📚 Year 13 CCEA Chemistry: Formula & Theorem Quick Reference Handbook | CCEA A2化学公式定理速查手册
This quick reference handbook compiles essential formulae, theorems, and constants for Year 13 CCEA Chemistry. It covers physical chemistry topics from thermodynamics to electrochemistry, serving as a streamlined revision aid for assessments and examinations.
本速查手册汇编了 Year 13 CCEA 化学的核心公式、定理与常数，涵盖从热力学到电化学的物理化学主题，可作为备考复习的高效工具。
1. Thermodynamics and Hess’s Law | 热力学与盖斯定律
Enthalpy change (ΔH) is the heat energy transferred under constant pressure. It is measured in kJ mol⁻¹.
焓变 (ΔH) 是恒压下传递的热能，单位为 kJ mol⁻¹。
Standard enthalpy of formation (ΔH°f) is the enthalpy change when one mole of a compound is formed from its elements under standard conditions.
标准生成焓 (ΔH°f) 是在标准条件下，由单质生成 1 mol 化合物时的焓变。
Standard enthalpy of combustion (ΔH°c) is the enthalpy change when one mole of a substance is completely burned in oxygen under standard conditions.
标准燃烧焓 (ΔH°c) 是在标准条件下，1 mol 物质在氧气中完全燃烧的焓变。
Hess’s Law states that the total enthalpy change for a reaction is independent of the pathway between initial and final states.
盖斯定律指出，反应总焓变仅与起始和终了状态有关，与反应途径无关。
ΔH°reaction = Σ ΔH°f(products) – Σ ΔH°f(reactants)
ΔH°reaction = Σ ΔH°f(生成物) – Σ ΔH°f(反应物)
Bond enthalpy calculations approximate ΔH by summing bonds broken minus bonds formed.
通过键焓估算 ΔH：ΔH ≈ 反应物断键总键焓 – 生成物成键总键焓。
2. Entropy and Gibbs Free Energy | 熵与吉布斯自由能
Entropy (S) is a measure of disorder or randomness of a system. Units: J K⁻¹ mol⁻¹.
熵 (S) 是系统混乱度的量度，单位为 J K⁻¹ mol⁻¹。
The standard entropy change is ΔS° = Σ S°(products) – Σ S°(reactants).
标准熵变 ΔS° = Σ S°(生成物) – Σ S°(反应物)。
Gibbs free energy change determines reaction feasibility at constant temperature.
吉布斯自由能变用于判断恒温下反应的自发方向。
ΔG° = ΔH° – TΔS°
- ΔG° < 0 → spontaneous / feasible
- ΔG° = 0 → equilibrium
- ΔG° > 0 → non-feasible
ΔG° = ΔH° – TΔS°
- ΔG° < 0 → 自发可行
- ΔG° = 0 → 平衡
- ΔG° > 0 → 不可行
Temperature T is in kelvin (K). Standard conditions: 298 K, 100 kPa.
温度 T 以开尔文 (K) 表示，标准条件为 298 K、100 kPa。
ΔG° relates to the equilibrium constant: ΔG° = –RT lnK.
ΔG° 与平衡常数的关系：ΔG° = –RT lnK。
3. Chemical Kinetics and Arrhenius Equation | 化学动力学与阿伦尼乌斯方程
Rate equation links reaction rate to reactant concentrations.
速率方程表示反应速率与反应物浓度的关系。
For a reaction aA + bB → products, rate = k[A]ᵐ[B]ⁿ, where m and n are orders with respect to A and B.
对反应 aA + bB → 产物，速率 = k[A]ᵐ[B]ⁿ，m 和 n 为对 A 和 B 的反应级数。
The overall order = m + n. The rate constant k is temperature-dependent.
总反应级数 = m + n。速率常数 k 依赖于温度。
The Arrhenius equation quantifies the temperature dependence of k.
阿伦尼乌斯方程定量描述 k 与温度 T 的关系。
k = A e⁻ᴱᵃ/ᴿᵀ
ln k = ln A – Ea/(RT)
A plot of ln k against 1/T gives a straight line: slope = –Ea/R, intercept = ln A.
