📚 Year 12 Cambridge Chemistry: Formula & Theorem Quick Reference Handbook | 剑桥12年级化学：公式定理速查手册
This quick reference handbook collects all essential formulas, equations and key theorems required for the Cambridge AS Level Chemistry (9701) syllabus, covering physical chemistry topics from moles and stoichiometry to energetics, equilibria and kinetics. Use it as a daily revision companion to check your understanding and to speed up problem‑solving.
本速查手册汇集了剑桥 AS 化学（9701）课程所有核心公式、方程式和重要定理，涵盖从摩尔与计量学到能量学、平衡和动力学的物理化学主题。请您将其作为日常复习伴侣，随时核对自己对公式的理解，并提高解题速度。
1. The Mole and Mass Relationships | 摩尔与质量关系
The amount of substance (n) is measured in moles. One mole contains 6.02 × 10²³ specified particles (Avogadro constant, L). Molar mass M is the mass of one mole of a substance, in g mol⁻¹.
物质的量（n）以摩尔（mol）为单位。1 摩尔含有 6.02 × 10²³ 个指定粒子（阿伏伽德罗常数 L）。摩尔质量 M 是 1 摩尔物质的质量，单位为 g mol⁻¹。
n = m / M
where n = amount in mol, m = mass in g, M = molar mass in g mol⁻¹.
其中 n 为物质的量（mol），m 为质量（g），M 为摩尔质量（g mol⁻¹）。
- Number of particles N = n × L (L ≈ 6.02 × 10²³ mol⁻¹)
- 粒子数 N = n × L（L ≈ 6.02 × 10²³ mol⁻¹）
Always show your unit cancellation to avoid errors when converting between mass, moles and number of particles.
在质量、摩尔和粒子数之间换算时，始终写出单位约分以避免错误。
2. Ideal Gas Equation and Molar Volume | 理想气体方程与摩尔体积
For an ideal gas, the relationship between pressure, volume, temperature and amount is given by the ideal gas equation:
对于理想气体，压强、体积、温度和物质的量之间的关系由理想气体方程表达：
PV = nRT
P = pressure in Pa, V = volume in m³, n = amount in mol, R = 8.31 J mol⁻¹ K⁻¹ (gas constant), T = temperature in K (T/K = θ/°C + 273).
P 为压强（Pa），V 为体积（m³），n 为物质的量（mol），R = 8.31 J mol⁻¹ K⁻¹（气体常数），T 为热力学温度（T/K = θ/°C + 273）。
At room temperature and pressure (r.t.p.: 20 °C, 101 kPa), the molar volume Vm of an ideal gas is approximately 24 dm³ mol⁻¹ (24 000 cm³ mol⁻¹). At standard temperature and pressure (s.t.p.: 0 °C, 100 kPa), Vm ≈ 22.7 dm³ mol⁻¹.
在常温常压（r.t.p.：20 °C，101 kPa）下，理想气体的摩尔体积 Vm 约为 24 dm³ mol⁻¹（24000 cm³ mol⁻¹）。在标准状况（s.t.p.：0 °C，100 kPa）下，Vm ≈ 22.7 dm³ mol⁻¹。
- Total gas volume V = n × Vm (at a specified T and P)
- 气体总体积 V = n × Vm（在指定温度和压强下）
- Partial pressure of a gas A: pA = (nA/ntotal) × Ptotal
- 气体 A 的分压：pA = (nA/n总) × P总
3. Empirical and Molecular Formulas | 实验式与分子式
The empirical formula is the simplest whole‑number ratio of atoms in a compound. The molecular formula gives the actual number of atoms in one molecule.
实验式表示化合物中原子个数的最简整数比，分子式表示一个分子中实际的原子个数。
To find empirical formula from % by mass: (1) divide % by relative atomic mass Aᵣ to get mole ratio, (2) divide by smallest to get whole numbers.
由质量百分比求实验式：(1) 将各元素%除以相对原子质量 Aᵣ，得到摩尔比；(2) 除以最小值并化为整数比。
- Molecular formula = (empirical formula)n, where n = (relative molecular mass Mᵣ / empirical formula mass)
- 分子式 =（实验式）n，其中 n =（相对分子质量 Mᵣ / 实验式式量）
Combustion analysis data can be used to calculate mass of C, H and O in a compound, leading to the empirical formula.
通过燃烧分析数据可计算化合物中碳、氢、氧的质量，进而得出实验式。
4. Concentration and Solution Stoichiometry | 浓度与溶液计量
The concentration of a solution is the amount of solute dissolved per unit volume of solution.
