📚 Year 13 CIE Chemistry: Formulas & Theorems Quick Reference | CIE A2化学公式定理速查手册
This quick reference handbook compiles the essential formulas, equations, and theorems required for the CIE A2 Chemistry syllabus. It serves as a revision aid for Year 13 students who wish to consolidate their understanding of physical chemistry, equilibrium, thermodynamics, kinetics, and other key quantitative topics. Each entry provides the formula together with a concise explanation in both English and Chinese.
本速查手册汇集了 CIE A2 化学大纲所要求的关键公式、方程式与定理。它旨在为 Year 13 学生提供复习参考，帮助巩固物理化学、平衡、热力学、动力学及其他核心定量内容。每一条目均以英文和中文配对形式给出公式及简要解释。
1. Equilibrium Constants: Kc and Kp | 平衡常数 Kc 与 Kp
For a reversible reaction at equilibrium aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration, Kc, is defined as the ratio of product concentrations to reactant concentrations, each raised to the power of its stoichiometric coefficient.
对于达到平衡的可逆反应 aA + bB ⇌ cC + dD，以浓度表示的平衡常数 Kc 定义为生成物浓度与反应物浓度之比，各浓度项以其化学计量数为指数。
Kc = [C]ᶜ [D]ᵈ / ([A]ᵃ [B]ᵇ)
Square brackets denote equilibrium concentrations in mol dm⁻³. Kc is dimensionless when there is no change in the total number of moles of gas, but its units vary with Δn according to (mol dm⁻³)^Δn, where Δn = (c + d) – (a + b).
方括号表示平衡时的物质的量浓度，单位为 mol dm⁻³。当气体总摩尔数不变时 Kc 无量纲；一般而言其单位随 Δn 变化，为 (mol dm⁻³)^Δn，其中 Δn = (c + d) – (a + b)。
The equilibrium constant in terms of partial pressures, Kp, is expressed similarly using equilibrium partial pressures p measured in atm, Pa, or bar.
以分压表示的平衡常数 Kp 相似地定义为用平衡分压 p（单位 atm、Pa 或 bar）表达的比值：
Kp = (p_C)ᶜ (p_D)ᵈ / (p_A)ᵃ (p_B)ᵇ
The relationship between Kp and Kc is given by Kp = Kc (RT)^Δn, where R is the ideal gas constant (8.31 J K⁻¹ mol⁻¹) and T is the absolute temperature in kelvin. This equation is crucial when converting between concentration-based and pressure-based equilibrium constants.
Kp 与 Kc 的关系为 Kp = Kc (RT)^Δn，其中 R 为理想气体常数（8.31 J K⁻¹ mol⁻¹），T 为绝对温度（开尔文）。该方程在浓度型与压力型平衡常数之间转换时至关重要。
2. Acid–Base Equilibria and pH | 酸碱平衡与 pH 计算
The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration.
溶液的 pH 定义为氢离子浓度的负对数（底数为 10）。
pH = –log₁₀[H⁺] [H⁺] = 10⁻ᵖᴴ
For a weak acid HA dissociating according to HA ⇌ H⁺ + A⁻, the acid dissociation constant Ka quantifies the strength of the acid.
对于弱酸 HA 的电离 HA ⇌ H⁺ + A⁻，酸解离常数 Ka 用以衡量酸的强度。
Ka = [H⁺][A⁻] / [HA]
The pKa is then pKa = –log₁₀ Ka. The smaller the pKa, the stronger the acid. For weak bases, an analogous base dissociation constant Kb and pKb are defined.
pKa 定义为 pKa = –log₁₀ Ka。pKa 越小，酸性越强。对于弱碱，可类似定义碱解离常数 Kb 与 pKb。
The ionic product of water, Kw, links the concentrations of H⁺ and OH⁻ in any aqueous solution at a given temperature. At 25°C, Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶, so pKw = 14.