以 ln k 对 1/T 作图得直线：斜率 = –Ea/R，截距 = ln A。
| Ea = activation energy (J mol⁻¹) | Ea = 活化能 (J mol⁻¹) |
| R = 8.314 J K⁻¹ mol⁻¹ | R = 8.314 J K⁻¹ mol⁻¹ |
| T = temperature in K | T = 温度 (K) |
| A = pre-exponential factor | A = 指前因子 |
4. Chemical Equilibrium: Kc and Kp | 化学平衡：Kc 与 Kp
The equilibrium constant Kc is expressed in terms of concentrations of species at equilibrium.
平衡常数 Kc 以平衡时各物种的浓度表示。
For aA + bB ⇌ cC + dD,
Kc = [C]ᶜ [D]ᵈ / ([A]ᵃ [B]ᵇ)
If gases are involved, Kp uses partial pressures: Kp = (p_C)ᶜ (p_D)ᵈ / ((p_A)ᵃ (p_B)ᵇ).
若涉及气体，Kp 以分压表示：Kp = (p_C)ᶜ (p_D)ᵈ / ((p_A)ᵃ (p_B)ᵇ)。
Relationship between Kp and Kc: Kp = Kc (RT)Δn, where Δn = moles of gaseous products – moles of gaseous reactants.
Kp 与 Kc 关系：Kp = Kc (RT)Δn，Δn = 气体生成物系数之和 – 气体反应物系数之和。
Le Chatelier’s principle predicts the direction of shift when conditions change.
勒夏特列原理用于预测条件改变时平衡移动的方向。
5. Acid-Base Equilibria: pH, Ka, Kb, Kw | 酸碱平衡：pH、Ka、Kb、Kw
pH = –log₁₀[H⁺], where [H⁺] is hydrogen ion concentration in mol dm⁻³.
pH = –log₁₀[H⁺]，[H⁺] 为氢离子浓度 (mol dm⁻³)。
pOH = –log₁₀[OH⁻].
Water autoionisation: Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K.
水自耦电离：Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ (298 K)。
For a weak acid HA: HA ⇌ H⁺ + A⁻, Ka = [H⁺][A⁻]/[HA].
弱酸 HA 的电离：HA ⇌ H⁺ + A⁻，Ka = [H⁺][A⁻]/[HA]。
pKa = –log₁₀ Ka. The smaller the pKa, the stronger the acid.
pKa = –log₁₀ Ka。pKa 越小，酸性越强。
For a weak base: Kb = [BH⁺][OH⁻]/[B]; pKb = –log₁₀ Kb.
弱碱：Kb = [BH⁺][OH⁻]/[B]；pKb = –log₁₀ Kb。
Relationship: Ka × Kb = Kw for a conjugate acid-base pair.
对于一个共轭酸碱对：Ka × Kb = Kw。
Approximations: for weak acids, if [HA] >> [H⁺], [H⁺] ≈ √(Ka × [HA]).
近似处理：弱酸在解离度很小时，[H⁺] ≈ √(Ka × [HA])。
6. Buffer Solutions and Henderson-Hasselbalch Equation | 缓冲溶液与亨德森-哈塞尔巴赫方程
A buffer solution resists changes in pH upon addition of small amounts of acid or base.
缓冲溶液能抵抗少量酸或碱引起的 pH 变化。
Acidic buffer: mixture of a weak acid and its salt (e.g., CH₃COOH / CH₃COO⁻).
酸性缓冲液：弱酸与其盐的混合溶液 (如 CH₃COOH / CH₃COO⁻)。
pH of a buffer is given by the Henderson-Hasselbalch equation.
缓冲液的 pH 可通过亨德森-哈塞尔巴赫方程计算。
pH = pKa + log₁₀([A⁻]/[HA])
pH = pKa + log₁₀([共轭碱]/[弱酸])
For a basic buffer (weak base and its salt): pOH = pKb + log₁₀([BH⁺]/[B]).
碱性缓冲液 (弱碱与其盐)：pOH = pKb + log₁₀([共轭酸]/[弱碱])。
Buffer capacity is greatest when [HA] ≈ [A⁻] (i.e., pH ≈ pKa).
当 [HA] ≈ [A⁻] 时 (即 pH ≈ pKa)，缓冲容量最大。
7. Redox and Electrode Potentials | 氧化还原与电极电势
Oxidation is loss of electrons; reduction is gain of electrons (OIL RIG).
氧化是失去电子；还原是得到电子 (OIL RIG)。
Standard electrode potential (E°) is measured under standard conditions (298 K, 100 kPa, 1.0 mol dm⁻³ ion concentration) against the standard hydrogen electrode (SHE).
