📚 Year 12 AQA Chemistry: Formula & Theorem Quick-Reference Guide | Year 12 AQA 化学：公式定理速查手册
This quick-reference guide brings together the essential formulas, theorems and quantitative relationships you need for Year 12 AQA Chemistry. From the mole concept to energetics, kinetics, equilibria and acid–base calculations, every key equation is presented with its units, conditions and typical applications. Use this handbook alongside your practical work and past-paper practice to build confidence in numerical problem-solving.
本速查手册汇集了 Year 12 AQA 化学所需的核心公式、定理与定量关系。从摩尔概念到能量学、动力学、化学平衡和酸碱计算，每条关键公式都配有单位、适用条件及典型应用说明。将本手册与实验操作及历年真题练习相结合，可有效提升解决化学计算问题的信心。
1. The Mole and Avogadro's Constant | 摩尔与阿伏伽德罗常数
ied elementary entities (atoms, molecules, ions, electrons, etc.). This number is Avogadro's constant, NA.
摩尔是物质的量的国际单位。1 摩尔精确包含 6.022 × 10²³ 个指定的基本单元（原子、分子、离子、电子等）。这个数值即为阿伏伽德罗常数 NA。
The relationship between number of particles N and amount of substance n is:
n = N / NA
粒子数 N 与物质的量 n 的关系为：n = N / NA。
The mass of one mole of a substance is its molar mass M, usually expressed in g mol⁻¹. The number of moles can be calculated from mass m (in g) using:
n = m / M
每摩尔物质的质量为其摩尔质量 M，通常以 g mol⁻¹ 表示。利用质量 m (g) 计算物质的量时，公式为 n = m / M。
| Quantity (量) | Symbol (符号) | Common unit (常用单位) |
|---|---|---|
| Amount of substance (物质的量) | n | mol |
| Mass (质量) | m | g |
| Molar mass (摩尔质量) | M | g mol⁻¹ |
| Avogadro's constant (阿伏伽德罗常数) | NA | mol⁻¹ |
2. Empirical and Molecular Formulas | 实验式与分子式
The empirical formula gives the simplest whole-number ratio of atoms of each element in a compound. It is determined from the masses or percentage masses of the elements.
实验式表示化合物中各类原子的最简整数比，由元素的质量或质量百分比确定。
To find the empirical formula, divide the mass or percentage of each element by its relative atomic mass Ar to obtain the number of moles, then divide each value by the smallest number of moles to get the ratio.
求实验式时，用各元素的质量或质量百分比除以其相对原子质量 Ar 得到摩尔数，再将各值除以最小的摩尔数即得原子个数比。
The molecular formula gives the actual number of atoms of each element in one molecule. It is a whole-number multiple of the empirical formula:
Molecular formula = (Empirical formula) × n, where n = Mr / (mass of empirical formula)
分子式表示一个分子中各元素原子的实际数目，是实验式的整数倍：分子式 = (实验式) × n，其中 n = 相对分子质量 Mr / 实验式质量。
3. Gas Volumes and the Ideal Gas Equation | 气体体积与理想气体状态方程
At room temperature and pressure (RTP, 298 K and 100 kPa), one mole of any gas occupies approximately 24.0 dm³. This is the molar gas volume Vm:
n = V / Vm (Vm = 24.0 dm³ mol⁻¹ at RTP)
在常温常压（RTP，298 K、100 kPa）下，1 摩尔任何气体所占体积约为 24.0 dm³，这就是气体摩尔体积 Vm：n = V / Vm（RTP 下 Vm = 24.0 dm³ mol⁻¹）。
For conditions other than RTP, use the ideal gas equation:
pV = nRT
若条件与 RTP 不同，需使用理想气体状态方程 pV = nRT。
In this equation, p is pressure in pascals (Pa), V is volume in cubic metres (m³), n is the amount in mol, T is temperature in kelvin (K), and R is the gas constant, 8.31 J K⁻¹ mol⁻¹.
方程中，p 为压强，单位帕斯卡 (Pa)；V 为体积，单位立方米 (m³)；n 为物质的量 (mol)；T 为热力学温度 (K)；R 为摩尔气体常数，8.31 J K⁻¹ mol⁻¹。
Unit conversions required (必须的单位换算):
1000 dm³ = 1 × 10⁶ cm³; temperature in K = temperature in °C + 273; 100 kPa = 100 000 Pa.
4. Concentration and Titration Calculations | 浓度与滴定计算
The concentration of a solution, c, is the amount of solute (in mol) dissolved in 1 dm³ of solution:
c = n / V (mol dm⁻³)
溶液的浓度 c 表示每 dm³ 溶液中溶质的物质的量 (mol)：c = n / V (mol dm⁻³)。
In a titration, the reacting volumes and known concentration allow calculation of an unknown concentration or molar mass. The key relation at the equivalence point is:
nacid / nbase = (cacidVacid) / (cbaseVbase)
滴定中，通过反应体积和已知浓度可计算出未知浓度或摩尔质量。化学计量点时的核心关系为：酸与碱物质的量之比 nacid / nbase = (cacidVacid) / (cbaseVbase)。
olumes are usually measured in cm³; convert to dm³ by dividing by 1000 when using c = n/V.