水的离子积 Kw 将给定温度下水溶液中 H⁺ 和 OH⁻ 的浓度联系起来。在 25°C 时，Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶，故 pKw = 14。
Kw = [H⁺][OH⁻] pKw = pH + pOH = 14 (at 25°C)
3. Buffer Solutions | 缓冲溶液公式
A buffer solution resists changes in pH upon addition of small amounts of acid or base. It consists of a weak acid and its conjugate base, or a weak base and its conjugate acid. The Henderson–Hasselbalch equation allows direct calculation of pH from the ratio of conjugate base to acid.
缓冲溶液能抵抗加入少量酸或碱引起的 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–哈塞尔巴赫方程可直接通过共轭碱与酸的比例计算 pH。
pH = pKa + log₁₀( [A⁻] / [HA] )
This equation is valid when the concentrations of the weak acid and its salt are both significantly larger than the [H⁺] arising from dissociation. It explains why the buffer’s pH is centred around the pKa of the weak acid and how the buffering capacity depends on the total concentration of the buffer components.
该方程在弱酸及其盐的浓度远大于由解离产生的 [H⁺] 时成立。它解释了为什么缓冲溶液的 pH 围绕弱酸的 pKa 且缓冲容量取决于缓冲组分总浓度。
Preparation of a buffer with a desired pH often involves choosing an acid whose pKa is close to the target pH, and adjusting the ratio [A⁻]/[HA].
配制特定 pH 的缓冲液时，常选择 pKa 接近目标 pH 的弱酸，并调节 [A⁻]/[HA] 比值。
4. Thermodynamics: ΔG, ΔH, ΔS | 热力学公式
The Gibbs free energy change, ΔG, determines the spontaneity of a process at constant temperature and pressure. It is related to the enthalpy change ΔH and entropy change ΔS by the Gibbs–Helmholtz equation.
吉布斯自由能变 ΔG 决定了恒温恒压过程的自发性，它与焓变 ΔH 和熵变 ΔS 的关系由吉布斯–亥姆霍兹方程给出。
ΔG = ΔH – TΔS
A negative ΔG indicates a spontaneous (thermodynamically feasible) reaction under the given conditions. For a reaction at standard conditions, the standard Gibbs free energy change ΔG° is linked to the equilibrium constant K.
负的 ΔG 表示该反应在给定条件下可自发进行（热力学可行）。对于标准条件下的反应，标准吉布斯自由能变 ΔG° 与平衡常数 K 相关联。
ΔG° = –RT ln K
Where R = 8.31 J K⁻¹ mol⁻¹, T is temperature in kelvin, and K is the equilibrium constant (Kc or Kp). This equation is fundamental for calculating K from thermodynamic data or vice versa.
其中 R = 8.31 J K⁻¹ mol⁻¹，T 为开尔文温度，K 为平衡常数（Kc 或 Kp）。该式是热力学数据与平衡常数相互转化的核心。
The overall entropy change for a reaction can be obtained from standard molar entropies: ΔS° = Σ S°(products) – Σ S°(reactants). Combined with ΔH° from Hess’s law, one can determine ΔG° and predict feasibility.
总熵变可通过标准摩尔熵求得：ΔS° = Σ S°(产物) – Σ S°(反应物)。结合由赫斯定律确定的 ΔH°，即可计算 ΔG° 并预测反应的可行性。
5. Electrode Potentials and the Nernst Equation | 电极电势与能斯特方程
The cell potential under non-standard conditions is calculated using the Nernst equation, which adjusts the standard electrode potential E° by taking into account the concentrations (or pressures) of the species involved.
非标准条件下的电池电动势由能斯特方程计算，该方程通过考虑相关物种的浓度（或分压）对标准电极电势 E° 进行校正。
E = E° – (RT / nF) ln Q
At 298 K, using base-10 logarithms and substituting the constants, the equation simplifies to a commonly used form:
在 298 K 下，改用底数为 10 的对数并代入常数值，方程简化成常用形式：
E = E° – (0.0592 / n) log₁₀ Q
Here n is the number of moles of electrons transferred in the redox reaction, F is the Faraday constant (96 500 C mol⁻¹), and Q is the reaction quotient. For a cell reaction aA + bB → cC + dD, Q = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ.
