📚 Year 12 WJEC Chemistry: Formula & Theorem Quick Reference Handbook | Year 12 WJEC 化学：公式定理速查手册
This handbook gathers the essential formulas, relationships, and key constants you will use throughout Year 12 WJEC Chemistry. It is designed as a quick-lookup tool to support problem-solving in physical, inorganic, and organic topics. Each entry is paired with concise bilingual explanations so you can switch effortlessly between English and Chinese terminology.
本手册汇总了 Year 12 WJEC 化学课程中必须掌握的核心公式、定量关系和重要常数，可作为快速查阅工具，帮助你在物理化学、无机化学和有机化学题目中快速调用。每条内容均配有中英双语简明解释，便于你在英文术语和中文思维之间自如切换。
1. Amount of Substance & Mole Calculations | 物质的量与摩尔计算
ntifying matter. One mole contains exactly 6.02214076 × 10²³ elementary entities (Avogadro's constant, Nₐ).
摩尔是物质量的中心单位。1 摩尔恰好包含 6.02214076 × 10²³ 个基本单元（阿伏伽德罗常数，Nₐ）。
Key equations:
关键公式：
n = m / M (amount = mass / molar mass)
n = m / M（物质的量 = 质量 / 摩尔质量）
n = V(gas) / Vₘ (at RTP, Vₘ = 24.0 dm³ mol⁻¹ or 24 000 cm³ mol⁻¹)
n = V(气体) / Vₘ（在常温常压下，Vₘ = 24.0 dm³ mol⁻¹ 或 24 000 cm³ mol⁻¹）
n = c × V(solution) (c in mol dm⁻³, V in dm³)
n = c × V(溶液)（c 单位为 mol dm⁻³，V 单位为 dm³）
Number of particles = n × Nₐ
粒子数 = n × Nₐ
Always convert volumes to dm³ when using concentration in mol dm⁻³, and ensure mass is in grams.
使用浓度 mol dm⁻³ 时务必先将体积换算为 dm³，并确保质量以克为单位。
2. Empirical & Molecular Formulae | 经验式与分子式
The empirical formula gives the simplest whole-number ratio of atoms of each element in a compound. The molecular formula is a multiple of the empirical formula.
经验式表示化合物中各元素原子的最简整数比。分子式是经验式的整数倍。
To find empirical formula: convert % es, and adjust to whole numbers. Then molecular formula mass = n × empirical formula mass.
求经验式的步骤：将质量分数或质量换算为物质的量，除以最小的物质的量，调整为整数比。分子式量 = n × 经验式量。
3. Ideal Gas Equation | 理想气体状态方程
The ideal gas equation links pressure, volume, amount, and temperature: pV = nRT
理想气体状态方程关联压强、体积、物质的量和温度：pV = nRT
| Symbol | Meaning | Units (common) |
| p | Pressure | Pa (or kPa, atm; must match R) |
| V | Volume | m³ |
| n | Amount of gas | mol |
| R | Gas constant | 8.31 J mol⁻¹ K⁻¹ (when p in Pa, V in m³) |
| T | Temperature | K (Kelvin: °C + 273) |
can be adjusted, but the safest pathway is to convert everything to SI units (Pa, m³, K).
若使用 kPa 和 dm³，R 需相应调整。最可靠的方法是统一转换为 SI 单位：Pa、m³、K。
4. Enthalpy Changes & Hess's Law | 焓变与盖斯定律
Enthalpy change (ΔH) is the heat transferred at constant pressure. Standard enthalpy changes refer to 100 kPa and a stated temperature (usually 298 K).
焓变（ΔH）是恒压条件下传递的热量。标准焓变指 100 kPa 和指定温度（通常 298 K）下的数值。
Key definitions to memorise:
必须熟记的定义：
Standard enthalpy of formation ΔH°f: enthalpy change when one mole of a compound is formed from its elements under standard conditions.
标准生成焓 ΔH°f：在标准条件下，从元素生成 1 mol 化合物时的焓变。
Standard enthalpy of combustion ΔH°c: enthalpy change when one mole of a substance is completely burned in oxygen under standard conditions.
