📚 Year 13 WJEC Chemistry: Formula and Theorems Quick Reference Handbook | Year 13 WJEC 化学：公式定理速查手册
This quick reference handbook collects the essential formulas, theorems and constants you will need for Year 13 WJEC Chemistry. Each entry is presented with key definitions and paired Chinese explanations, organised for fast revision before your A2 examinations.
本速查手册收集了 Year 13 WJEC 化学所需的核心公式、定理与常数。每一条目均配有关键定义与中文解释，按专题编排，便于 A2 考试前快速复习。
1. The Ideal Gas Equation | 理想气体方程
PV = nRT is the fundamental relationship linking pressure (P), volume (V), amount in moles (n) and absolute temperature (T) for an ideal gas. R is the molar gas constant.
PV = nRT 是联系理想气体压力 (P)、体积 (V)、物质的量 (n) 和热力学温度 (T) 的基本关系式。R 为摩尔气体常数。
atm mol⁻¹ K⁻¹ when using atm and dm³. Always convert temperature to kelvin (K = °C + 273).
R 的取值取决于单位：当压力用 Pa、体积用 m³ 时 R = 8.31 J mol⁻¹ K⁻¹；若用 atm 和 dm³，则 R = 0.0821 dm³ atm mol⁻¹ K⁻¹。计算时务必使温度单位为开尔文 (K = °C + 273)。
2. Enthalpy Changes & Hess’s Law | 焓变与盖斯定律
ΔH = ΣΔHf°(products) − ΣΔHf°(reactants) is used to calculate the standard enthalpy change of a reaction from standard enthalpies of formation.
ΔH = ΣΔHf°(生成物) − ΣΔHf°(反应物) 用于由标准生成焓计算反应的标准焓变。
Hess’s Law states that the total enthalpy change for a reaction is independent of the route taken, allowing the use of enthalpy cycles for indirect determination.
盖斯定律指出，一个反应的总焓变与反应途径无关，这使得我们可以利用焓变循环间接测定难以直接测量的焓变。
Common enthalpy changes to remember: ΔHc° (combustion), ΔHneut° (neutralisation), ΔHsol° (solution), ΔHhyd° (hydration), and ΔHatom° (atomisation).
常见的焓变术语：ΔHc° (燃烧焓)、ΔHneut° (中和焓)、ΔHsol° (溶解焓)、ΔHhyd° (水合焓) 和 ΔHatom° (原子化焓)。
3. Entropy and Gibbs Free Energy | 熵与吉布斯自由能
The total entropy change of the universe is ΔStotal = ΔSsystem + ΔS_surroundings, where ΔS_surroundings = −ΔH/T.
宇宙的总熵变为 ΔStotal = ΔSsystem + ΔS_surroundings，其中 ΔS_surroundings = −ΔH/T。
The Gibbs free energy change is ΔG = ΔH − TΔS. A reaction is thermodynamically feasible when ΔG < 0.
吉布斯自由能变定义为 ΔG = ΔH − TΔS。当 ΔG < 0 时，反应在热力学上可行。
Under standard conditions, the relationship between ΔG° and the equilibrium constant K is ΔG° = −RT ln K. This links thermodynamics directly to the position of equilibrium.
在标准条件下，ΔG° 与平衡常数 K 的关系为 ΔG° = −RT ln K。该式将热力学与平衡位置直接联系起来。
4. Chemical Equilibrium | 化学平衡
For a reaction aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration is Kc = [C]c [D]d / ([A]a [B]b). Square brackets denote equilibrium concentrations in mol dm⁻³.
对于反应 aA + bB ⇌ cC + dD，以浓度表示的平衡常数为 Kc = [C]c [D]d / ([A]a [B]b)，方括号表示平衡浓度 (mol dm⁻³)。
For gases, Kp uses partial pressures: Kp = (pC)c (pD)d / ((pA)a (pB)b). The relation between Kp and Kc is Kp = Kc (RT)^Δn, where Δn = (c+d) − (a+b) for gases only.
对于气体反应，Kp 使用分压：Kp = (pC)c (pD)d / ((pA)a (pB)b)。Kp 与 Kc 的换算关系为 Kp = Kc (RT)^Δn，其中 Δn 仅针对气体组分：Δn = (c+d) − (a+b)。
Le Chatelier’s principle predicts the qualitative shift, but the magnitude of K shows the actual position of equilibrium. K is affected only by temperature.
勒夏特列原理定性预测平衡移动的方向，而 K 值大小则显示平衡的实际位置。K 只受温度影响。
5. Acid-Base Equilibria | 酸碱平衡
The acid dissociation constant Ka = [H⁺][A⁻] / [HA]; pKa = −log₁₀(Ka). A larger Ka (smaller pKa) indicates a stronger acid.
