📚 A-Level Chemistry: Formula Summary Handbook | A-Level 化学：公式汇总手册
Mastering the essential formulae is a key part of success in A-Level Chemistry. This handbook brings together the most important equations and relationships you will encounter across physical, inorganic, and organic chemistry, presented with clear explanations and unified notation. Use it for quick reference, targeted revision, and building confidence in calculations.
掌握核心公式是 A-Level 化学成功的关键。本手册汇集了物理化学、无机化学和有机化学中最重要的方程与关系，并配以清晰的解释和统一的符号。可用作快速参考、针对性复习以及提升计算题信心。
1. Mole and Concentration | 摩尔与浓度公式
The mole is the fundamental counting unit in chemistry, linking mass to the number of particles. The amount of substance (n) in moles is found by dividing the mass (m) of a sample by its molar mass (M).
摩尔是化学的基本计数单位，将质量与粒子数联系起来。物质的量（n，单位 mol）等于样品质量（m）除以摩尔质量（M）。
n = m / M
When working with solutions, the concentration (c) is defined as the amount of solute per unit volume. The standard unit of volume is dm³, so c has units of mol dm⁻³.
对于溶液，浓度（c）定义为单位体积中溶质的物质的量。体积的标准单位是 dm³，因此 c 的单位为 mol dm⁻³。
c = n / V
These two equations are combined in titrations and gravimetric analysis. For example, n = cV and m = cVM. Remember that 1 dm³ = 1000 cm³ and 1 m³ = 1000 dm³.
这两条公式可组合用于滴定和重量分析。例如 n = cV 以及 m = cVM。注意 1 dm³ = 1000 cm³，1 m³ = 1000 dm³。
n = cV m = cVM
The Avogadro constant (Nₐ ≈ 6.02 × 10²³ mol⁻¹) relates the number of entities (N) to the amount in moles, and the molar volume of an ideal gas at RTP (20 °C, 1 atm) is 24 dm³ mol⁻¹.
阿伏伽德罗常数（Nₐ ≈ 6.02 × 10²³ mol⁻¹）将微粒数（N）与物质的量联系起来，理想气体在常温常压（20 °C，1 atm）下的摩尔体积为 24 dm³ mol⁻¹。
N = n Nₐ Vgas = n × 24 dm³ (at RTP)
2. Ideal Gas Equation | 理想气体方程
The ideal gas equation combines the empirical gas laws into a single relation. It is widely used to find the molar mass of a volatile liquid or to calculate the volume of gas produced in a reaction.
理想气体方程将经验气体定律综合为单一关系。广泛用于求算挥发性液体的摩尔质量或计算反应产生的气体体积。
pV = nRT
In this equation, p is the pressure in pascals (Pa), V is the volume in m³, n is the number of moles, R is the gas constant (8.31 J K⁻¹ mol⁻¹), and T is the absolute temperature in kelvin (K). Always convert °C to K by adding 273.15.
式中 p 为压强（帕斯卡，Pa），V 为体积（m³），n 为物质的量，R 为气体常数（8.31 J K⁻¹ mol⁻¹），T 为开尔文温度（K）。摄氏度转开尔文需加 273.15。
If you are given pressure in kPa or atm, convert to Pa (1 atm = 101 325 Pa ≈ 1.01 × 10⁵ Pa). Volumes in cm³ or dm³ must be turned into m³ (1 m³ = 1000 dm³ = 10⁶ cm³).
若已知压强单位为 kPa 或 atm，须换算为 Pa（1 atm = 101 325 Pa ≈ 1.01 × 10⁵ Pa）。体积 cm³ 或 dm³ 也须转为 m³（1 m³ = 1000 dm³ = 10⁶ cm³）。
pV = (m / M) RT → M = mRT / pV
3. Enthalpy Changes and Calorimetry | 焓变与量热法
Calorimetry experiments measure the heat energy transferred during a reaction. The heat absorbed or released by a solution is calculated from its mass, specific heat capacity, and temperature change.
量热实验测量反应过程中转移的热量。溶液吸收或释放的热量由其质量、比热容和温度变化求出。
q = mcΔT
Here m is the mass of the solution (often approximated from volume and density of water, 1 g cm⁻³), c is the specific heat capacity (4.18 J g⁻¹ °C⁻¹ for water), and ΔT is the temperature change. The enthalpy change of reaction is then related to the limiting reactant.
其中 m 为溶液质量（常由体积和水的密度 1 g cm⁻³ 近似），c 为比热容（水为 4.18 J g⁻¹ °C⁻¹），ΔT 为温度变化值。反应的焓变与限量反应物的物质的量有关。
ΔH = –q / nlimiting
The negative sign indicates that for an exothermic reaction the surroundings gain heat (q positive) but the system loses energy (ΔH negative). For bond energy calculations, use ΔH ≈ Σ(bond energies broken) – Σ(bond energies made).
