📚 IB WJEC Chemistry: Formula Handbook | IB WJEC 化学：公式汇总手册
This handbook brings together the essential quantitative relationships you will need for IB and WJEC Chemistry examinations. From the mole concept to electrochemistry, these formulas form the backbone of problem‑solving across all topics. Memorise them, understand when to use each one, and practise applying them under timed conditions. Every formula is presented with standard notation and a brief commentary so you can move confidently between mass, moles, volume, energy and equilibrium.
本手册汇集了IB和WJEC化学考试中所需的重要定量关系。从摩尔概念到电化学，这些公式构成了所有专题中解题的基石。请熟记它们，理解每条公式的适用情境，并在限时条件下练习运用。每条公式均以标准符号和简要说明呈现，使你能自信地在质量、摩尔、体积、能量和平衡之间转换。
1. Mole Concept & Stoichiometry | 摩尔概念与化学计量
The mole is the chemist’s counting unit, linking the microscopic world of atoms to macroscopic masses we can measure. The number of moles n is calculated from mass m and molar mass M. For gases at room temperature and pressure (RTP), one mole occupies 24 dm³ (WJEC) or 22.7 dm³ at STP (IB); always check the conditions given in the question.
摩尔是化学家的计数单位，它将原子的微观世界与我们可测量的宏观质量联系起来。物质的量 n 可由质量 m 与摩尔质量 M 计算得出。对于室温常压 (RTP) 下的气体，1 摩尔占据 24 dm³ (WJEC) 或在标准状况 (STP) 下占据 22.7 dm³ (IB)；务必核对题目所给的条件。
- n = m / M – moles from mass and molar mass / 由质量和摩尔质量求物质的量
- n = N / L – moles from number of particles (L = 6.02 × 10²³ mol⁻¹) / 由粒子数求物质的量
- n = V / Vₘ – moles of gas from volume (Vₘ = 24 dm³ at RTP, 22.7 dm³ at STP) / 由气体体积求物质的量
- m = c × V × M (for solutions in a reaction) / 用于反应中溶液的质量计算
n = m / M • n = N / L • n = V / Vₘ
Using these three relationships you can interconvert mass, particle number and gas volume. Stoichiometric ratios from a balanced equation then allow you to scale these quantities between reactants and products.
利用这三个关系式，你可以在质量、粒子数和气体体积之间相互换算。然后，借助配平方程式中的化学计量比，就能在反应物和产物之间按比例缩放这些量。
2. Empirical & Molecular Formulae | 实验式与分子式
The empirical formula gives the simplest whole‑number ratio of atoms in a compound, while the molecular formula shows the actual number of each atom in a molecule. You often need to find the empirical formula from combustion data or percentage composition and then use the molar mass to determine the molecular formula.
实验式表示化合物中各原子的最简整数比，而分子式显示一个分子中每种原子的实际数目。你经常需要从燃烧数据或质量分数求出实验式，再利用摩尔质量确定分子式。
Mᵣ = (empirical formula mass) × n
To find the multiplier n, divide the relative molecular mass by the mass of the empirical formula unit. Always round to the nearest whole number.
求倍数 n 时，用相对分子质量除以实验式单元的质量，并四舍五入至最接近的整数。
3. Ideal Gas Equation | 理想气体方程式
The ideal gas equation links pressure, volume, temperature and the number of moles for a gas that behaves ideally. It is essential when conditions differ from RTP or STP. The value of the gas constant R depends on the units used: 8.31 J K⁻¹ mol⁻¹ when pressure is in kPa and volume in dm³, or 0.0821 L atm K⁻¹ mol⁻¹ in older specifications.
理想气体方程式将压力、体积、温度和物质的量联系起来，适用于行为理想的气体。当条件不同于 RTP 或 STP 时，该公式不可或缺。气体常数 R 的取值取决于所用单位：若压力用 kPa、体积用 dm³，则 R = 8.31 J K⁻¹ mol⁻¹；若用旧制 L·atm，则为 0.0821 L atm K⁻¹ mol⁻¹。
PV = nRT
o Always convert temperature to kelvin (K = °C + 273) and ensure volume and pressure units match the R value you select.