溶液的浓度是指单位体积溶液中溶解的溶质的物质的量。
c = n / V
c = concentration (mol dm⁻³), n = amount (mol), V = volume of solution (dm³). Note: 1 dm³ = 1000 cm³.
c 为浓度（mol dm⁻³），n 为物质的量（mol），V 为溶液体积（dm³）。注意：1 dm³ = 1000 cm³。
- Mass concentration (g dm⁻³) = mass (g) / volume (dm³) or = c × M
- 质量浓度（g dm⁻³）= 质量（g）/ 体积（dm³）或 = c × M
- For dilution: c₁V₁ = c₂V₂
- 稀释公式：c₁V₁ = c₂V₂
In titration calculations, use the balanced equation to find the mole ratio between reactants, then convert moles to concentration or volume.
在滴定计算中，利用配平的化学方程式找出反应物的物质的量之比，再将摩尔数换算为浓度或体积。
5. Enthalpy Changes and Hess’s Law | 焓变与盖斯定律
Enthalpy change ΔH (kJ mol⁻¹) is the heat energy transferred under constant pressure. Standard conditions (⦵) refer to 100 kPa and a stated temperature, usually 298 K.
焓变 ΔH（kJ mol⁻¹）是在恒压下传递的热能。标准状态（⦵）指 100 kPa 和指定的温度，通常为 298 K。
ΔH = Hproducts – Hreactants
Measured using q = mcΔT, where q = heat energy (J), m = mass of water/solution (g), c = specific heat capacity (4.18 J g⁻¹ K⁻¹ for water) and ΔT = temperature change. Then ΔH = –q / n (exothermic if ΔH negative).
实验测定用 q = mcΔT，其中 q 为热量（J），m 为水或溶液的质量（g），c = 比热容（水为 4.18 J g⁻¹ K⁻¹），ΔT 为温度变化。然后 ΔH = –q / n（放热时 ΔH 为负值）。
Hess’s Law states that the total enthalpy change for a reaction is independent of the route taken. Use enthalpy cycles or summation of known ΔH values to find an unknown ΔH.
盖斯定律指出，一个反应的总焓变与所走路径无关。可使用焓循环或已知 ΔH 的代数和来求算未知的 ΔH。
- ΔH⦵reaction = ΣΔH⦵f (products) – ΣΔH⦵f (reactants)
- ΔH⦵反应 = ΣΔH⦵f (生成物) – ΣΔH⦵f (反应物)
- ΔH⦵combustion routes: ΔH⦵reaction = ΣΔH⦵c (reactants) – ΣΔH⦵c (products)
- 燃烧焓路径：ΔH⦵反应 = ΣΔH⦵c (反应物) – ΣΔH⦵c (生成物)
6. Bond Enthalpies | 键焓
Bond enthalpy is the energy required to break one mole of a specific covalent bond in the gaseous state, averaged over a range of compounds (mean bond enthalpy).
键焓是在气态中断裂 1 mol 特定共价键所需的能量，是在一系列化合物中得到的平均值（平均键焓）。
The enthalpy change of a reaction can be estimated using:
可依据下列关系估算反应的焓变：
ΔH ≈ Σ (bond enthalpies broken) – Σ (bond enthalpies formed)
Because bond breaking is endothermic (+) and bond making is exothermic (–). Note that values obtained from mean bond enthalpies are approximate and only apply to gaseous species.
因为断键是吸热的（+），成键是放热的（–）。注意：由平均键焓计算得到的值只是一个近似值，且仅适用于气态物质。
7. Chemical Equilibrium and the Equilibrium Constant Kc | 化学平衡与平衡常数 Kc
Many reactions are reversible. At dynamic equilibrium, the rates of the forward and backward reactions are equal and the concentrations of reactants and products remain constant.
许多反应是可逆的。在动态平衡时，正、逆反应速率相等，反应物和生成物的浓度保持恒定。
For a homogeneous reaction: aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration is:
对于均相反应 aA + bB ⇌ cC + dD，以浓度表示的平衡常数为：
Kc = [C]c[D]d / [A]a[B]b
The units of Kc depend on the stoichiometry and must be derived from the expression. Solids and pure liquids are omitted from the Kc expression.
Kc 的单位取决于化学计量数，必须从表达式中推导得出。固体和纯液体不写入 Kc 表达式。
- If Kc >> 1, products are favoured at equilibrium.
- 若 Kc >> 1，平衡以生成物为主。
- If Kc << 1, reactants are favoured.
