反应物中断裂的所有键和生成物中形成的所有键。断键吸热为正值，成键放热为负贡献。
8. Rate of Reaction | 反应速率
The rate of a chemical reaction is usually expressed as change in concentration of a reactant or product per unit time: Rate = Δ[concentration] / Δt. Units are commonly mol dm⁻³ s⁻¹.
化学反应速率通常表示为反应物或生成物浓度随时间的变化率：速率 = Δ[浓度] / Δt。常用单位为 mol dm⁻³ s⁻¹。
The rate equation relates rate to reactant concentrations: Rate = k [A]ᵐ [B]ⁿ, where k is the rate constant, m and n are orders of reaction with respect to A and B, determined experimentally. The overall order is m + n.
速率方程将速率与反应物浓度关联：速率 = k [A]ᵐ [B]ⁿ，其中 k 为速率常数，m 和 n 分别为对 A、B 的反应级数，由实验确定。总反应级数为 m + n。
A catalyst provides an alternative pathway with lower activation energy (Ea), increasing the value of k and hence the rate, without being consumed.
催化剂提供具有更低活化能(Ea)的替代路径，增大速率常数 k，从而加快反应速率，而本身不被消耗。
9. Equilibrium Constant Kc | 平衡常数 Kc
For a reversible reaction aA + bB ⇌ cC + dD at equilibrium, the equilibrium constant in terms of concentration is: Kc = ([C]ᶜ [D]ᵈ) / ([A]ᵃ [B]ᵇ). The expression uses equilibrium concentrations (mol dm⁻³).
对于可逆反应 aA + bB ⇌ cC + dD，达平衡时的浓度平衡常数为：Kc = ([C]ᶜ [D]ᵈ) / ([A]ᵃ [B]ᵇ)。表达式中使用各物质的平衡浓度(mol dm⁻³)。
Kc has a constant value at a given temperature. Its magnitude indicates the position of equilibrium: Kc ≫ 1 means products are favoured; Kc ≪ 1 means reactants are favoured. Solids and pure liquids are omitted from the expression.
Kc 在给定温度下为定值。其大小反映平衡位置：Kc ≫ 1 表明产物占优，Kc ≪ 1 表明反应物占优。固体和纯液体不写入表达式。
10. Le Chatelier’s Principle | 勒夏特列原理
Le Chatelier’s Principle states that if a system at dynamic equilibrium is subjected to a change in concentration, pressure or temperature, the position of equilibrium shifts so as to partially counteract the imposed change.
勒夏特列原理指出，若处于动态平衡的体系受到浓度、压强或温度的改变，平衡位置会向减弱该改变的方向移动。
Increasing reactant concentration shifts equilibrium to the right (towards products). For gaseous reactions, increasing pressure shifts the equilibrium to the side with fewer moles of gas. Raising temperature favours the endothermic direction; lowering temperature favours the exothermic direction.
增大反应物浓度使平衡右移（向产物方向）。对于气体反应，增大压强使平衡向气体分子数较少的一侧移动。升高温度有利于吸热方向，降低温度有利于放热方向。
Catalysts do not affect equilibrium position; they only speed up the attainment of equilibrium by lowering Ea for both forward and reverse reactions equally.
催化剂不改变平衡位置，只通过同等降低正逆反应的活化能 Ea 来加快达到平衡的速率。
11. Oxidation Numbers | 氧化数
Oxidation number (oxidation state) is a bookkeeping tool for electron transfer. Key rules: free elements have oxidation number 0; for simple ions it equals the charge; oxygen is usually –2 (except in peroxides –1, OF₂ +2); hydrogen is +1 (except in metal hydrides –1); the sum of oxidation numbers in a neutral compound is 0, in a polyatomic ion equals the ion charge.
氧化数（氧化态）是用于判断电子转移的工具。主要规则：游离态元素氧化数为 0；简单离子的氧化数等于其电荷；氧通常为 –2（过氧化物中为 –1，OF₂ 中为 +2）；氢通常为 +1（金属氢化物中为 –1）；中性化合物中各元素氧化数之和为 0，多原子离子中等于离子电荷。
Oxidation is an increase in oxidation number (loss of electrons); reduction is a decrease in oxidation number (gain of electrons).
氧化是氧化数升高（失电子）；还原是氧化数降低（得电子）。
12. Redox Titrations | 氧化还原滴定
In redox titrations, the equivalence point is reached when the oxidizing and reducing agents have reacted in the exact stoichiometric ratio given by the balanced half‑equations. The key formula is (n₁ × c₁ × V₁) = (n₂ × c₂ × V₂) after adjusting for the number of electrons transferred, or more practically, use the mole ratio from the overall equation.
在氧化还原滴定中，当氧化剂和还原剂按照配平的半反应式给出的化学计量比恰好反应完毕时即达等当点。核心计算式需考虑电子转移数，可使用整体反应式的摩尔比，通用计算式为 (n₁ × c₁ × V₁) 按化学计量比调整后等于 (n₂ × c₂ × V₂)。
Common oxidising agents are potassium manganate(VII) (KMnO₄, self‑indicating) and potassium dichromate(VI). For manganate(VII) titrations with iron(II) ions: MnO₄⁻ + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O. The mole ratio MnO₄⁻ : Fe²⁺ = 1 : 5.
常见氧化剂有高锰酸钾(KMnO₄，自身指示剂)和重铬酸钾。高锰酸钾滴定铁(II)离子：MnO₄⁻ + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O。MnO₄⁻ 与 Fe²⁺ 的摩尔比为 1 : 5。
Results are used to determine the concentration of the analyte, its purity, or the percentage by mass of a component. Always express volume in dm³ (cm³ ÷ 1000) for concentration calculations.
滴定结果可用来测定待测物浓度、纯度或组分的质量分数。计算浓度时体积务必以 dm³ 为单位（cm³ 除以 1000）。
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