负号表示放热反应中，环境吸热（q 为正），系统能量下降（ΔH 为负）。使用键能计算时，ΔH ≈ Σ(断裂键的键能) – Σ(形成键的键能)。
ΔH = ΣBE(broken) – ΣBE(made)
Hess’s law allows the combination of known enthalpy changes to find an unknown one, provided the overall route is the same.
赫斯定律允许通过已知焓变路径的组合求出未知焓变，只要总反应一致。
4. Reaction Rate and Rate Equation | 反应速率与速率方程
The rate of a reaction tells us how quickly a reactant is consumed or a product is formed. Experimentally, rate equations link the rate to the concentrations of reactants raised to some power.
反应速率表示反应物消耗或产物生成的快慢。实验上，速率方程将速率与反应物浓度的若干次幂联系起来。
Rate = k [A]m [B]n
The exponents m and n are the orders with respect to A and B; they are not simply the stoichiometric coefficients. The overall order is m + n. The rate constant k is specific to a given reaction at a particular temperature.
指数 m 和 n 分别是关于 A 和 B 的反应级数，并不简单等于化学计量系数。总级数为 m + n。速率常数 k 在特定温度和反应下为一常数。
The Arrhenius equation describes how the rate constant varies with temperature:
阿伦尼乌斯方程描述速率常数如何随温度变化：
k = A e–Ea / RT or ln k = –Ea / RT + ln A
Ea is the activation energy (J mol⁻¹), R is the gas constant (8.31 J K⁻¹ mol⁻¹), T is temperature in K, and A is the pre‑exponential factor. A graph of ln k against 1/T gives a straight line with gradient = –Ea / R.
Ea 为活化能（J mol⁻¹），R 为气体常数，T 为开尔文温度，A 为指前因子。以 ln k 对 1/T 作图得一直线，斜率为 –Ea / R。
5. Chemical Equilibrium and Equilibrium Constant | 化学平衡与平衡常数
When a reversible reaction reaches dynamic equilibrium, the concentrations of reactants and products remain constant. The equilibrium constant Kc is defined in terms of concentrations raised to the stoichiometric coefficients.
当可逆反应达到动态平衡，反应物和产物浓度保持恒定。平衡常数 Kc 用各物种浓度以其化学计量系数为指数来定义。
For aA + bB ⇌ cC + dD: Kc = [C]c[D]d / [A]a[B]b
The units of Kc depend on the total number of moles on each side and can be derived by inserting the units of concentration (mol dm⁻³) into the expression.
Kc 的单位取决于反应两侧的总摩尔数，可通过将浓度单位（mol dm⁻³）代入表达式导出。
For gas‑phase equilibria, the equilibrium constant Kp uses partial pressures:
对于气相平衡，平衡常数 Kp 使用分压：
Kp = (pCc pDd) / (pAa pBb)
Partial pressure of a gas = mole fraction × total pressure. Mole fraction = moles of that gas / total moles of all gases.
某气体的分压 = 摩尔分数 × 总压。摩尔分数 = 该气体的物质的量 / 所有气体的总物质的量。
6. Acid–Base Equilibria and pH | 酸碱平衡与pH
The pH scale measures the hydrogen ion concentration in an aqueous solution. The key definitions are:
pH 标度衡量水溶液中的氢离子浓度。核心定义如下：
pH = –log₁₀ [H⁺] [H⁺] = 10–pH
Water itself undergoes slight autoionisation, described by the ionic product of water, Kw:
水本身发生轻微的自耦电离，由水的离子积 Kw 描述：
Kw = [H⁺][OH⁻]
At 298 K, Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶. In pure water and neutral solutions, [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³, giving pH = 7.
在 298 K 时，Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶。纯水和中性溶液中，[H⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol dm⁻³，pH = 7。
For a weak acid HA that dissociates partially, the acid dissociation constant Ka is used:
对于部分电离的弱酸 HA，使用酸解离常数 Ka：
Ka = [H⁺][A⁻] / [HA] pKa = –log₁₀ Ka
For weak bases, Kb = [BH⁺][OH⁻] / [B] and pKb = –log₁₀ Kb. Note that Ka × Kb = Kw for a conjugate acid‑base pair at 298 K.
对于弱碱，Kb = [BH⁺][OH⁻] / [B]；pKb = –log₁₀ Kb。共轭酸碱对在 298 K 时满足 Ka × Kb = Kw。
7. Buffer Solutions | 缓冲溶液
A buffer solution resists changes in pH when small amounts of acid or base are added. It contains a weak acid and its conjugate base (or a weak base and its conjugate acid). The Henderson–Hasselbalch equation is the quickest way to calculate the pH of an acidic buffer.
缓冲溶液能在加入少量酸或碱时抵抗 pH 变化。它含有弱酸及其共轭碱（或弱碱及其共轭酸）。亨德森‑哈塞尔巴尔赫方程是计算酸性缓冲溶液 pH 的最快捷方法。
pH = pKa + log₁₀ ([salt] / [acid])
This equation assumes that the salt provides the conjugate base fully dissociated, so [A⁻] = [salt]. It is valid when the concentrations of acid and salt are much larger than [H⁺].
