Pre-U CIE Chemistry: Formula & Theorem Quick Reference Handbook | Pre-U CIE 化学：公式定理速查手册

📚 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

The amount of substance n (mol) is 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)。

At room temperature and 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。

For solutions, concentration c = n / V (mol dm⁻³). 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

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2. Gas Laws | 气体定律

The ideal gas equation is PV = nRT. P is 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: P_total = Σ P_i. The partial pressure of gas A in a mixture is P_A = (n_A / n_total) × P_total.

道尔顿分压定律：P_总 = Σ P_i。混合气体中 A 的分压 P_A = (n_A / n_总) × P_总。

The combined gas law for 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 ; P_total = P₁ + P₂ + P₃ …

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3. Thermochemistry | 热化学

The heat transferred to a substance is Q = mcΔT, where m is mass, c is specific heat capacity, and 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: ΔH_reaction = ΣΔH_f°(products) − ΣΔH_f°(reactants). Alternatively, ΔH = Σ(bond energies broken) − Σ(bond energies formed), using average bond enthalpies.

盖斯定律：ΔH_反应 = ΣΔH_f°(产物) − ΣΔH_f°(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 ΔH_c° and standard enthalpy of formation ΔH_f° 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 ΔH_c° 和标准生成焓 ΔH_f° 均对应于每摩尔物质。强酸强碱中和焓约为 −57 kJ mol⁻¹。

ΔH = ΣΔH_f°(products) − ΣΔH_f°(reactants)

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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: t_½ = 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：t_½ = 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^−E_a/RT, or ln k = ln A − E_a / (RT). A two-point form is ln(k₂ / k₁) = (E_a / R)(1/T₁ − 1/T₂). E_a is activation energy, A the pre-exponential factor.

阿伦尼乌斯方程：k = A e^−E_a/RT，或 ln k = ln A − E_a / (RT)。两点式为 ln(k₂ / k₁) = (E_a / R)(1/T₁ − 1/T₂)。E_a 为活化能，A 为指前因子。

t_½ = ln2 / k ; k = A e^−E_a/RT

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5. Chemical Equilibrium | 化学平衡

For a reaction aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration is K_c = [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 K_c = [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: K_p = (P_C)^c(P_D)^d / ((P_A)^a(P_B)^b). The relationship with Gibbs free energy is ΔG° = −RT ln K. If ΔG° = 0, then K = 1.

使用分压时：K_p = (P_C)^c(P_D)^d / ((P_A)^a(P_B)^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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