标准燃烧焓 ΔH°c：在标准条件下，1 mol 物质在氧气中完全燃烧时的焓变。
Standard enthalpy of neutralisation: enthalpy change when one mole of water is formed from the reaction of an acid and an alkali under standard conditions (approx. -57 kJ mol⁻¹ for strong acid–strong base).
标准中和焓：在标准条件下，酸与碱反应生成 1 mol 水时的焓变（强酸强碱约为 -57 kJ mol⁻¹）。
Hess's Law: The total enthalpy change for a reaction is independent of the route taken.
盖斯定律：反应的总焓变与反应途径无关。
Equation using enthalpies of formation:
利用生成焓的计算公式：
ΔH° = Σ ΔH°f (products) − Σ ΔH°f (reactants)
ΔH° = Σ ΔH°f（产物）− Σ ΔH°f（反应物）
Equation using enthalpies of combustion:
利用燃烧焓的计算公式：
ΔH° = Σ ΔH°c (reactants) − Σ ΔH°c (products)
ΔH° = Σ ΔH°c（反应物）− Σ ΔH°c（产物）
5. Bond Enthalpies & Mean Bond Enthalpies | 键焓与平均键焓
Bond breaking is endothermic (ΔH positive); bond making is exothermic (ΔH negative).
化学键断裂吸热（ΔH > 0）；化学键形成放热（ΔH < 0）。
ΔH ≈ Σ (bonds broken) − Σ (bonds formed)
ΔH ≈ Σ（断裂键的键焓）− Σ（形成键的键焓）
Mean bond enthalpies are average values taken over a range of compounds, so calculated ΔH values are approximate and may differ from experimental values.
平均键焓是对不同化合物中同类键取平均值，因此计算所得的 ΔH 仅为近似值，可能与实验值有差异。
6. Calorimetry & Heat Calculations | 量热法与热量计算
he heat transferred in a solution or combustion experiment is calculated using: q = m c ΔT
在溶液或燃烧实验中传递的热量用下式计算：q = m c ΔT
| Symbol | Meaning | Typical units |
| q | Heat transferred | J |
| m | Mass of the substance heated (often solution) | g |
| c | Specific heat capacity (for water, 4.18 J g⁻¹ °C⁻¹) | J g⁻¹ °C⁻¹ |
| ΔT | Temperature change | °C or K (the interval is the same) |
H = −q / n (negative sign because exothermic reaction gives out heat to the surroundings).
计算每摩尔焓变：ΔH = −q / n（负号表示放热反应将热量传给环境）。
7. Rate of Reaction & Rate Equations | 反应速率与速率方程
ant or product per unit time. For a reaction aA + bB → products, the rate equation may be:
速率定义为反应物或产物浓度随时间的变化率。对于反应 aA + bB → 产物，速率方程可能为：
rate = k [A]ᵐ [B]ⁿ
nstant k is determined experimentally. Orders are not necessarily equal to stoichiometric coefficients a and b.
m 和 n 分别是反应对 A 和 B 的分级数；总级数 = m + n。速率常数 k 由实验测定。分级数不一定等于化学计量系数 a 和 b。
Graphical determination of rate: draw tangents to concentration–time curves. The gradient of a tangent gives the instantaneous rate.
图解法求速率：在浓度-时间曲线上作切线，切线斜率即瞬时速率。
8. Equilibrium Constant Kc | 平衡常数 Kc
For a homogeneous system in equilibrium: aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration is:
对于均相平衡体系：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 expression uses equilibrium concentrations (mol dm⁻³). Kc is temperature-dependent; its value changes with temperature but not with concentration or pressure.
表达式中使用平衡浓度（mol dm⁻³）。Kc 与温度有关，温度改变会引起 Kc 值变化，但浓度或压强变化不会改变 Kc。
If Kc >> 1, equilibrium lies to the right (products favoured); if Kc << 1, equilibrium lies to the left.
若 Kc >> 1，平衡偏向右侧（产物为主）；若 Kc << 1，平衡偏向左侧。
9. Acid-Base Equilibria: pH, Ka & Kw | 酸碱平衡：pH、Ka 与 Kw
pH is defined as: pH = −log₁₀ [H⁺]
pH 定义为：pH = −log₁₀ [H⁺]
The ionic product of water, Kw: Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K.
