📚 AQA A-Level Chemistry Formula Summary Handbook | AQA A-Level 化学公式汇总手册
This comprehensive handbook collates the essential formulas you need to master for the AQA A-Level Chemistry specification. From mole calculations and energetics to equilibria, kinetics, and thermodynamics, each equation is presented with a clear explanation of its variables and units. Use this guide as a quick-reference revision tool to boost your confidence in tackling numerical problems.
本手册整理了 AQA A-Level 化学考试中必须掌握的核心公式。涵盖摩尔计算、能量学、平衡、动力学和热力学等主题，每个公式都清晰标注了变量和单位。可将本文作为快速查阅的复习利器，帮助你自信应对各类定量计算题目。
1. Moles, Mass and Molar Mass | 摩尔、质量与摩尔质量
The mole is the central unit for counting chemical entities. The amount of substance (n) is calculated by dividing the mass of a sample (m) by its molar mass (M). Molar mass is numerically equal to the relative atomic or formula mass in g mol⁻¹.
摩尔是计量化学微粒的核心单位。物质的量 (n) 通过样品的质量 (m) 除以摩尔质量 (M) 求得，摩尔质量在数值上等于相对原子质量或相对分子质量，单位为 g mol⁻¹。
n = m ÷ M
Where / 其中: n = amount of substance (mol); m = mass (g); M = molar mass (g mol⁻¹).
To find the number of particles, multiply the amount in moles by the Avogadro constant (6.02 × 10²³ mol⁻¹). For gases at room temperature and pressure (RTP, 298 K and 100 kPa), the molar volume Vₘ is taken as 24.0 dm³ mol⁻¹.
微粒数可由物质的量乘以阿伏伽德罗常数 (6.02 × 10²³ mol⁻¹) 得到。在常温常压 (298 K, 100 kPa) 下，气体摩尔体积 Vₘ 取 24.0 dm³ mol⁻¹。
Number of particles = n × Nₐ
n(gas) = V(gas) ÷ Vₘ
2. Empirical and Molecular Formulae | 实验式与分子式
The empirical formula gives the simplest whole‑number ratio of atoms in a compound. It is determined from percentage composition or mass data by converting masses to moles, then dividing by the smallest number of moles.
实验式表示化合物中原子最简整数比。通过将质量或百分组成转化为物质的量，再除以最小的物质的量来求得。
Moles of atom = mass (g) ÷ Aᵣ
The molecular formula is a multiple of the empirical formula. The multiplier (n) is found by dividing the relative molecular mass (Mᵣ) by the empirical formula mass. Molecular formula = (empirical formula) × n.
分子式是实验式的整数倍。倍数 n 由相对分子质量 (Mᵣ) 除以实验式质量得出：分子式 = (实验式) × n。
3. The Ideal Gas Equation | 理想气体状态方程
When conditions deviate from RTP, the ideal gas equation links pressure (p), volume (V), amount (n) and temperature (T) using the gas constant R (8.31 J K⁻¹ mol⁻¹). Remember to convert volume to m³, pressure to Pa and temperature to kelvin.
当条件偏离常温常压时，需使用理想气体状态方程关联压强 (p)、体积 (V)、物质的量 (n) 和温度 (T)，气体常数 R 为 8.31 J K⁻¹ mol⁻¹。务必注意单位换算：体积用 m³，压强用 Pa，温度用开尔文。
pV = nRT
Where / 其中: p = pressure (Pa); V = volume (m³); n = amount (mol); R = 8.31 J K⁻¹ mol⁻¹; T = temperature (K).
Standard conversions: 1 m³ = 1000 dm³; 1 atm = 101 325 Pa; 100 kPa = 1.00 × 10⁵ Pa. Always use SI units to obtain consistent results.
标准换算：1 m³ = 1000 dm³；1 atm = 101 325 Pa；100 kPa = 1.00 × 10⁵ Pa。始终使用国际单位制以获得一致结果。
4. Concentration of Solutions | 溶液浓度
The concentration of a solution (c) is the amount of solute (n) dissolved per unit volume (V). The standard unit is mol dm⁻³. You can also interconvert between mass concentration (g dm⁻³) and molarity.
溶液浓度 (c) 是单位体积 (V) 中溶质的物质的量 (n)，常用单位为 mol dm⁻³。也可在质量浓度 (g dm⁻³) 和摩尔浓度之间进行换算。
c = n ÷ V
For dilution problems: c₁V₁ = c₂V₂, where c₁ and V₁ refer to the concentrated solution, and c₂ and V₂ refer to the diluted solution.
稀释问题：c₁V₁ = c₂V₂，其中 c₁、V₁ 指浓溶液的浓度与体积，c₂、V₂ 指稀释后的浓度与体积。
Titration calculations rely on combining the concentration formula with stoichiometric ratios. Example: for the reaction aA + bB → products, n(A)/a = n(B)/b.
