📚 Year 12 CAIE Chemistry: Formula & Theorem Quick Reference Handbook | Year 12 CAIE 化学：公式定理速查手册
This quick reference handbook brings together all the essential formulas, equations, and relationships required in the Year 12 CAIE Chemistry syllabus. It is designed for rapid revision, problem-solving, and exam preparation. Each section provides the core quantitative tools you need – from stoichiometry and gas laws to equilibria, pH, and redox. Keep it close and use it often.
本速查手册汇集了 Year 12 CAIE 化学课程要求掌握的全部关键公式、方程式和定量关系。手册旨在方便快速复习、解决问题和备考。每一节都提供了您所需的核心定量工具——从化学计量和气体定律到化学平衡、pH 及氧化还原。请随时查阅，经常使用。
1. Mole Concept and Stoichiometry | 摩尔概念与化学计量
xactly 6.02 × 10²³ elementary entities. This number is known as the Avogadro constant, Nₐ.
摩尔（符号 mol）是物质的量的 SI 单位。任何物质的 1 摩尔恰好含有 6.02×10²³ 个基本单元，这个数字称为阿伏伽德罗常数，Nₐ。
The amount of substance n is calculated from mass and molar mass:
n = m / M
where m is mass in grams (g) and M is molar mass in grams per mole (g mol⁻¹).
物质的量 n 由质量和摩尔质量计算：n = m / M，其中 m 为质量，单位克 (g)；M 为摩尔质量，单位克每摩尔 (g mol⁻¹)。
For gases at room temperature and pressure (RTP, 20 °C and 1 atm), the molar volume Vₘ is approximately 24 dm³ mol⁻¹ (or 24 000 cm³ mol⁻¹). The amount of a gas can be found using:
n = V(gas) / Vₘ
在室温和常压下（RTP，20 °C、1 atm），气体的摩尔体积 Vₘ 约为 24 dm³ mol⁻¹（或 24 000 cm³ mol⁻¹）。气体的物质的量可用下式计算：n = V(气体) / Vₘ。
For solutions, concentration c (in mol dm⁻³) is related to amount and volume:
c = n / V
where V is the volume of the solution in dm³. To convert cm³ to dm³, divide by 1000.
对于溶液，浓度 c（单位 mol dm⁻³）与物质的量和体积的关系为：c = n / V，其中 V 是溶液的体积，单位 dm³。若体积以 cm³ 表示，需除以 1000 换算为 dm³。
The percentage yield and atom economy are key measures of reaction efficiency:
% yield = (actual yield / theoretical yield) × 100%
% atom economy = (molar mass of desired product / sum of molar masses of all products) × 100%
产率和原子经济性是衡量反应效率的关键指标：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. Atomic Structure: Key Equations | 原子结构关键方程
es on the ¹²C = 12 scale, calculated from isotopic masses and their percentage abundances:
Aᵣ = Σ (isotopic mass × % abundance) / 100
元素的相对原子质量 Aᵣ 是以 ¹²C=12 为基准的、各同位素质量的加权平均值，通过同位素质量和丰度百分数计算：Aᵣ = Σ (同位素质量 × 丰度%) / 100。
The relationship between the speed of light c, frequency ν and wavelength λ is fundamental to spectroscopy:
c = ν λ
where c = 3.00 × 10⁸ m s⁻¹. The energy of a photon is given by Planck’s equation:
E = h ν or ΔE = h c / λ
k constant h ≈ 6.63 × 10⁻³⁴ J s. These equations explain lines in atomic emission spectra.
光速 c、频率 ν 和波长 λ 之间的关系是光谱学的基础：c = ν λ，其中 c = 3.00×10⁸ m s⁻¹。光子的能量由普朗克方程给出：E = h ν 或 ΔE = h c / λ，普朗克常数 h ≈ 6.63×10⁻³⁴ J s。这些方程解释了原子发射光谱中的谱线。
Ionisation energy is the energy required to remove one mole of electrons from gaseous atoms. While there is no single explicit formula at AS level, the trend across a period or down a group can be rationalised using nuclear charge, shielding, and atomic radius.
电离能是指从气态原子中移除一摩尔电子所需的能量。虽然在 AS 阶段没有单一明确的公式，但可以用核电荷、屏蔽效应和原子半径来解释同周期和同族的递变规律。
3. Ideal Gas Equation and Gas Laws | 理想气体方程与气体定律
The ideal gas equation unites pressure p, volume V, amount n, and temperature T:
pV = nRT
nt. The value of R depends on the units chosen: R = 8.31 J K⁻¹ mol⁻¹ when using Pa and m³.
