📚 Year 13 OCR Chemistry Formula & Theorem Quick Reference | Year 13 OCR 化学：公式定理速查手册
This handbook brings together the essential equations, constants, and conceptual theorems required for mastery of the Year 13 OCR A-Level Chemistry syllabus. From rate laws to thermodynamics, from electrode potentials to transition metal chemistry, every formula is presented with clear definitions of symbols and units, followed immediately by its Chinese counterpart. Use this as a revision checklist and a rapid lookup when practising past-paper questions.
本手册汇集了掌握 Year 13 OCR A-Level 化学课程所需的关键公式、常数和概念定理。从速率方程到热力学，从电极电势到过渡金属化学，每个公式都以清晰的符号定义和单位呈现，并紧随中文解释。您可以将本文用作复习清单，也可在练习往年真题时进行速查。
1. Rate Equations & The Arrhenius Equation | 速率方程与阿伦尼乌斯方程
The rate of a reaction can often be expressed in terms of the concentrations of reactants raised to some power: rate = k [A]ᵐ [B]ⁿ. Here k is the rate constant, m and n are the orders with respect to A and B. The overall order is m + n. The units of k depend on the overall order: for zero order, mol dm⁻³ s⁻¹; first order, s⁻¹; second order, dm³ mol⁻¹ s⁻¹; third order, dm⁶ mol⁻² s⁻¹.
反应速率通常可以用反应物浓度的幂次方表示：rate = k [A]ᵐ [B]ⁿ。其中 k 为速率常数，m 和 n 分别是对应于 A 和 B 的反应级数。总反应级数为 m + n。k 的单位取决于总级数：零级反应，mol dm⁻³ s⁻¹；一级反应，s⁻¹；二级反应，dm³ mol⁻¹ s⁻¹；三级反应，dm⁶ mol⁻² s⁻¹。
The temperature dependence of k is given by the Arrhenius equation: k = A e^(-Ea/RT), where A is the pre-exponential factor, Ea is the activation energy (J mol⁻¹), R is the gas constant (8.314 J K⁻¹ mol⁻¹), and T is the absolute temperature (K). A linear plot of ln k against 1/T yields a slope of –Ea/R and an intercept of ln A.
k 与温度的关系由阿伦尼乌斯方程表达：k = A e^(–Ea/RT)，其中 A 为指前因子，Ea 为活化能（J mol⁻¹），R 为摩尔气体常数（8.314 J K⁻¹ mol⁻¹），T 为绝对温度（K）。以 ln k 对 1/T 作图可得斜率 –Ea/R，截距 ln A。
- Arrhenius equation in logarithmic form: ln k = –Ea/(RT) + ln A
- 对数形式：ln k = –Ea/(RT) + ln A
2. Equilibrium Constants Kc and Kp | 平衡常数 Kc 与 Kp
For a reversible reaction aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration is: Kc = ([C]ᶜ [D]ᵈ) / ([A]ᵃ [B]ᵇ). Square brackets denote equilibrium concentrations in mol dm⁻³. Kc is dimensionless only when the sum of the stoichiometric coefficients of products equals that of reactants; otherwise it has units derived from concentration.
对于可逆反应 aA + bB ⇌ cC + dD，以浓度表示的平衡常数为：Kc = ([C]ᶜ [D]ᵈ) / ([A]ᵃ [B]ᵇ)。方括号表示平衡浓度，单位为 mol dm⁻³。仅当生成物和反应物计量系数之和相等时，Kc 无量纲；否则 Kc 带有由浓度衍生的单位。
For gaseous equilibria, the equilibrium constant in terms of partial pressure is: Kp = (p_Cᶜ × p_Dᵈ) / (p_Aᵃ × p_Bᵇ). Partial pressures are usually expressed in kPa or atm. The relationship between Kp and Kc is given by: Kp = Kc (RT)^Δn, where Δn = (c+d) – (a+b) for gases only, R = 8.314 J K⁻¹ mol⁻¹, T in Kelvin.
对于气相平衡，以分压表示的平衡常数为：Kp = (p_Cᶜ × p_Dᵈ) / (p_Aᵃ × p_Bᵇ)。分压通常以 kPa 或 atm 表示。Kp 与 Kc 的关系为：Kp = Kc (RT)^Δn，其中 Δn = (c+d) – (a+b)（仅计气体），R = 8.314 J K⁻¹ mol⁻¹，T 以开尔文为单位。
- Le Chatelier’s principle is applied to predict shifts in equilibrium position when temperature, pressure, or concentration is changed.
- 勒夏特列原理用于预测温度、压强或浓度变化时平衡位置的移动方向。
- The value of K changes only with temperature; catalysts do not alter K.