滴定计算需要结合浓度公式与化学计量比。例如：对于反应 aA + bB → 产物，n(A)/a = n(B)/b。
5. Enthalpy Change and Calorimetry | 焓变与量热法
Enthalpy change (ΔH) is measured experimentally from the heat transferred to or from a known mass of water (or solution). The basic calorimetry equation uses the specific heat capacity (c) of the surroundings, assumed to be 4.18 J g⁻¹ K⁻¹ for dilute aqueous solutions.
焓变 (ΔH) 通过测量已知质量的水 (或溶液) 吸收或放出的热量进行实验测定。基础量热方程采用环境的比热容 (c)，稀溶液通常取 4.18 J g⁻¹ K⁻¹。
q = mcΔT
Where / 其中: q = heat transferred (J); m = mass of solution (g); c = 4.18 J g⁻¹ K⁻¹; ΔT = temperature change (K or °C).
The molar enthalpy change is obtained by dividing the heat transferred by the amount of the limiting reactant: ΔH = –q ÷ n (a negative sign is added for exothermic processes). Enthalpy changes are reported in kJ mol⁻¹.
摩尔焓变由传递的热量除以限速反应物的物质的量得到：ΔH = –q ÷ n (放热过程加负号)。焓变单位用 kJ mol⁻¹ 表示。
6. Hess’s Law and Bond Enthalpies | 赫斯定律与键焓
Hess’s law states that the total enthalpy change for a reaction is independent of the route taken. You can use known enthalpy changes of formation or combustion to construct cycles and solve for an unknown ΔH.
赫斯定律指出，一个反应的总焓变与途径无关。你可以利用已知的生成焓或燃烧焓构建循环，求解未知的 ΔH。
ΔH⦵(reaction) = Σ ΔfH⦵(products) – Σ ΔfH⦵(reactants)
ΔH⦵(reaction) = Σ ΔcH⦵(reactants) – Σ ΔcH⦵(products)
Mean bond enthalpy calculations: ΔH ≃ Σ(bond enthalpies broken) – Σ(bond enthalpies formed). These are approximate because mean bond enthalpies are averages from many compounds.
平均键焓计算：ΔH ≃ Σ(断裂键的键焓) – Σ(形成键的键焓)。这是近似值，因为平均键焓取自多种化合物的平均值。
7. Equilibrium Constants: Kc | 平衡常数 Kc
For a homogeneous reaction aA + bB ⇌ cC + dD, the equilibrium constant Kc is expressed in terms of equilibrium concentrations. Pure solids and liquids are omitted from the expression; only gases and aqueous species appear.
对于均相反应 aA + bB ⇌ cC + dD，平衡常数 Kc 用平衡浓度表示。纯固体和纯液体不出现在表达式中，仅包含气体和溶液物种。
Kc = [C]ᶜ [D]ᵈ ÷ [A]ᵃ [B]ᵇ
Concentrations are in mol dm⁻³. The value of Kc is only affected by temperature; changes in concentration or pressure do not alter Kc but shift the position of equilibrium.
浓度单位为 mol dm⁻³。Kc 的数值只受温度影响；浓度或压强的改变不会改变 Kc，但会使平衡位置发生移动。
8. Equilibrium Constants: Kp | 平衡常数 Kp
For gaseous equilibria, Kp uses partial pressures instead of concentrations. The partial pressure of a gas is its mole fraction multiplied by the total pressure.
对于气体平衡，Kp 采用分压代替浓度。某气体的分压等于其摩尔分数乘以总压。
pₐ = xₐ × Pₜₒₜₐₗ
Kp = (pC)ᶜ (pD)ᵈ ÷ (pA)ᵃ (pB)ᵇ
Units of Kp depend on the stoichiometry; they are derived in the same way as Kc units. Like Kc, Kp is constant only at a given temperature.
Kp 的单位取决于计量数，与 Kc 单位推导方式相同。与 Kc 类似，Kp 只在特定温度下为常数。
9. pH, Kw and Strong Acids | pH、Kw 与强酸
The pH scale is a logarithmic measure of hydrogen ion concentration. For aqueous solutions at 25 °C, the ionic product of water Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶.
pH 标度是氢离子浓度的对数度量。25 °C 时，水的离子积 Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶。
pH = –log₁₀[H⁺]
[H⁺] = 10⁻ᵖᴴ
Kw = [H⁺][OH⁻]
For a strong monoprotic acid, the hydrogen ion concentration equals the acid concentration after complete dissociation: [H⁺] = [HA]. The pH is then calculated directly.
对于一元强酸，完全解离后氢离子浓度等于酸的浓度：[H⁺] = [HA]，可直接计算 pH。
10. Weak Acids, Ka and pKa | 弱酸、Ka 与 pKa
Weak acids partially dissociate in water. The acid dissociation constant Ka indicates the strength of the acid. The pKa is the negative logarithm of Ka, analogous to pH.