该方程假设盐完全解离提供共轭碱，因此 [A⁻] = [salt]。当酸和盐的浓度远大于 [H⁺] 时成立。
You can also derive the pH directly from Ka:
也可以从 Ka 直接推导：
[H⁺] = Ka × ([acid] / [salt]) then pH = –log[H⁺]
For a basic buffer (weak base + salt), use pOH = pKb + log₁₀ ([salt] / [base]) and then pH = 14 – pOH at 298 K.
对于碱性缓冲溶液（弱碱 + 盐），使用 pOH = pKb + log₁₀ ([salt] / [base])，然后在 298 K 下 pH = 14 – pOH。
8. Entropy and Gibbs Free Energy | 熵与吉布斯自由能
Entropy (S) is a measure of disorder; total entropy change determines whether a process is feasible. The Gibbs free energy change combines enthalpy and entropy to predict spontaneity at constant temperature and pressure.
熵（S）是混乱度的量度；总熵变决定过程是否可行。吉布斯自由能变结合了焓和熵，用于预测恒温恒压下的自发性。
ΔG = ΔH – TΔS
ΔG must be negative for a reaction to be thermodynamically feasible. T is the absolute temperature in kelvin, and ΔS is the entropy change of the system in J K⁻¹ mol⁻¹. ΔH is usually in kJ mol⁻¹, so ΔS must be converted to kJ K⁻¹ mol⁻¹ by dividing by 1000 before using this equation.
反应热力学可行要求 ΔG < 0。T 为开尔文温度，ΔS 为系统熵变（J K⁻¹ mol⁻¹）。ΔH 通常以 kJ mol⁻¹ 给出，故使用此方程前 ΔS 须除以 1000 转为 kJ K⁻¹ mol⁻¹。
The standard entropy change of a reaction is calculated from standard entropies of products and reactants:
反应的标准熵变由产物和反应物的标准熵计算：
ΔS° = Σ S°(products) – Σ S°(reactants)
For a reaction at equilibrium, ΔG° = –RT ln K, linking thermodynamics to the equilibrium constant.
反应处于平衡时，ΔG° = –RT ln K，将热力学与平衡常数联系起来。
ΔG° = –RT ln K (R = 8.31 J K⁻¹ mol⁻¹)
9. Electrochemistry (Nernst and Faraday) | 电化学（能斯特与法拉第）
The electromotive force (EMF) of a cell is the difference between the reduction potentials of the two half‑cells under standard conditions.
电池的电动势（EMF）为标准条件下两个半电池还原电位的差值。
E°cell = E°right – E°left
When conditions deviate from standard, the Nernst equation allows calculation of the half‑cell potential or the full cell EMF. For a reaction aA + bB ⇌ cC + dD, the cell potential is given by:
当条件偏离标准时，能斯特方程可用于计算半电池电位或全电池电动势。对于反应 aA + bB ⇌ cC + dD，电池电位为：
E = E° – (RT / nF) ln Q
At 298 K, RT / F = 0.0257 V, so the Nernst equation becomes E = E° – (0.0257 / n) ln Q, or using base‑10 logs: E = E° – (0.0592 / n) log₁₀ Q, where n is the number of electrons transferred and Q is the reaction quotient.
在 298 K 下，RT / F = 0.0257 V，因此能斯特方程简化为 E = E° – (0.0257 / n) ln Q，或采用常用对数形式：E = E° – (0.0592 / n) log₁₀ Q，其中 n 为转移电子数，Q 为反应商。
Quantitative electrolysis uses Faraday’s laws to relate the amount of substance liberated to the electric charge passed.
定量电解利用法拉第定律将析出的物质量与通过的电量关联起来。
Q = It Q = n(e⁻) F
Q is the charge in coulombs (C), I is current in amperes (A), t is time in seconds (s), n(e⁻) is the amount of electrons, and the Faraday constant F = 96 500 C mol⁻¹.
Q 为电量（库仑，C），I 为电流（安培，A），t 为时间（秒），n(e⁻) 为电子的物质的量，法拉第常数 F = 96 500 C mol⁻¹。
n(product) = (I t) / (n(e⁻) per ion × F)
10. Atom Economy and Percentage Yield | 原子经济与产率
These two concepts evaluate the efficiency of a chemical synthesis. Percentage yield compares the actual mass of product obtained to the theoretical maximum, while atom economy assesses how much of the starting materials ends up in the desired product.
这两个概念用于评价化学合成的效率。百分比产率比较实际获得的产品质量与理论最大值，而原子经济则衡量起始原料有多少最终进入目标产物。
% Yield = (actual mass / theoretical mass) × 100%
% Atom Economy = (Mr of desired product / Σ Mr of all reactants) × 100%
High atom economy is desirable for sustainability, as it means less waste. When multiple steps are involved, overall yield is the product of individual yields.
高原子经济有利于可持续性，因为废物更少。涉及多步反应时，总产率为各步产率的乘积。
11. Spectroscopy and Related Formulae |
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