理想气体方程将压强 p、体积 V、物质的量 n 和温度 T 联系在一起：pV = nRT。p 的单位为帕斯卡（Pa），V 为 m³，n 为 mol，T 为开尔文（K），R 为气体常数。当采用 Pa 和 m³ 时，R = 8.31 J K⁻¹ mol⁻¹。
| Quantity | SI unit | Other common units |
| Pressure p | Pa (N m⁻²) | atm, kPa, mmHg |
| Volume V | m³ | dm³, cm³ |
| Temperature T | K | T(K) = θ(°C) + 273 |
When any two variables are kept constant, the gas laws are obtained:
- Boyle’s law (constant T, n): p₁V₁ = p₂V₂
- Charles’s law (constant p, n): V₁/T₁ = V₂/T₂
- Pressure law (constant V, n): p₁/T₁ = p₂/T₂
- Avogadro’s law (constant T, p): V₁/n₁ = V₂/n₂
当其中两个变量保持不变时，即可得到气体定律：波义耳定律（T 和 n 不变）：p₁V₁ = p₂V₂；查理定律（p 和 n 不变）：V₁/T₁ = V₂/T₂；压强定律（V 和 n 不变）：p₁/T₁ = p₂/T₂；阿伏伽德罗定律（T 和 p 不变）：V₁/n₁ = V₂/n₂。
For a mixture of gases, Dalton’s law states that the total pressure is the sum of the partial pressures: ptotal = pA + pB + ... . The partial pressure of gas A is pA = (nA / ntotal) × ptotal.
对于混合气体，道尔顿定律指出，总压等于各组分分压之和：ptotal = pA + pB + ... 。气体 A 的分压为 pA = (nA / ntotal) × ptotal。
4. Enthalpy Changes and Hess’s Law | 焓变与盖斯定律
Enthalpy change ΔH is the heat absorbed or released under constant pressure. The standard enthalpy change of reaction, ΔH°ᵣ, can be determined using calorimetry:
q = m c ΔT and ΔH = –q / n
where q is the heat transferred, m is the mass of water or solution (g), c is the specific heat capacity (usually 4.18 J g⁻¹ K⁻¹ for water), ΔT is the temperature change (K), and n is the amount of the limiting reactant that reacted.
焓变 ΔH 是在恒压下吸收或放出的热量。反应的标准焓变 ΔH°ᵣ 可通过量热法测定：q = m c ΔT，ΔH = –q / n。其中 q 为传递的热量，m 为水或溶液的质量（g），c 为比热容（水通常为 4.18 J g⁻¹ K⁻¹），ΔT 为温度变化（K），n 为已反应限制试剂的物质的量。
Hess’s law states that the total enthalpy change for a reaction is independent of the path taken. It allows ΔH to be calculated from standard enthalpies of formation or combustion:
ΔH°ᵣ = Σ ΔH°f (products) – Σ ΔH°f (reactants)
ΔH°ᵣ = Σ ΔH°c (reactants) – Σ ΔH°c (products)
盖斯定律指出，一个反应的总焓变与所采取的路径无关。利用盖斯定律，可通过标准生成焓或标准燃烧焓计算 ΔH：ΔH°ᵣ = Σ ΔH°f (产物) – Σ ΔH°f (反应物)；ΔH°ᵣ = Σ ΔH°c (反应物) – Σ ΔH°c (产物)。
Standard conditions are 298 K, 100 kPa, and all substances in their standard states. The standard enthalpy of formation of an element in its most stable form is zero.
标准条件为 298 K、100 kPa 以及所有物质均处于标准态。最稳定单质的标准生成焓为零。
5. Bond Enthalpies | 键焓
Bond enthalpy is the energy required to break one mole of a particular covalent bond in the gaseous state. Mean bond enthalpies are averages over a range of compounds and are used to estimate ΔH:
ΔH ≈ Σ (bond enthalpies of bonds broken) – Σ (bond enthalpies of bonds formed)
键焓是在气态中断裂一摩尔某特定共价键所需的能量。平均键焓是不同化合物中同种键焓的平均值，可用于估算 ΔH：ΔH ≈ Σ (断裂键的键焓) – Σ (生成键的键焓)。
This approach gives approximate ΔH values because bond enthalpies are average values and do not account for the specific molecular environment. Energy is absorbed to break bonds (endothermic) and released when bonds form (exothermic).