- K 的数值仅随温度变化；催化剂不改变 K 值。
3. Acid–Base Equilibria: pH, Ka, Kw | 酸碱平衡：pH、Ka、Kw
The pH scale is defined as: pH = –log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration in mol dm⁻³. Similarly, pOH = –log₁₀[OH⁻] and pH + pOH = 14 at 298 K.
pH 定义为：pH = –log₁₀[H⁺]，其中 [H⁺] 为氢离子浓度（mol dm⁻³）。类似地，pOH = –log₁₀[OH⁻]，且在 298 K 时，pH + pOH = 14。
The ionic product of water, Kw, is: Kw = [H⁺][OH⁻]. At 298 K, Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶. The dissociation of a weak acid HA is described by the acid dissociation constant: Ka = [H⁺][A⁻] / [HA]. pKa = –log₁₀ Ka. For a weak acid, [H⁺] ≈ √(Ka × [HA]) if the acid is very weak and [HA] remains close to its initial value.
水的离子积 Kw 为：Kw = [H⁺][OH⁻]。298 K 时，Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶。弱酸 HA 的解离用酸解离常数描述：Ka = [H⁺][A⁻] / [HA]；pKa = –log₁₀ Ka。对于极弱的酸，若 [HA] 近似等于初始浓度，则 [H⁺] ≈ √(Ka × [HA])。
- For strong acids, [H⁺] equals the acid concentration (for monoprotic acids). For strong bases, [OH⁻] equals the base concentration times basicity.
- 对于强酸（一元），[H⁺] 等同于酸浓度；对于强碱，[OH⁻] 等于碱浓度乘以碱的元数。
4. Buffer Solutions | 缓冲溶液
A buffer solution resists changes in pH upon addition of small amounts of acid or alkali. It typically contains a weak acid and its conjugate base (or a weak base and its conjugate acid). The pH of an acidic buffer can be calculated using the Henderson–Hasselbalch equation: pH = pKa + log₁₀ ([A⁻]/[HA]). Here [A⁻] is the concentration of the conjugate base and [HA] the concentration of the weak acid.
缓冲溶液在加入少量酸或碱时能抵抗 pH 的变化。它通常含有一种弱酸及其共轭碱（或弱碱及其共轭酸）。酸性缓冲溶液的 pH 可用 Henderson–Hasselbalch 方程计算：pH = pKa + log₁₀ ([A⁻]/[HA])。其中 [A⁻] 为共轭碱的浓度，[HA] 为弱酸的浓度。
When preparing a buffer, the ratio [A⁻]/[HA] is critical. The buffering capacity is greatest when this ratio is between 0.1 and 10, and ideally when pH = pKa. In calculations, if the volumes are the same, the ratio of moles can be used directly.
配制缓冲溶液时，[A⁻]/[HA] 比值至关重要。当该比值在 0.1 至 10 之间时缓冲能力最强，理想情况是 pH = pKa。计算中若体积相同，可直接使用物质的量之比。
- Basic buffers follow an analogous expression: pOH = pKb + log₁₀ ([BH⁺]/[B]), where B is the weak base and BH⁺ its conjugate acid.
- 碱性缓冲遵循类似表达式：pOH = pKb + log₁₀ ([BH⁺]/[B])，其中 B 为弱碱，BH⁺ 为其共轭酸。
5. Thermodynamics: Entropy & Gibbs Free Energy | 热力学：熵与吉布斯自由能
Entropy, S, is a measure of the dispersal of energy in a system. The total entropy change of the universe, ΔS_total, determines spontaneity: ΔS_total = ΔS_system + ΔS_surroundings > 0 for a feasible reaction. ΔS_surroundings = –ΔH/T (at constant pressure and temperature). The standard entropy change of a reaction is calculated from standard entropies: ΔS° = Σ S°(products) – Σ S°(reactants).
熵 S 是体系能量分散程度的量度。宇宙的总熵变 ΔS_total 决定反应的自发性：ΔS_total = ΔS_system + ΔS_surroundings > 0，反应可行。ΔS_surroundings = –ΔH/T（恒压恒温）。反应的标准熵变由标准熵计算：ΔS° = Σ S°(产物) – Σ S°(反应物)。
The Gibbs free energy change provides a direct criterion at constant T and P: ΔG = ΔH – TΔS. A reaction is thermodynamically feasible when ΔG ≤ 0. ΔG° refers to standard conditions (100 kPa, 298 K, 1 mol dm⁻³). The relationship with the equilibrium constant is: ΔG° = –RT ln K. Thus, a large equilibrium constant corresponds to a very negative ΔG°.
