📚 Year 13 WJEC Chemistry: Formula & Theorem Quick Reference Handbook | Year 13 WJEC 化学：公式定理速查手册
This quick-reference handbook summarises the key formulas, equations, and theorems required for the WJEC Year 13 Chemistry specification. It covers physical, inorganic, and organic chemistry topics, providing a concise revision aid for calculations and conceptual understanding. Each entry is presented with clear notation and brief explanations to support learners in mastering quantitative aspects of the curriculum. The content maps onto Unit 3 (Physical and Inorganic Chemistry), Unit 4 (Organic Chemistry and Analysis) and the practical skills assessed across Unit 5, so it can be used both for lesson support and for final examination revision.
本速查手册概括了 WJEC Year 13 化学大纲所要求的核心公式、方程式和定理。内容涵盖物理化学、无机化学和有机化学，为计算和概念理解提供简洁的复习辅助。每个条目均以清晰的符号和简要说明呈现，帮助学习者掌握课程中的定量内容。内容对应 Unit 3（物理与无机化学）、Unit 4（有机化学与分析）以及 Unit 5 所考查的实验技能，既可用于课堂辅助，也可用于考前总复习。
1. Gas Laws and the Ideal Gas Equation | 气体定律与理想气体方程
be in pascals (Pa), volume in cubic metres (m³) and temperature in kelvin (K), with the gas constant R = 8.31 J K⁻¹ mol⁻¹. Two conversion traps catch many candidates: dm³ to m³ is a division by 1000, and °C to K is an addition of 273.
理想气体方程用一个表达式把压强、体积、温度与物质的量联系起来。在 WJEC 计算中，压强必须用帕斯卡（Pa），体积用立方米（m³），温度用开尔文（K），气体常数 R = 8.31 J K⁻¹ mol⁻¹。两个单位换算陷阱最容易失分：dm³ 换算为 m³ 要除以 1000，℃ 换算为 K 要加 273。
pV = nRT
roximately 24 dm³ mol⁻¹, giving the shortcut V = n × 24 dm³. This shortcut is only valid at RTP and must not be mixed with the full ideal gas equation in the same calculation.
标准条件定义为 298 K 与 100 kPa。在室温常压（RTP，取 20 ℃ 与 1 atm）下，任何气体的摩尔体积约为 24 dm³ mol⁻¹，由此得到简式 V = n × 24 dm³。该简式仅在 RTP 下成立，不可在同一次计算中与完整理想气体方程混用。
The combined gas law allows a fixed mass of gas to be followed through a change of state, and Dalton's law extends the treatment to mixtures. Partial pressures are needed later for Kp calculations, so the mole fraction relationship should be learned together with the gas laws.
联合气体定律可追踪一定质量气体在状态变化中的行为，道尔顿分压定律则把处理扩展到混合气体。分压在后面的 Kp 计算中会用到，因此摩尔分数关系应与气体定律一并记忆。
p₁V₁ / T₁ = p₂V₂ / T₂ pₐ = xₐ × ptotal xₐ = nₐ / ntotal
2. Mole Calculations, Concentration and Volumetric Analysis | 摩尔计算、浓度与滴定分析
Every quantitative question in WJEC Chemistry ultimately rests on the mole. The mass-mole relationship uses molar mass M in g mol⁻¹, while solution concentration uses amount per cubic decimetre. When a titration is used to find an unknown concentration, the reliable route is always: moles of known substance, then mole ratio from the balanced equation, then moles and concentration of the unknown.
WJEC 化学中的每一道定量题最终都落在"摩尔"上。质量与摩尔的换算使用摩尔质量 M（g mol⁻¹），溶液浓度则用每立方分米中的物质的量表示。用滴定求未知浓度时，可靠路径永远是：先求已知物的物质的量，再按配平方程式的计量比换算，最后求未知物的物质的量与浓度。
n = m / M n = c × V n = V / 24 (gas at RTP)
For dilution, the total number of moles is conserved, which gives the dilution equation used to prepare standard solutions from a stock bottle. For back titrations, the excess reagent is determined first and subtracted from the initial amount, which is the standard method when a reaction is slow or incomplete.
稀释时溶质的物质的量守恒，由此得到用浓溶液配制标准溶液的稀释方程。返滴定则先测定过量试剂的量，再从初始量中扣除，这是反应较慢或进行不完全时的标准方法。
c₁V₁ = c₂V₂ nexcess = n_initial − n_reacted
Percentage yield and atom economy are frequently examined together because they measure different things: yield measures how much of the expected product was actually obtained, whereas atom economy measures how much of the reactant mass ends up in the desired product by design.