- 若 Kc << 1，平衡以反应物为主。
- Kc only changes with temperature; catalysts do not alter Kc.
- Kc 只随温度变化；催化剂不改变 Kc。
8. Le Chatelier’s Principle | 勒夏特列原理
Le Chatelier’s Principle states that if a system at dynamic equilibrium is subjected to a change in concentration, pressure or temperature, the position of equilibrium will shift to oppose the change.
勒夏特列原理指出，处于动态平衡的体系受到浓度、压强或温度的变化时，平衡位置将发生移动，以削弱这种变化的影响。
- Increasing concentration of a reactant favours the forward reaction.
- 增加反应物的浓度有利于正反应。
- Increasing pressure favours the side with fewer gas molecules.
- 增大压强有利于气体分子数较少的一侧。
- Increasing temperature favours the endothermic direction (ΔH positive).
- 升高温度有利于吸热方向（ΔH 为正）。
- A catalyst increases the rate of both forward and backward reactions equally; it does not shift the equilibrium position but allows equilibrium to be reached faster.
- 催化剂同等程度地加快正、逆反应速率；它不改变平衡位置，但使平衡更快达到。
9. Reaction Kinetics – Rate Equations and Activation Energy | 反应动力学——速率方程与活化能
The rate of a chemical reaction measures how quickly a reactant is used up or a product is formed. It can be expressed as:
化学反应速率衡量反应物消耗或产物生成的快慢。可表示为：
rate = Δ[A] / Δt or rate = k [A]m[B]n
where k is the rate constant, and m and n are the orders of reaction with respect to A and B. The overall order is m + n. Orders are determined experimentally, not from the stoichiometric coefficients.
其中 k 为速率常数，m 和 n 分别为对 A 和 B 的反应级数，总级数为 m + n。级数必须通过实验测定，不能由化学计量数直接得出。
- Zero order (0) → rate independent of concentration.
- 零级反应（0）→ 速率与浓度无关。
- First order (1) → rate ∝ concentration¹.
- 一级反应（1）→ 速率 ∝ 浓度¹。
- Second order (2) → rate ∝ concentration².
- 二级反应（2）→ 速率 ∝ 浓度²。
The effect of temperature on rate is explained by the Boltzmann distribution and the Arrhenius concept: only particles with energy greater than the activation energy Ea can react. Raising temperature increases the proportion of particles with energy ≥ Ea, greatly increasing rate.
温度对速率的影响可通过玻尔兹曼分布和阿仑尼乌斯概念解释：只有能量大于活化能 Ea 的粒子才能反应。升高温度会增大能量 ≥ Ea 的粒子比例，从而显著加快速率。
A catalyst provides an alternative pathway with lower activation energy, increasing the rate without being consumed.
催化剂提供具有较低活化能的替代路径，在自身不被消耗的情况下加快反应速率。
10. Quick Reference Summary Table | 速查汇总表
The table below compiles the most frequently used formulas in AS Chemistry. Print it out or keep it handy during revision.
下表汇总了 AS 化学中最常用的公式，可供打印或复习时随身携带。
| Formula / Relationship | 公式 / 关系 | Notes |
|---|---|---|
| n = m/M | n = m/M | g ↔ mol using molar mass |
| N = nL | N = nL | L = 6.02×10²³ |
| PV = nRT | PV = nRT | P in Pa, V in m³, T in K |
| V = n × Vm | V = n × Vm | Vm ~ 24 dm³ at r.t.p. |
| pA = (nA/ntotal)Ptotal | pA = (nA/n总)P总 | Dalton’s law |
| c = n/V | c = n/V | V in dm³ for mol dm⁻³ |
| q = mcΔT | q = mcΔT | J, g, K |
| ΔH = –q / n | ΔH = –q / n | Exothermic negative |
| ΔH = ΣΔHf products – ΣΔHf reactants | ΔH = ΣΔHf 生成物 – ΣΔHf 反应物 | Using formation data |
| ΔH ≈ ΣB.E. broken – ΣB.E. formed | ΔH ≈ Σ断键键焓 – Σ成键键焓 | Gaseous species |
| Kc = [C]c[D]d / [A]a[B]b | Kc = [C]c[D]d / [A]a[B]b | Units vary |
| rate = k [A]m[B]n | 速率 = k [A]m[B]n | Orders from experiment |
Always check units, use brackets for concentrations in Kc expressions, and remember that solids and pure liquids do not appear in equilibrium constants.
请始终检查单位，在 Kc 表达式中使用方括号表示浓度，并记住固体和纯液体不写入平衡常数表达式。
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