📚 Pre-U CIE Chemistry: Formula & Theorem Quick Reference Handbook | Pre-U CIE 化学：公式定理速查手册
This guide provides a concise summary of the essential formulas, constants and theorems required for the Cambridge Pre-U Chemistry syllabus. It is designed for quick revision and reference before examinations, covering everything from stoichiometry to spectroscopy.
本指南简明扼要地总结了剑桥 Pre-U 化学课程所必需的核心公式、常数和定理，涵盖从化学计量到光谱学的全部内容，旨在为考试前的快速复习和查阅提供便利。
1. The Mole Concept & Stoichiometry | 摩尔概念与化学计量
s the central counting unit: n = m / M, where m is mass (g) and M is molar mass (g mol⁻¹).
物质的量 n (mol) 是核心计量单位：n = m / M，其中 m 为质量 (g)，M 为摩尔质量 (g mol⁻¹)。
pressure (RTP, 20 °C, 1 atm), the molar volume Vₘ ≈ 24.0 dm³ mol⁻¹; thus n = V(gas) / Vₘ.
在室温常压 (20 °C, 1 atm) 下，摩尔体积 Vₘ ≈ 24.0 dm³ mol⁻¹，因此 n = V(气体) / Vₘ。
Mass concentration (g dm⁻³) = c × M. For very dilute aqueous solutions, 1 ppm ≈ 1 mg dm⁻³.
对于溶液，浓度 c = n / V (mol dm⁻³)。质量浓度 (g dm⁻³) = c × M。极稀水溶液中，1 ppm ≈ 1 mg dm⁻³。
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 = (目标产物摩尔质量 / 所有产物摩尔质量之和) × 100%。
n = m / M ; n = V / Vₘ ; c = n / V
2. Gas Laws | 气体定律
pressure (Pa), V is volume (m³), T is temperature (K), and R is the gas constant (8.31 J K⁻¹ mol⁻¹).
理想气体方程为 PV = nRT。P 为压强 (Pa)，V 为体积 (m³)，T 为温度 (K)，R 为气体常数 (8.31 J K⁻¹ mol⁻¹)。
Dalton's law of partial pressures: Ptotal = Σ Pi. The partial pressure of gas A in a mixture is PA = (nA / ntotal) × Ptotal.
道尔顿分压定律：P总 = Σ Pi。混合气体中 A 的分压 PA = (nA / n总) × P总。
a fixed mass of gas: P₁V₁ / T₁ = P₂V₂ / T₂. For kinetic theory, root mean square speed u = √3RT / M, where M is molar mass in kg mol⁻¹.
一定质量气体的联合气体定律：P₁V₁ / T₁ = P₂V₂ / T₂。动理论中，均方根速率 u = √3RT / M，M 的单位为 kg mol⁻¹。
PV = nRT ; Ptotal = P1 + P2 + P3 ...
3. Thermochemistry | 热化学
nd ΔT is temperature change. The enthalpy change ΔH = ± Q / n (sign depends on direction).
物质传递的热量 Q = mcΔT，其中 m 为质量，c 为比热容，ΔT 为温度变化。焓变 ΔH = ± Q / n（符号取决于放热/吸热方向）。
Hess's law: ΔHreaction = ΣΔHf°(products) − ΣΔHf ly, ΔH = Σ(bond energies broken) − Σ(bond energies formed), using average bond enthalpies.
盖斯定律：ΔH反应 = ΣΔHf°(产物) − ΣΔHf°(反应物)。也可用平均键焓：ΔH = Σ(断裂键能) − Σ(形成键能)。
Standard enthalpy of combustion ΔHc° and standard enthalpy of formation ΔHf° are defined per mole of substance. Enthalpy of neutralisation for strong acid–strong base is approximately −57 kJ mol⁻¹.
标准燃烧焓 ΔHc° 和标准生成焓 ΔHf° 均对应于每摩尔物质。强酸强碱中和焓约为 −57 kJ mol⁻¹。
ΔH = ΣΔHf°(products) − ΣΔHf°(reactants)
4. Kinetics | 化学动力学
The rate equation: rate = k[A]m[B]n, where m and n are orders of reaction. The overall order is m + n. Units of k depend on the overall order: for first order overall, k has units s⁻¹.
速率方程：rate = k[A]m[B]n，m 和 n 为反应级数，总级数为 m + n。k 的单位取决于总级数，如一级反应 k 的单位为 s⁻¹。
For a first-order reaction, the half-life is independent of concentration: t½ = ln 2 / k ≈ 0.693 / k. The integrated rate law is ln[A] = ln[A]₀ − kt.
一级反应的半衰期与浓度无关：t½ = ln 2 / k ≈ 0.693 / k。积分速率方程为 ln[A] = ln[A]₀ − kt。
The Arrhenius equation: k = A e−Ea/RT, or ln k = ln A − Ea / (RT). A two-point form is ln(k₂ / k₁) = (Ea / R)(1/T₁ − 1/T₂). Ea is activation energy, A the pre-exponential factor.
阿伦尼乌斯方程：k = A e−Ea/RT，或 ln k = ln A − Ea / (RT)。两点式为 ln(k₂ / k₁) = (Ea / R)(1/T₁ − 1/T₂)。Ea 为活化能，A 为指前因子。
t½ = ln2 / k ; k = A e−Ea/RT
5. Chemical Equilibrium | 化学平衡
For a reaction aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration is Kc = [C]c[D]d / ([A]a[B]b). Each concentration is the equilibrium value in mol dm⁻³.
对于反应 aA + bB ⇌ cC + dD，浓度平衡常数 Kc = [C]c[D]d / ([A]a[B]b)。各浓度均为平衡时的 mol dm⁻³ 值。
In terms of partial pressures: Kp = (PC)c(PD)d / ((PA)a(PB)b). The relationship with Gibbs free energy is ΔG° = −RT ln K. If ΔG° = 0, then K = 1.
使用分压时：Kp = (PC)c(PD)d / ((PA)a(PB)b)。与吉布斯自由能的关系为 ΔG° = −RT ln K。ΔG° = 0 时 K = 1。
Le Chatelier's principle predicts the direction of shift in response to changes in concentration
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