式中 n 为氧化还原反应转移的电子摩尔数，F 为法拉第常数（96 500 C mol⁻¹），Q 为反应商。对于电池反应 aA + bB → cC + dD，Q = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ。
The standard cell potential is related to the standard Gibbs free energy change: ΔG° = –n F E°. A positive E° corresponds to a negative ΔG° and thus a spontaneous reaction.
标准电池电动势与标准吉布斯自由能变的关系为 ΔG° = –n F E°。正的 E° 对应负的 ΔG°，即反应可自发进行。
6. Reaction Kinetics and the Arrhenius Equation | 反应动力学与阿伦尼乌斯方程
The rate equation expresses the relationship between the rate of reaction and the concentrations of reactants, with each concentration raised to a power equal to its order.
速率方程表达了反应速率与反应物浓度之间的关系，各浓度项的指数等于该反应物的反应级数。
Rate = k [A]ᵐ [B]ⁿ
Here k is the rate constant, and m and n are the partial orders with respect to A and B, respectively. The overall order is m + n. The units of k depend on the overall order: for a zero-order reaction mol dm⁻³ s⁻¹; first order s⁻¹; second order dm³ mol⁻¹ s⁻¹, etc.
其中 k 为速率常数，m 和 n 分别为对 A 和 B 的分级数，总反应级数为 m + n。k 的单位取决于总级数：零级反应为 mol dm⁻³ s⁻¹，一级为 s⁻¹，二级为 dm³ mol⁻¹ s⁻¹ 等。
The effect of temperature on the rate constant is described by the Arrhenius equation, which can be written in exponential form or as a linear relationship.
温度对速率常数的影响由阿伦尼乌斯方程描述，可写成指数形式或线性关系。
k = A e^(–Ea / RT)
ln k = ln A – (Ea / R)(1/T)
A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the absolute temperature. A plot of ln k against 1/T gives a straight line with slope –Ea/R, allowing experimental determination of activation energy.
A 为指前因子，Ea 为活化能，R 为气体常数，T 为绝对温度。以 ln k 对 1/T 作图可得一直线，斜率为 –Ea/R，由此可实验测定活化能。
7. Lattice Energy and Born–Haber Cycles | 晶格能与玻恩–哈伯循环
Lattice energy is the enthalpy change when one mole of an ionic compound is formed from its gaseous ions. The Born–Haber cycle applies Hess’s law to relate lattice energy to other measurable thermodynamic quantities such as enthalpy of formation, ionisation energy, electron affinity and atomisation enthalpy.
晶格能是一摩尔离子化合物由其气态离子形成时的焓变。玻恩–哈伯循环运用赫斯定律，将晶格能与生成焓、电离能、电子亲和能、原子化焓等可测量热力学量联系起来。
ΔH°_f = ΔH°_at + IE + EA + ΔH°_lattice
This simplified relationship shows that the standard enthalpy of formation ΔH°_f of an ionic solid is equal to the sum of the atomisation enthalpy of the metal, the ionisation energy(ies) of the metal, the atomisation enthalpy of the non-metal, the electron affinity(ies) (often exothermic), and the lattice energy (negative for a stable lattice). The cycle allows the calculation of any one of these terms if the others are known.
这一简化关系表明，离子固体的标准生成焓 ΔH°_f 等于金属原子化焓、金属的电离能、非金属的原子化焓、电子亲和能（通常放热）以及晶格能（稳定晶格为负值）之和。该循环使得在已知其他项时，可计算出任一项。
Lattice energy can also be estimated theoretically using the Born–Landé equation, which depends on ionic charges, radii, and the Madelung constant, but at A-level the Born–Haber cycle is the primary focus.
理论上也可用玻恩–朗德方程估算晶格能，它取决于离子电荷、半径和马德隆常数，但在 A-level 阶段主要考察玻恩–哈伯循环。
8. Solubility Product (Ksp) and Partition Coefficient | 溶度积与分配系数
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