弱酸在水中部分解离。酸解离常数 Ka 表示酸的强度，pKa 是 Ka 的负对数，类似于 pH 的概念。
Ka = [H⁺][A⁻] ÷ [HA]
pKa = –log₁₀Ka
For a weak acid where [H⁺] ≪ initial concentration, the approximation [HA]ₑq ≈ [HA]ᵢₙᵢₜᵢₐₗ is used. Then [H⁺] = √(Ka × [HA]) provides a direct estimate of pH.
当弱酸 [H⁺] 远小于初始浓度时，可使用近似 [HA]ₑq ≈ [HA]ᵢₙᵢₜᵢₐₗ，此时 [H⁺] = √(Ka × [HA]) 可直接估算 pH。
11. Buffer Solutions | 缓冲溶液
Buffer solutions resist changes in pH when small amounts of acid or base are added. An acidic buffer is typically made from a weak acid and its conjugate base. The Henderson–Hasselbalch equation rearranges the Ka expression to find pH directly.
缓冲溶液能抵抗外加少量酸或碱引起的 pH 变化。酸性缓冲液通常由弱酸及其共轭碱组成。亨德森–哈塞尔巴尔赫方程由 Ka 表达式重排，直接计算 pH。
[H⁺] = Ka × [HA] ÷ [A⁻]
pH = pKa + log₁₀([A⁻] ÷ [HA])
When preparing a buffer, the [A⁻]/[HA] ratio can be adjusted by partial neutralisation of the weak acid or by mixing calculated volumes of the acid and its salt. The buffer capacity is highest when [A⁻] = [HA], i.e. pH = pKa.
配制缓冲液时，可通过部分中和弱酸或按计算量混合弱酸与其盐来调节 [A⁻]/[HA] 比值。当 [A⁻] = [HA] 即 pH = pKa 时，缓冲容量最大。
12. Rate Equations and the Arrhenius Equation | 速率方程与阿伦尼乌斯方程
The rate equation shows how the rate of a reaction depends on the concentrations of reactants. The order with respect to each species is determined experimentally; it is not simply the stoichiometric coefficient.
速率方程表示反应速率随反应物浓度的变化关系。各组分的反应级数由实验确定，并非简单等于计量系数。
Rate = k [A]ᵐ [B]ⁿ
Where m and n are partial orders, overall order = m + n. k is the rate constant, whose units vary with overall order.
其中 m、n 为分级数，总级数 = m + n。k 为速率常数，其单位随总级数而变化。
The Arrhenius equation links the rate constant to temperature and activation energy Eₐ. Its logarithmic form allows determination of Eₐ from a graph of ln k against 1/T.
阿伦尼乌斯方程将速率常数与温度和活化能 Eₐ 关联。其对数形式可用于通过 ln k 对 1/T 作图求算 Eₐ。
k = A e^(–Eₐ/RT)
ln k = –Eₐ/(R) × (1/T) + ln A
Where / 其中: A = pre-exponential factor; Eₐ = activation energy (J mol⁻¹); R = 8.31 J K⁻¹ mol⁻¹; T = temperature (K).
13. Thermodynamics: Gibbs Free Energy and Electrode Potentials | 热力学：吉布斯自由能与电极电势
The feasibility of a reaction at constant temperature and pressure is predicted by the Gibbs free energy change. A negative ΔG indicates a thermodynamically feasible process.
恒温恒压下反应的可行性由吉布斯自由能变判据。ΔG 为负值表示反应在热力学上是可行的。
ΔG⦵ = ΔH⦵ – TΔS⦵
Calculate entropy changes from standard entropy values: ΔS⦵ = ΣS⦵(products) – ΣS⦵(reactants). Remember to convert ΔS to kJ K⁻¹ mol⁻¹ to match ΔH in kJ mol⁻¹.
由标准熵值计算熵变：ΔS⦵ = ΣS⦵(产物) – ΣS⦵(反应物)。注意将 ΔS 单位换算为 kJ K⁻¹ mol⁻¹，以匹配 ΔH 的 kJ mol⁻¹。
For electrochemical cells, the standard cell potential is calculated from the two half‑cell reduction potentials (E⦵ values). The relation between free energy and cell potential is fundamental.
对于电化学池，标准电池电动势由两个半电池的还原电势 (E⦵) 计算得出。自由能与电池电动势之间的关系至关重要。
E⦵cell = E⦵(right) – E⦵(left)
ΔG⦵ = –nFE⦵cell
Where n = number of moles of electrons transferred, F = Faraday constant (96 500 C mol⁻¹). A positive E⦵cell corresponds to a negative ΔG⦵, indicating a feasible reaction.
其中 n 为转移电子的物质的量，F 为法拉第常数 (96 500 C mol⁻¹)。正的 E⦵cell 对应负的 ΔG⦵，表明反应可行。
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