标准电极电势 (E°) 在标准条件下 (298 K, 100 kPa, 1.0 mol dm⁻³ 离子浓度) 相对于标准氢电极 (SHE) 测定。
A more positive E° indicates a greater tendency to gain electrons (stronger oxidising agent).
E° 正值越大，越易得电子 (氧化剂越强)。
Cell emf (E°cell) is calculated as:
E°cell = E°(right electrode) – E°(left electrode)
E°cell = E°(正极) – E°(负极)
A positive E°cell means the reaction is thermodynamically feasible.
E°cell 大于零表示反应在热力学上可行。
Gibbs free energy and cell potential are linked:
ΔG° = –nFE°cell
n = number of electrons transferred; F = Faraday constant 96 500 C mol⁻¹.
n = 转移电子数；F = 法拉第常数 96 500 C mol⁻¹。
8. Nernst Equation and Cell EMF under Non-Standard Conditions | 能斯特方程与非标准条件下的电池电动势
The Nernst equation corrects cell potential for non-standard concentrations or pressures.
能斯特方程用于将电池电势修正至非标准浓度或压力条件。
For an electrode reaction: aOx + ne⁻ ⇌ bRed,
E = E° – (RT/nF) lnQ
At 298 K, using base-10 logarithms:
E = E° – (0.0592/n) log₁₀Q
Q = [Red]ᵇ/[Ox]ᵃ (or pressure ratio for gases).
Q = [还原型]ᵇ/[氧化型]ᵃ (气体用分压比)。
For a complete cell: Ecell = Ecathode – Eanode, each half-cell potential corrected with Nernst.
全电池：Ecell = E阴极 – E阳极，每个半电池电势均用能斯特方程校正。
9. Faraday’s Laws of Electrolysis | 法拉第电解定律
Faraday’s first law: the mass of a substance produced at an electrode is directly proportional to the quantity of electricity passed.
法拉第第一定律：电极上析出物质的质量与通过的电量成正比。
m = (Q × M) / (n × F)
m = (Q × M) / (n × F)
Q = charge (coulombs, C) = current (A) × time (s); m = mass (g); M = molar mass (g mol⁻¹); n = number of electrons in the half-equation.
Q = 电量 (库仑, C) = 电流 (A) × 时间 (s)；m = 质量 (g)；M = 摩尔质量 (g mol⁻¹)；n = 半反应中电子数。
Faraday constant F = 96 500 C mol⁻¹. It is the charge on one mole of electrons.
法拉第常数 F = 96 500 C mol⁻¹，是 1 mol 电子的电量。
To calculate the volume of gas evolved at an electrode, use the molar gas volume (24.0 dm³ mol⁻¹ at r.t.p.) and the stoichiometry.
计算电极上析出气体的体积时，要结合气体摩尔体积 (室温常压 24.0 dm³ mol⁻¹) 和化学计量数。
10. Key Constants and Unit Conversions | 重要常数与单位换算
| Gas constant R | 8.314 J K⁻¹ mol⁻¹ |
| Faraday constant F | 96 500 C mol⁻¹ |
| Avogadro constant Nₐ | 6.022 × 10²³ mol⁻¹ |
| Ionic product of water Kw | 1.0 × 10⁻¹⁴ mol² dm⁻⁶ (298 K) |
| Molar volume of gas at r.t.p. | 24.0 dm³ mol⁻¹ (298 K, 100 kPa) |
| 1 dm³ | 1000 cm³ |
| 0 °C | 273 K |
When using the ideal gas equation pV = nRT, ensure units are consistent: p in Pa, V in m³, T in K. 100 kPa = 1.0 × 10⁵ Pa; 1 m³ = 1000 dm³.
使用理想气体状态方程 pV = nRT 时，确保单位一致：p 用 Pa，V 用 m³，T 用 K。100 kPa = 1.0 × 10⁵ Pa；1 m³ = 1000 dm³。
When using the Arrhenius equation, Ea must be in J mol⁻¹ to match R in J K⁻¹ mol⁻¹.
使用阿伦尼乌斯方程时，Ea 必须以 J mol⁻¹ 为单位，才能与 R (J K⁻¹ mol⁻¹) 匹配。
Remember to convert kJ to J for R-containing calculations (1 kJ = 1000 J).
涉及 R 的计算时，切记将 kJ 转换为 J (1 kJ = 1000 J)。
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