水的离子积 Kw：Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶（298 K 时）。
For a weak acid HA: HA ⇌ H⁺ + A⁻, the acid dissociation constant is:
对于弱酸 HA：HA ⇌ H⁺ + A⁻，酸解离常数 Ka 为：
Ka = [H⁺][A⁻] / [HA]
The higher the Ka, the stronger the weak acid. To approximate [H⁺] for a weak acid: [H⁺] ≈ √Ka × [HA]₀, valid when acid is weak and ionisation less than 5%.
pKa = −log₁₀ Ka。Ka 越大，弱酸越强。弱酸中 [H⁺] 的近似计算公式：[H⁺] ≈ √Ka × [HA]₀，适用于电离度小于 5% 的弱酸。
Buffer solutions: pH of an acidic buffer can be estimated using the Henderson–Hasselbalch equation:
缓冲溶液：酸性缓冲溶液的 pH 可用 Henderson–Hasselbalch 方程估算：
pH = pKa + log₁₀ ([conjugate base] / [acid])
pH = pKa + log₁₀ ([共轭碱] / [酸])
10. Oxidation Numbers & Redox | 氧化数与氧化还原
0; H usually +1; O usually −2; sum of oxidation numbers equals overall charge of species.
氧化数是电子转移的记账工具。基本规则：单质为零；H 通常为 +1；O 通常为 −2；总氧化数之和等于物种所带电荷。
Half-equations: Write the species as it exists, balance atoms (except O and H), then add H₂O to balance O, H⁺ to balance H, and electrons to balance charge. In alkaline solution, add OH⁻ to remove H⁺.
半反应式书写：先写出实际存在的物种形式，配平非 O、H 原子；然后加 H₂O 配平 O，加 H⁺ 配平 H；最后加电子配平电荷。在碱性溶液中，可加 OH⁻ 消除 H⁺。
Combining half-equations ensures electrons cancel exactly, giving the overall redox equation.
合并半反应时要使电子恰好抵消，得到总氧化还原方程式。
11. Key Mathematical Skills & Units | 核心数学技能与单位
or small numbers. Be comfortable rearranging equations: pV = nRT, ΔG = ΔH − TΔS, and mole–mass–volume conversions.
计算时务必写明单位并进行系统约分。极大或极小的数值使用科学记数法。需要熟练掌握方程的移项和重组：pV = nRT、ΔG = ΔH − TΔS 以及摩尔-质量-体积的转换。
Significant figures: Use the least number of significant figures from the data given in the question. For pH, the number of decimal places equals the significant figures in [H⁺].
有效数字：按题目所给数据中最少的有效数字位数保留结果。pH 的小数位数应与 [H⁺] 的有效数字位数一致。
Percentage error = (|experimental − true| / true) × 100%. Percentage uncertainty = (uncertainty / measurement) × 100%.
百分误差 = (|实验值 − 真值| / 真值) × 100%。百分不确定度 = (不确定度 / 测量值) × 100%。
12. Thermochemical Cycles & Born–Haber | 热化学循环与玻恩–哈伯循环
Born–Haber cycles use Hess's Law to calculate lattice enthalpy. Key steps: atomisation of elements, ionisation energies (for cations), electron affinities (for anions), and the lattice formation enthalpy.
玻恩–哈伯循环利用盖斯定律计算晶格焓。关键步骤包括：元素的原子化、电离能（生成阳离子）、电子亲合能（生成阴离子）以及晶格形成焓。
The enthalpy of lattice formation is the enthalpy change when one mole of an ionic solid is formed from its gaseous ions. It is always exothermic (negative).
晶格形成焓是指从气态离子生成 1 mol 离子固体时的焓变，总是放热（负值）。
The equation linking lattice enthalpy to the other terms can be summarised as:
晶格焓与其他项的关系可概括为：
ΔH°f(salt) = Σ ΔH°(atomisation) + Σ IE + Σ ΔH°(electron affinity) + ΔH°(lattice)
盐的 ΔH°f = Σ 原子化焓 + Σ 电离能 + Σ 电子亲合能 + 晶格形成焓
Remember to account for the appropriate number of moles of each species and the sign conventions (exothermic steps negative).
注意各物种的物质的量要匹配，并牢记放热步骤为负值的符号约定。
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