产率与原子经济性常被放在一起考查，因为它们衡量的是不同的事情：产率衡量实际得到的产物占理论产物的比例，而原子经济性衡量反应物质量中有多少在设计上进入目标产物。
% moles) × 100 atom economy = (M of desired product / ΣM of all products) × 100
3. Enthalpy Changes, Hess's Law and Bond Enthalpies | 焓变、盖斯定律与键焓
Calorimetry in WJEC practical work relies on the assumption that the heat released or absorbed by the reaction is transferred entirely to the surrounding water. The heat energy is calculated from the mass of water, its specific heat capacity (4.18 J g⁻¹ K⁻¹), and the temperature change. Dividing by the number of moles converts the heat energy into a molar enthalpy change.
WJEC 实验中的量热法基于一个假设：反应放出或吸收的热量全部传递给周围的水。热能用水的质量、比热容（4.18 J g⁻¹ K⁻¹）与温度变化计算，再除以物质的量即得摩尔焓变。
q = m c ΔT ΔH = −q / n
The negative sign appears because an exothermic reaction raises the water temperature: the surroundings gain energy, so the system loses it. A common error is forgetting the sign, which reverses the meaning of the answer even when the arithmetic is correct.
负号出现的原因是：放热反应使水温升高，即环境获得能量，因此体系失去能量。常见错误是漏掉符号，即使算术正确，答案的含义也会被颠倒。
Hess's law states that the enthalpy change of a reaction is independent of the route taken, provided initial and final conditions are identical. This theorem allows an unknown enthalpy change to be constructed from standard enthalpy changes of formation or of combustion, or from an enthalpy cycle.
盖斯定律指出，只要始态与终态相同，反应的焓变与路径无关。该定理使我们能用标准生成焓、标准燃烧焓或焓循环来构造未知焓变。
ΔH = ΣΔHf(products) − ΣΔHf(reactants) ΔH = ΣΔHc(reactants) − ΣΔHc(products)
Bond enthalpy calculations use the principle that breaking bonds absorbs energy and forming bonds releases it. Because mean bond enthalpies are averages over many compounds, the value obtained is an estimate rather than an exact value, and this limitation is often worth one mark in an extended answer.
键焓计算依据的原则是：断键吸热，成键放热。由于平均键焓是许多化合物的平均值，所得结果只是估算值而非精确值，这一局限性在长答题中常可得分。
ΔH = Σ(bonds broken) − Σ(bonds formed)
4. Entropy, Gibbs Free Energy and Reaction Feasibility | 熵、吉布斯自由能与反应自发性
Entropy is a measure of the dispersal of energy among the available states, so gases have far higher entropy than liquids or solids, and a reaction that increases the number of gaseous moles usually has a positive entropy change. The total entropy change decides whether a reaction is feasible.
熵是能量在可用状态之间分散程度的量度，因此气体的熵远高于液体或固体；凡是使气态物质的量增加的反应，熵变通常为正值。总熵变决定反应是否自发可行。
ΔStotal = ΔSsystem + ΔS_surroundings ΔS_surroundings = −ΔH / T
Gibbs free energy combines the enthalpy and entropy terms into a single criterion. A reaction is thermodynamically feasible when the free energy change is zero or negative; if ΔG is positive, the reaction is not feasible under those conditions, although it may still occur very slowly because feasibility says nothing about rate.
吉布斯自由能把焓与熵两项合并为单一判据。当自由能变为零或负值时，反应在热力学上可行；若 ΔG 为正值，则该条件下反应不可行。不过反应仍可能进行得很慢，因为可行性并不涉及速率。
ΔG = ΔH − TΔS feasible when ΔG ≤ 0
The temperature at which a reaction changes from feasible to non-feasible is found by setting ΔG equal to zero. Four standard cases follow from the signs of ΔH and ΔS: exothermic with positive entropy change is always feasible; endothermic with negative entropy change is never feasible; the two mixed cases become feasible only above or only below a particular temperature.
把 ΔG 设为零即可求出反应由可行转为不可行的温度。由 ΔH 与 ΔS 的符号可得四种标准情形：放热且熵增者始终可行；吸热且熵减者始终不可行；两种混合情形则只在某一温度以上或以下才可行。
T = ΔH / ΔS (at the boundary, ΔG = 0)
5. Chemical Equilibrium: Kc, Kp and Le Chatelier | 化学平衡：Kc、Kp 与勒夏特列原理
The equilibrium constant expresses the position of equilibrium at a given temperature. Its magnitude indicates whether the equilibrium mixture is dominated by products or by reactants, and its value is unaffected by changes in pressure, concentration, or the presence of a catalyst.