务必将温度换算为开尔文 (K = °C + 273)，并确保体积和压力单位与你所选用的 R 值匹配。
4. Solution Concentration & Titration | 溶液浓度与滴定
ionship c₁V₁/n₁ = c₂V₂/n₂, where n refers to the stoichiometric coefficient in the balanced equation.
浓度表示一定体积溶液中溶质的量，标准单位为 mol dm⁻³。滴定计算依赖于关系式 c₁V₁/n₁ = c₂V₂/n₂，其中 n 为配平方程式中的化学计量系数。
n = c × V • c₁V₁ / n₁ = c₂V₂ / n₂
For dilution problems, use c₁V₁ = c₂V₂ ant. Always express volume in dm³ (1 dm³ = 1000 cm³) before substituting into any formula.
稀释问题使用 c₁V₁ = c₂V₂，因为物质的量保持不变。在任何公式中代入前，始终将体积以 dm³ 表示 (1 dm³ = 1000 cm³)。
5. Thermochemistry | 热化学
alculate the heat absorbed or released by a solution, while ΔH is obtained by dividing q by the number of moles of the limiting reactant.
热化学测量化学反应过程中的热量变化。核心公式 q = mcΔT 可用于计算溶液吸收或释放的热量，ΔH 则由 q 除以限制反应物的物质的量得到。
q = mcΔT • ΔH = –q / n
The negative sign for ΔH in an exothermic reaction reflects that energy is lost to the surroundings. Hess's Law and bond enthalpy calculations are also built on these two basic expressions.
放热反应中 ΔH 取负号，表示能量散失到环境中。赫斯定律和键焓计算也以这两个基本表达式为基础。
6. Chemical Equilibrium | 化学平衡
For a reversible reaction at equilibrium, the equilibrium constant Kc is expressed in terms of concentrations, while Kp uses partial pressures. The expression follows directly from the balanced equation, with each concentration raised to the power of its stoichiometric coefficient. Only gaseous and aqueous species appear in the expression; solids and pure liquids are omitted.
对于达到平衡的可逆反应，平衡常数 Kc 以浓度表示，而 Kp 使用分压。表达式直接来源于配平方程式，各浓度以其化学计量系数为指数。只有气态和溶液中的物种才出现在表达式中；固体和纯液体被略去。
Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ
The magnitude of Kc indicates the position of equilibrium; large values favour products. Le Chatelier’s principle explains shifts qualitatively, but the equilibrium constant itself only changes with temperature.
Kc 的大小指示平衡的位置；大数值有利于产物。勒夏特列原理定性地解释了平衡移动，但平衡常数本身只随温度变化。
7. Acids & Bases | 酸与碱
Acid‑base calculations centre on pH, pOH, Ka and Kw y Kw. For strong acids and bases, pH is directly calculated from the concentration of H⁺ or OH⁻. For weak acids, the approximation [H⁺] = √Ka × [HA] is frequently used, provided the acid is less than 5 % dissociated.
酸碱计算围绕 pH、pOH、Ka 和 Kw 展开。对于强酸和强碱，pH 可直接由 H⁺ 或 OH⁻ 浓度求得。对于弱酸，常使用近似式 [H⁺] = √Ka × [HA]，前提是酸的电离度小于 5 %。
pH = –log₁₀[H⁺] • pOH = –log₁₀[OH⁻] • Kw = [H⁺][OH⁻] = 1.0×10⁻¹⁴ at 298 K
The Henderson–Hasselbalch equation for buffer solutions is pH = pKa + log₁₀([A⁻]/[HA]). This is vital for designing buffers and predicting pH changes upon addition of small amounts of acid or base.
缓冲溶液的亨德森-哈塞尔巴尔赫方程为 pH = pKa + log₁₀([A⁻]/[HA])。这对于设计缓冲液和预测加入少量酸或碱时的 pH 变化至关重要。
8. Electrochemistry | 电化学
Electrochemical cells convert chemical energy into electrical energy. The cell potential Ecell is the difference between the reduction potentials of the two half‑cells. Under non‑standard conditions, the Nernst equation relates the cell potential to the reaction quotient Q.
电化学电池将化学能转化为电能。电池电动势 Ecell 是两个半电池还原电势之差。在非标准条件下，能斯特方程将电池电动势与反应商 Q 联系起来。
Ecell = E°(cathode) – E°(anode)
E = E° – (RT / nF) ln Q
At 298 K the Nernst equation simplifies to E = E° – (0.0592 / n) log₁₀ Q. The relationship ΔG° = –nFE° links thermodynamics to electrochemistry and helps predict spontaneity.