酸的解离常数 Ka = [H⁺][A⁻] / [HA]；pKa = −log₁₀(Ka)。Ka 值越大 (pKa 越小)，酸性越强。
The ionic product of water Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K. Therefore, pH + pOH = 14.00 at this temperature.
水的离子积 Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ (298 K)。因此在该温度下，pH + pOH = 14.00。
pH = −log₁₀[H⁺] and [H⁺] = 10⁻ᵖᴴ. For a strong monoprotic acid, [H⁺] = cacid; for a strong base, [OH⁻] = cbase, then convert to pH.
pH = −log₁₀[H⁺]，[H⁺] = 10⁻ᵖᴴ。对于强一元酸，[H⁺] = cacid；对于强碱，[OH⁻] = cbase，再换算为 pH。
6. Buffer Solutions | 缓冲溶液
A buffer is a mixture of a weak acid (HA) and its conjugate base (A⁻). The Henderson-Hasselbalch equation for buffer pH is pH = pKa + log₁₀([A⁻] / [HA]). This is derived from the Ka expression.
缓冲溶液由弱酸 (HA) 及其共轭碱 (A⁻) 混合而成。缓冲溶液 pH 的 Henderson-Hasselbalch 方程为 pH = pKa + log₁₀([A⁻] / [HA])，由 Ka 表达式推导而来。
a buffer does not change its pH significantly because the ratio [A⁻]/[HA] stays constant.
配制缓冲溶液时，最有效的 pH 范围是 pKa ± 1。稀释缓冲溶液不会显著改变其 pH，因为 [A⁻]/[HA] 的比值保持不变。
| Buffer type | Example | pH calculation |
|---|---|---|
| Acidic | CH₃COOH / CH₃COONa | pH = pKa + log₁₀([CH₃COO⁻]/[CH₃COOH]) |
| Basic | NH₃ / NH₄Cl | pOH = pKb + log₁₀([NH₄⁺]/[NH₃]), then pH = 14 − pOH |
缓冲类型 | 实例 | pH 计算: 酸性缓冲 (乙酸/乙酸钠)；碱性缓冲 (氨/氯化铵)。
7. Electrochemistry & Nernst Equation | 电化学与能斯特方程
The cell potential under standard conditions is E°_cell = E°_cathode − E°_anode. For non-standard conditions, use the Nernst equation:
标准条件下的电池电动势为 E°_cell = E°_cathode − E°_anode。对于非标准条件，使用 能斯特方程：
E = E° − (RT / nF) ln Q
ent; n is the number of electrons transferred; F = 96,500 C mol⁻¹ is the Faraday constant.
Q 为反应商；n 为转移电子数；F = 96,500 C mol⁻¹ 是法拉第常数。
At 298 K, the equation simplifies to E = E° − (0.0592 / n) log₁₀ Q (in volts). The link to free energy is ΔG° = −nFE°_cell and at equilibrium ln K = nFE°_cell / (RT).
在 298 K 时，方程简化为 E = E° − (0.0592 / n) log₁₀ Q (单位 V)。与自由能的关系：ΔG° = −nFE°_cell，平衡时 ln K = nFE°_cell / (RT)。
8. Kinetics: Rate Laws and Arrhenius | 动力学：速率方程与阿伦尼乌斯
The rate equation for a reaction with respect to reactants A and B is Rate = k [A]m [B]n, where m and n are orders of reaction determined experimentally (not from stoichiometry).
反应的速率方程可表示为 Rate = k [A]m [B]n，其中 m 与 n 为反应级数，由实验确定（而非化学计量系数）。
The temperature dependence of the rate constant is given by the Arrhenius equation: k = A exp(−Ea / (RT)) or in logarithmic form ln k = ln A − Ea / (RT).
速率常数与温度的关系由 阿伦尼乌斯方程给出：k = A exp(−Ea / (RT))，其对数形式为 ln k = ln A − Ea / (RT)。
aight line with slope = −Ea/R. Activation energy Ea is given in J mol⁻¹ (convert from kJ).
以 ln k 对 1/T 作图得一直线，斜率 = −Ea/R。活化能 Ea 的单位为 J mol⁻¹ (注意由 kJ 换算)。
For a first-order reaction, half-life is independent of initial concentration: t½ = ln 2 / k ≈ 0.693 / k.
对于一级反应，半衰期与初始浓度无关：t½ = ln 2 / k ≈ 0.693 / k。
9. Born-Haber Cycles & Lattice Energy | 波恩-哈伯循环与晶格能
The Born-Haber cycle applies Hess’s law to ionic solids, linking enthalpy of formation
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