吉布斯自由能变在恒温恒压下提供直接判据：ΔG = ΔH – TΔS。当 ΔG ≤ 0 时，反应在热力学上可行。ΔG° 指标准条件下的值（100 kPa、298 K、1 mol dm⁻³）。与平衡常数的关系为：ΔG° = –RT ln K。因此，很大的平衡常数对应绝对值很大的负 ΔG°。
- When ΔH is negative and ΔS positive, the reaction is always feasible. When ΔH is positive and ΔS negative, the reaction is never feasible. At intermediate signs, feasibility depends on temperature.
- 当 ΔH 为负、ΔS 为正时，反应总可行；当 ΔH 为正、ΔS 为负时，反应总不可行。其余情况可行性取决于温度。
6. Electrode Potentials & The Nernst Equation | 电极电势与能斯特方程
The standard electrode potential, E°, is measured under standard conditions (298 K, 100 kPa, 1.0 mol dm⁻³ ion concentrations) relative to the standard hydrogen electrode. The cell potential is E_cell = E_right – E_left (reduction potentials). For a spontaneous reaction, E_cell > 0.
标准电极电势 E° 是在标准条件（298 K、100 kPa、1.0 mol dm⁻³ 离子浓度）下相对于标准氢电极测得的。电池电动势为 E_cell = E_right – E_left（还原电势）。对自发反应，E_cell > 0。
Under non-standard conditions, the Nernst equation gives the electrode potential: E = E° – (RT/nF) ln Q, where n is the number of electrons transferred, F = 96485 C mol⁻¹, and Q is the reaction quotient. At 298 K, this simplifies to: E = E° – (0.0592/n) log₁₀ Q.
在非标准条件下，能斯特方程给出电极电势：E = E° – (RT/nF) ln Q，其中 n 为转移电子数，F = 96485 C mol⁻¹，Q 为反应商。在 298 K 下可简化为：E = E° – (0.0592/n) log₁₀ Q。
The effect of concentration on cell EMF explains how concentration cells work and why batteries run down. A high resistance voltmeter must be used to measure E_cell so that no current flows.
浓度对电池电动势的影响解释了浓差电池的工作原理以及电池为何会耗尽。测量 E_cell 必须使用高电阻电压表，以确保无电流通过。
7. Transition Metal Complexes & Color | 过渡金属配合物与颜色
Transition metals form complexes with ligands. The coordination number and geometry (octahedral, tetrahedral, square planar) depend on the metal ion and the ligands. The splitting of d-orbitals in an octahedral field results in two energy levels: e_g and t_2g. The energy gap, Δ_oct, corresponds to the energy of visible light absorbed, and the observed colour is the complementary colour.
过渡金属与配体形成配合物。配位数和几何构型（八面体、四面体、平面四边形）取决于金属离子和配体。在八面体场中 d 轨道分裂为两组能级：e_g 和 t_2g。能量差 Δ_oct 对应吸收的可见光能量，观察到的颜色是互补色。
The spectrochemical series orders ligands by the magnitude of Δ they produce: I⁻ < Br⁻ < S²⁻ < SCN⁻ < Cl⁻ < NO₃⁻ < F⁻ < OH⁻ < C₂O₄²⁻ < H₂O < NCS⁻ < NH₃ < en < NO₂⁻ < CN⁻ < CO. Stronger field ligands cause larger splitting and often result in low-spin complexes.
光谱化学序列按产生的 Δ 大小排列配体：I⁻ < Br⁻ < S²⁻ < SCN⁻ < Cl⁻ < NO₃⁻ < F⁻ < OH⁻ < C₂O₄²⁻ < H₂O < NCS⁻ < NH₃ < en < NO₂⁻ < CN⁻ < CO。强场配体导致更大的分裂，常形成低自旋配合物。
- Colour arises from d–d transitions. Complexes with d⁰ or d¹⁰ configurations are colourless (unless charge-transfer transitions occur).
- 颜色的产生源于 d–d 跃迁。d⁰ 或 d¹⁰ 组态的配合物一般为无色（除非发生电荷转移跃迁）。
- The formula ΔE = hf = hc/λ relates the energy gap to the wavelength of absorbed light, where h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹.
- 公式 ΔE = hf = hc/λ 将能级差与吸收光波长关联，其中 h = 6.63 × 10⁻³⁴ J s，c = 3.00 × 10⁸ m s⁻¹。
8. Organic Analysis: NMR & Chromatography | 有机分析：核磁共振与色谱
Proton NMR (¹H NMR) provides information about the number and environment of hydrogen atoms. Chemical shift δ is measured in ppm relative to TMS. The number of signals indicates different proton environments; integration ratios give the relative number of protons; splitting patterns follow the n+1 rule (where n = number of protons on adjacent carbons). Coupling constants are measured in Hz.