在 298 K 时，能斯特方程简化为 E = E° – (0.0592 / n) log₁₀ Q。关系式 ΔG° = –nFE° 将热力学与电化学联系起来，并有助于预测反应的自发性。
9. Kinetics | 动力学
The rate of a chemical reaction is expressed either as the change in concentration of a reactant or product per unit time. The rate equation shows how the rate depends on the concentrations of reactants raised to certain powers, the orders of reaction.
化学反应速率可用单位时间内反应物或产物浓度的变化来表示。速率方程表明速率如何取决于反应物浓度的某次幂，即反应级数。
Rate = k [A]ᵐ[B]ⁿ
The rate constant k is temperature‑dependent, and its units vary with the overall order of reaction. The Arrhenius equation, k = A e–Eₐ/RT, quantifies this temperature dependence, where Eₐ is the activation energy.
速率常数 k 与温度相关，其单位随总反应级数而变化。阿伦尼乌斯方程 k = A e–Eₐ/RT 定量描述了这种温度依赖性，其中 Eₐ 为活化能。
10. Yield & Atom Economy | 产率与原子经济
Green chemistry and industrial efficiency are assessed through percentage yield and atom economy. Percentage yield compares the actual mass of product obtained to the theoretical maximum predicted by stoichiometry. Atom economy evaluates how much of the starting materials ends up in the desired product.
绿色化学与工业效率通过产率和原子经济性来评估。产率将实际获得的产品质量与由化学计量预测的理论最大质量进行比较。原子经济性则评价有多少起始原料进入了目标产物。
% Yield = (actual mass / theoretical mass) × 100
% Atom economy = (Mᵣ of desired product / Σ Mᵣ of all reactants) × 100
High atom economy reduces waste and is a key principle in sustainable chemistry. Both calculations are common in IB and WJEC data‑response questions.
高原子经济性可减少废物，是可持续化学的核心原则。这两个计算常见于IB和WJEC的数据分析题中。
11. Bond Enthalpy & Hess’s Law | 键焓与赫斯定律
Bond enthalpies offer a route to estimate ΔH for reactions involving covalent molecules. The energy required to break bonds is taken from data tables, and the energy released when new bonds form is subtracted. Hess’s Law states that the enthalpy change for a reaction is the same regardless of the pathway taken, allowing ΔH to be found by combining known enthalpies of combustion or formation.
键焓为估算涉及共价分子的反应的 ΔH 提供了一条途径。断开化学键所需的能量来自数据表，形成新键所释放的能量则被减去。赫斯定律指出，无论途径如何，反应的焓变相同，从而使我们可以通过组合已知的燃烧焓或生成焓来求得 ΔH。
ΔH ≈ Σ (bond enthalpies broken) – Σ (bond enthalpies made)
ΔH (target) = Σ ΔH (known steps)
Remember that bond‑enthalpy calculations give an approximate value because average bond energies are used. Hess’s Law cycles provide exact values when formation or combustion data are available.
请记住，键焓计算只能给出近似值，因为使用的是平均键能。而当有生成焓或燃烧焓数据时，赫斯定律循环可提供精确数值。
12. Redox & Half‑Equations | 氧化还原与半反应式
Redox reactions are split into oxidation (loss of electrons) and reduction (gain of electrons). Balancing half‑equations and combining them correctly ensures both mass and charge are conserved. Oxidation numbers help identify which species is oxidised and which is reduced.
氧化还原反应被拆分为氧化（失去电子）和还原（得到电子）。正确配平半反应式并将其合并，可确保质量与电荷均守恒。氧化数有助于识别哪种物质被氧化、哪种物质被还原。
MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O
Fe²⁺ → Fe³⁺ + e⁻
When building overall equations, multiply half‑equations so that the number of electrons lost equals the number gained. Titration calculations involving manganate(VII) or thiosulfate ions rely on these balanced redox equations.
构建总反应式时，需将半反应式乘以适当系数，使失去的电子数等于获得的电子数。涉及高锰酸根或硫代硫酸根离子的滴定计算均依赖这些配平的氧化还原方程式。
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