平衡常数表示一定温度下平衡的位置。其大小说明平衡混合物以产物为主还是以反应物为主；改变压强、浓度或加入催化剂都不会改变其数值。
aA + bB ⇌ cC + dD Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ
For gaseous equilibria it is often more convenient to work with partial pressures, since pressure changes shift the position of equilibrium whenever the number of gaseous moles changes. The relationship between Kp and Kc depends on the change in gaseous moles, and both constants change in value if the temperature changes.
对于气体平衡，用分压处理往往更方便，因为只要气态物质的量发生变化，压强改变就会移动平衡位置。Kp 与 Kc 的关系取决于气态物质的量的变化；温度改变时，两个常数的数值都会改变。
Kp = pCᶜ pDᵈ / pAᵃ pB bsp; Kp = Kc(RT)^Δn Δn = gaseous product moles − gaseous reactant moles
Le Chatelier's principle predicts the direction of shift, and the equilibrium constant explains the reason: changing concentration or pressure alters the reaction quotient so that it is no longer equal to K, and the system responds to restore equality. Changing temperature is the only change that alters K itself.
勒夏特列原理预测移动方向，平衡常数则解释原因：改变浓度或压强会改变反应商，使其不再等于 K，体系随即作出响应以恢复相等。只有改变温度才会改变 K 本身。
Industrial applications show the compromise involved. In the Haber process, high pressure and a moderate temperature (around 450 °C) with an iron catalyst balance a favourable equilibrium position against an acceptable rate, whereas the Contact process uses excess air and a V₂O₅ catalyst to oxidise SO₂.
工业应用体现了这种权衡。哈伯法用高压、中等温度（约 450 ℃）配合铁催化剂，在有利的平衡位置与可接受的速率之间取得平衡；接触法则用过量空气与 V₂O₅ 催化剂氧化 SO₂。
6. Acid-Base Equilibria: pH, Ka, Kw and Buffers | 酸碱平衡：pH、Ka、Kw 与缓冲溶液
pH is defined through the concentration of hydrogen ions, and the relationship is logarithmic, so a change of one pH unit corresponds to a tenfold change in concentration. Strong acids are assumed to dissociate completely, which allows a direct calculation from concentration alone.
pH 由氢离子浓度定义，二者关系是对数的，因此 pH 变化一个单位相当于浓度变化十倍。强酸视为完全电离，故可直接由浓度求算。
pH = −log₁₀[H⁺] [H⁺] = 10⁻ᵖᴴ pH of a strong acid ≈ −log₁₀ c
Weak acids establish a position of equilibrium, described by the acid dissociation constant or its logarithmic form. Because only a small fraction of the molecules ionise, a simplifying approximation is permitted: the equilibrium concentration of the acid is taken as equal to its initial concentration.
弱酸建立平衡位置，用酸解离常数或其对数形式描述。由于只有很小一部分分子电离，可以采用简化近似：把酸的平衡浓度视为等于其初始浓度。
Ka = [H⁺][A⁻] / [HA] pKa = −log₁₀ Ka [H⁺] ≈ √Ka × c
water is not exactly pH 7 at every temperature. Note that Kw = 1.0 × 10⁻¹⁴ is strictly valid only at 298 K, so pKw = 14 holds at that temperature alone.
水的离子积使我们能求碱性与中性溶液的 pH；它对温度高度敏感，这解释了为什么中性水并非在任何温度下都恰好是 pH 7。需注意 Kw = 1.0 × 10⁻¹⁴ 仅在 298 K 严格成立，因此 pKw = 14 也只在 298 K 适用。
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 298 K pKw = pH + pOH = 14
he salt anion removes added H⁺. The buffer equation shows that when the acid and salt concentrations are equal, the pH equals the pKa; this also means that half-neutralisation in a titration occurs at pH = pKa.
缓冲溶液在加入少量酸或碱时能抵抗 pH 变化，因为未电离弱酸的储备可消耗外加的 OH⁻，盐的阴离子则消耗外加的 H⁺。缓冲方程表明，当酸与盐的浓度相等时 pH 等于 pKa；这也意味着滴定中的半中和点在 pH = pKa 处。
pH = pKa + log₁₀([A⁻] / [HA])
7. Reaction Kinetics: Rate Equations and the Arrhenius Equation | 反应动力学：速率方程与阿伦尼乌斯方程
The rate equation must be determined experimentally; the powers in it are the orders with respect to each reactant and are not taken from the stoichiometric equation. The overall order is the sum of the individual orders, and the units of the rate constant follow from the overall order.