务必先写出配平的化学方程式以确定正确的摩尔比。体积通常以 cm³ 为单位，代入 c = n/V 时需除以 1000 转为 dm³。
5. Enthalpy Changes and Calorimetry | 焓变与量热法
An enthalpy change ΔH is the heat energy transferred in a reaction at constant pressure. The standard enthalpy change of reaction, ΔH°r, is measured under standard conditions (100 kPa, 298 K, solutions 1 mol dm⁻³).
焓变 ΔH 是恒压条件下反应中传递的热量。标准反应焓变 ΔH°r 在标准条件（100 kPa、298 K、溶液浓度 1 mol dm⁻³）下测得。
In a simple calorimetry experiment, the heat absorbed or released by the solution (or water) is:
q = mcΔT
在简单量热实验中，溶液（或水）吸收或释放的热量 q = mcΔT。
ic heat capacity (for water, c = 4.18 J g⁻¹ K⁻¹), and ΔT is the temperature change (ΔT = Tfinal – Tinitial).
其中 m 为溶液质量（可用水的质量近似，密度按 1 g cm⁻³ 计），c 为比热容（水的 c = 4.18 J g⁻¹ K⁻¹），ΔT 为温度变化 (ΔT = Tfinal – Tinitial)。
To find the enthalpy change per mole, divide by the number of moles of the limiting reactant and include the appropriate sign:
ΔH = – q / n
欲求每摩尔的焓变，需除以限制反应物的物质的量并加上正负号：ΔH = – q / n。负号表示反应放热时体系损失能量。
6. Hess's Law and Bond Enthalpies | 盖斯定律与键焓
Hess's law states that the total enthalpy change for a reaction is independent of the route taken, provided the initial and final conditions are the same.
盖斯定律指出，只要始态与终态相同，反应的总焓变与途径无关。
It allows calculation of an unknown ΔH by combining known enthalpy changes, often using enthalpy of formation or combustion data.
利用该定律，可通过已知焓变（如生成焓或燃烧焓）的代数组合来求算未知的 ΔH。
Mean bond enthalpy is the average energy required to break one mole of a given covalent bond in the gaseous state, averaged over many compounds. The approximate enthalpy change of a reaction can be estimated using:
ΔH ≈ Σ (bond enthalpies of bonds broken) – Σ (bond enthalpies of bonds formed)
平均键焓是气态下断裂 1 摩尔某共价键所需的平均能量（多个化合物取均值）。反应焓变可用下式估算：ΔH ≈ Σ(断裂键的键焓) – Σ(形成键的键焓)。
Remember: bond breaking is endothermic (positive ΔH); bond making is exothermic (negative ΔH). This method gives approximate values because mean bond enthalpies ignore molecular environment.
注意：断键吸热 (ΔH 为正)，成键放热 (ΔH 为负)。由于平均键焓忽略了分子具体环境，此法所得仅为近似值。
7. Rate Equations and Rate Constants | 速率方程与速率常数
products, the rate equation links the rate of reaction to the concentrations of reactants:
Rate = k [A]ᵐ [B]ⁿ
对于一般反应 aA + bB → 产物，速率方程将反应速率与反应物浓度相关联：Rate = k [A]ᵐ [B]ⁿ。
m and n are the orders of reaction with respect to A and B; they can be 0, 1, 2 or fractions. The overall order is m + n.
m 和 n 分别为对 A 和 B 的反应级数，可取 0、1、2 或分数；总反应级数 = m + n。
The rate constant k is independent of concentration but increases with temperature. Its units depend on the overall order:
- Zero order overall: mol dm⁻³ s⁻¹
- First order overall: s⁻¹
- Second order overall: dm³ mol⁻¹ s⁻¹
速率常数 k 与浓度无关，随温度升高而增大。其单位取决于总反应级数：零级 mol dm⁻³ s⁻¹；一级 s⁻¹；二级 dm³ mol⁻¹ s⁻¹。
To determine the order from experimental data, compare initial rates when the concentration of one reactant is changed while the others are kept constant. The continuous monitoring or initial-rates method can be used.
由实验数据确定级数时，保持其他反应物浓度不变，改变一种反应物浓度并比较初速率变化。可采用连续监测法或初速率法。
8. Equilibrium Constant Kc | 平衡常数 Kc
For a reversible homogeneous reaction aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration is:
Kc = [C]ᶜ [D]ᵈ / [A]ᵃ [B]ᵇ
对于可逆的均相反应 aA + bB ⇌ cC + dD，以浓度表示的平衡常数 Kc = [C]ᶜ [D]ᵈ / [A]ᵃ [B]ᵇ。
Square brackets denote equilibrium concentrations in mol dm⁻³. The value of Kc is constant only at a given temperature. Catalysts do not affect Kc.
方括号表示平衡浓度，单位为 mol dm⁻³。Kc 只有在温度一定时才为常数，催化剂不影响 Kc 的数值。
The units of Kc depend on the stoichiometry and can be derived by cancelling concentration units. For example, if the sum of powers in the numerator equals that in the denominator, Kc has no units.
Kc 的单位由化学计量关系决定，可从浓度单位约简得出。若分子幂次总和与分母相等，则 Kc 无单位。
Le Chatelier's principle helps predict how the position of equilibrium shifts when temperature, pressure or concentration is changed, but the value of Kc is only affected by temperature.
勒夏特列原理可预测温度、压强或浓度变化时平衡移动的方向，但只有温度才会改变 Kc 的值。
9. pH of Strong Acids | 强酸的 pH 计算
The pH of a solution is defined as:
pH = –log₁₀[H⁺]
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