由于使用平均键焓且不考虑具体分子环境，这种方法只能给出近似值。断裂化学键吸收能量（吸热），形成化学键释放能量（放热）。
6. Reaction Kinetics | 反应动力学
The rate of a chemical reaction is defined as the change in concentration of a reactant or product per unit time:
rate = Δ[reactant] / Δt or rate = Δ[product] / Δt
化学反应速率定义为反应物或产物浓度在单位时间内的变化量：速率 = Δ[反应物] / Δt 或 速率 = Δ[产物] / Δt。
For a reaction aA + bB → products, the rate equation is often written as:
rate = k [A]ˣ [B]ʸ
where k is the rate constant, and x and y are the orders with respect to A and B respectively. The overall order is x + y. The units of k depend on the overall order.
对于反应 aA + bB → 产物，速率方程通常写作：rate = k [A]ˣ [B]ʸ。其中 k 为速率常数，x 和 y 分别为对 A 和 B 的反应级数。总反应级数为 x + y。k 的单位取决于总级数。
- Zero order: rate = k, units of k: mol dm⁻³ s⁻¹
- First order: rate = k[A], k units: s⁻¹
- Second order: rate = k[A][B] or k[A]², k units: dm³ mol⁻¹ s⁻¹
零级反应：rate = k，k 单位为 mol dm⁻³ s⁻¹；一级反应：rate = k[A]，k 单位为 s⁻¹；二级反应：rate = k[A][B] 或 k[A]²，k 单位为 dm³ mol⁻¹ s⁻¹。
An increase in temperature increases the rate constant k because a larger fraction of molecules possess energy greater than the activation energy Eₐ. The Boltzmann distribution describes this behaviour qualitatively.
温度升高会使速率常数 k 增大，因为有更多分子的能量超过活化能 Eₐ。玻尔兹曼分布可定性描述这一行为。
7. Chemical Equilibrium | 化学平衡
For a reversible reaction at equilibrium, the equilibrium constant in terms of concentration, Kc, is defined by the law of mass action. For the general reaction aA + bB ⇌ cC + dD:
Kc = ([C]ᶜ [D]ᵈ) / ([A]ᵃ [B]ᵇ)
where square brackets denote equilibrium concentrations in mol dm⁻³. Kc is temperature-dependent; its value changes only with temperature.
对于达到平衡的可逆反应，浓度平衡常数 Kc 由质量作用定律定义。对于通式 aA + bB ⇌ cC + dD：Kc = ([C]ᶜ [D]ᵈ) / ([A]ᵃ [B]ᵇ)，方括号表示平衡浓度，单位为 mol dm⁻³。Kc 受温度影响，其值只随温度变化。
For gaseous reactions, the equilibrium constant in terms of partial pressures, Kp, is used:
Kp = (PCᶜ PDᵈ) / (PAᵃ PBᵇ)
where PA, PB, etc. are the equilibrium partial pressures. The relationship between Kp and Kc is:
Kp = Kc (RT)Δn
with Δn = (c + d) – (a + b), the change in the number of moles of gas.
对于气体反应，使用分压平衡常数 Kp：Kp = (PCᶜ PDᵈ) / (PAᵃ PBᵇ)，PA、PB 等为平衡分压。Kp 与 Kc 的关系为：Kp = Kc (RT)Δn，其中 Δn = (c + d) – (a + b)，即气体摩尔数的变化。
Le Chatelier’s principle states that if a system at equilibrium is subjected to a change in concentration, pressure, or temperature, the equilibrium position shifts to partially oppose the change. Changing concentration or pressure does not alter Kc; changing temperature does.
勒夏特列原理指出，若平衡系统的浓度、压强或温度发生改变，平衡将朝减弱该改变的方向移动。改变浓度或压强不会改变 Kc；改变温度则会改变 Kc。
8. Acids and Bases: pH and Dissociation Constants | 酸碱：pH 与解离常数
The pH of an aqueous solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration:
pH = –log₁₀[H⁺]
Similarly, pOH = –log₁₀[OH⁻]. In water at 298 K, the ionic product Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶, and pH + pOH = 14.
水溶液的 pH 定义为氢离子浓度（mol dm⁻³）的负常用对数：pH = –log₁₀[H⁺]。类似地，pOH = –log₁₀[OH⁻]。在 298 K 的水中，离子积 Kw = [H⁺][OH⁻] = 1.0×10⁻¹⁴ mol² dm⁻⁶，且 pH + pOH
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