速率方程必须由实验确定；式中各次幂即各反应物的级数，不能直接取自化学计量方程。总级数是各分级数之和，速率常数的单位则由总级数决定。
rate = k[A]ᵐ[B]ⁿ overall order = m + n
Zero-order reactions have a constant rate, first-order reactions have a constant half-life, and a concentration-time graph is used to identify the order by shape: a straight line for zero order, a constant half-life for first order, and an increasingly steep curve for second order. The initial rate method and the colorimetric or gas-volume methods are the standard experimental approaches.
零级反应速率恒定，一级反应半衰期恒定；用浓度-时间图可由形状判断级数：零级为直线，一级半衰期恒定，二级曲线越来越陡。测定初始速率法，以及比色法或测气体体积法，是标准实验手段。
t½ = ln 2 / k = 0.693 / k (first order)
The Arrhenius equation links the rate constant to temperature and activation energy. Plotting the natural logarithm of k against the reciprocal of temperature gives a straight line whose gradient is −Ea/R, allowing the activation energy to be found graphically.
阿伦尼乌斯方程把速率常数与温度和活化能联系起来。以 ln k 对 1/T 作图得直线，其斜率为 −Ea/R，从而可用图解法求活化能。
k = A e−Ea / RT ln k = ln A − Ea / RT gradient = −Ea / R
The rate-determining step is the slowest step in a multi-step mechanism, and the species appearing in the experimentally determined rate equation must be those involved up to and including that step. Catalysts increase the rate by providing an alternative route of lower activation energy and are not consumed in the overall reaction.
速率决定步骤是多步机理中最慢的一步，出现在实验测得的速率方程中的物种，应是该步骤及之前各步所涉及的物种。催化剂通过提供活化能更低的替代路径提高速率，且在总反应中不被消耗。
8. Electrochemistry: Electrode Potentials, EMF and Faraday | 电化学：电极电势、电动势与法拉第定律
Standard electrode potentials are quoted for reduction half-equations under standard conditions of 298 K, 100 kPa and 1 mol dm⁻³. The more negative the potential, the greater the tendency of that species to be oxidised, so the more negative couple forms the negative electrode when the two are combined.
标准电极电势是针对还原半反应给出的，标准条件为 298 K、100 kPa 与 1 mol dm⁻³。电势越负，该物种越易被氧化，因此在两电对组合时，电势较负的一方构成负极。
E°cell = E°(reduction, right) − E°(reduction, left)
A positive cell potential shows that the reaction as written is feasible, and the value is related to the free energy change of the cell reaction. Because both n and F are positive, a positive E°cell necessarily corresponds to a negative ΔG.
电池电动势为正值说明所写方向反应可行，其数值与电池反应的自由能变相关。由于 n 与 F 均为正值，E°cell 为正值必然对应 ΔG 为负值。
ΔG = −nFE F = 96 500 C mol⁻¹
Quantitative electrolysis uses the relationship between charge, current and time, followed by Faraday's relationship between charge and moles of electrons. The mole ratio between electrons and product comes from the balanced half-equation, and this sequence is the standard route through any electrolysis calculation.
定量电解先用电量、电流与时间的关系求电量，再用法拉第关系把电量与电子的物质的量联系起来；电子与产物之间的计量比来自配平的半反应式。这一顺序是任何电解计算的标准路径。
Q = I t n(e⁻) = Q / F = I t / F
Under non-standard conditions the actual potential differs from the standard value, and concentration changes shift the value according to the Nernst relationship. In redox titration work, the permanence of the colour of an oxidising agent such as manganate(VII) is used to detect the end point visually.
在非标准条件下，实际电势与标准值不同，浓度变化会按能斯特关系使电势发生偏移。在氧化还原滴定中，可利用高锰酸盐等氧化剂自身颜色的持久性来目视判断终点。
MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O
9. Transition Metal Chemistry: Complexes, Ligands and Colour | 过渡金属化学：配合物、配体与颜色
Transition metal ions form complex ions in which ligands donate a lone pair into vacant d orbitals of the metal ion. Coordination number six gives an octahedral shape, four gives tetrahedral, and in some ions four gives a square planar arrangement. Ligands may be monodentate, bidentate such as ethane-1,2-diamine
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