质子核磁共振 (¹H NMR) 提供有关氢原子数目和化学环境的信息。化学位移 δ 以 ppm 为单位，参照 TMS。信号数表示不同质子环境；积分比例给出质子相对数目；分裂模式遵循 n+1 规则（n 为相邻碳上的质子数）。偶合常数以 Hz 为单位。
¹³C NMR spectroscopy shows distinct peaks for each unique carbon environment. The spectrum is proton-decoupled, so all signals appear as singlets. Chemical shifts help distinguish functional groups (e.g., C=O around 160–220 ppm, C–O around 50–90 ppm).
¹³C NMR 谱显示每个独特碳环境的独立峰。谱图为质子去耦谱，因此所有信号均呈单峰。化学位移有助于区分官能团（例如 C=O 约在 160–220 ppm，C–O 约在 50–90 ppm）。
Chromatography (TLC, GC, HPLC) separates mixtures based on differential partitioning between a stationary phase and a mobile phase. The retention factor in TLC is: R_f = distance travelled by spot / distance travelled by solvent front. In GC, retention time is compared to standards for identification.
色谱法（TLC、GC、HPLC）基于混合物在固定相与流动相之间分配系数的差异进行分离。TLC 中的比移值为：R_f = 斑点移动距离 / 溶剂前沿移动距离。在气相色谱中，通过与标准品保留时间的比较进行鉴定。
9. Key Organic Reaction Mechanisms | 关键有机反应机理
Year 13 OCR mechanisms include nucleophilic addition–elimination (acyl chlorides, acid anhydrides), electrophilic substitution (benzene), nucleophilic substitution (haloalkanes – S_N1 and S_N2), elimination, and addition–elimination in aromatic chemistry. Curly arrows show movement of electron pairs.
Year 13 OCR 涉及的机理包括：亲核加成–消除（酰氯、酸酐）、亲电取代（苯）、亲核取代（卤代烷 – S_N1 和 S_N2）、消除反应，以及芳香化学中的加成–消除反应。弯箭头表示电子对的移动。
The rate of S_N1 depends only on the substrate concentration: rate = k[RX]. It proceeds via a carbocation intermediate and results in racemisation. S_N2 rate = k[RX][Nu⁻] and occurs with inversion of configuration.
S_N1 反应速率仅取决于底物浓度：rate = k[RX]。反应经碳正离子中间体进行，导致外消旋化。S_N2 速率方程为 rate = k[RX][Nu⁻]，同时伴随构型翻转。
- Aromatic electrophilic substitution: nitration (HNO₃/H₂SO₄), halogenation (X₂/AlX₃), Friedel–Crafts alkylation and acylation. The general mechanism involves attack of the electrophile on the π system, formation of a Wheland intermediate, then loss of a proton to restore aromaticity.
- 芳香亲电取代：硝化（HNO₃/H₂SO₄）、卤代（X₂/AlX₃）、Friedel–Crafts 烷基化与酰基化。一般机理为亲电试剂进攻 π 体系，形成 Wheland 中间体，然后脱去质子恢复芳香性。
10. Born–Haber Cycles & Lattice Enthalpy | Born–Haber 循环与晶格焓
The Born–Haber cycle is an application of Hess’s law to ionic compounds, linking the standard enthalpy change of formation to ionisation energies, electron affinities, enthalpy of atomisation, and lattice enthalpy. Lattice enthalpy (ΔH_L) is the enthalpy change when one mole of an ionic solid is formed from its gaseous ions. It is always highly exothermic.
Born–Haber 循环是赫斯定律在离子化合物中的应用，将标准生成焓变与电离能、电子亲和势、原子化焓和晶格焓联系起来。晶格焓 ΔH_L 是指由气态离子形成一摩尔离子固体时的焓变，总是高度放热。
The Born–Lande equation or Kapustinskii equation can be used to estimate lattice enthalpy theoretically, but the OCR course emphasises calculation via the cycle: ΔH_f° = ΔH_atom(m) + Σ IE + ΔH_atom(non-metal) + Σ EA + ΔH_LE. (Signs must be handled carefully – lattice enthalpy is often defined as exothermic, but the cycle may use its magnitude with appropriate sign.)
Born–Lande 方程或 Kapustinskii 方程可用于理论估算晶格焓，但 OCR 课程强调通过循环计算：ΔH_f° = ΔH_atom(金属) + Σ IE + ΔH_atom(非金属) + Σ EA + ΔH_LE。须小心处理正负号——晶格焓通常定义为放热，但在循环中可取其绝对值并配以合适正负号。
- Enthalpy of solution (ΔH_sol) = –ΔH_LE + Σ ΔH_hyd. Hydration enthalpies are always exothermic. Solubility depends on the balance between lattice and hydration enthalpies.
- 溶解焓 ΔH_sol = –ΔH_LE + Σ ΔH_hyd。水合焓总是放热。溶解度取决于晶格焓与水合焓之间的平衡。
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