📚 Formula Summary Handbook for IB and CIE Chemistry | IB CIE 化学公式汇总手册
This comprehensive handbook brings together the essential formulae required for success in IB and CIE Chemistry examinations. From stoichiometric calculations to thermodynamics, equilibrium, kinetics, and electrochemistry, mastering these equations is vital for solving quantitative problems with confidence. Each section pairs English explanations with Chinese translations, allowing bilingual learners to reinforce their understanding of core chemical mathematics.
本手册汇总了 IB 和 CIE 化学考试中必备的核心公式。从化学计量、热力学到平衡、动力学和电化学，掌握这些方程式是自信地解决计算问题的关键。每个部分都配有中英文双语解释，帮助双语学习者加深对化学数学核心内容的理解。
1. The Mole Concept and Stoichiometry | 摩尔概念与化学计量
The mole is the central unit in quantitative chemistry, linking mass, particle number, and volume of gases. The number of moles (n) can be calculated from mass (m) and molar mass (M):
摩尔是化学计量中的核心单位，将质量、粒子数和气体体积联系起来。物质的量 (n) 可以通过质量 (m) 和摩尔质量 (M) 计算：
n = m ÷ M
Particles can be counted using Avogadro’s constant (NA = 6.02 × 10²³ mol⁻¹):
粒子数可以利用阿伏伽德罗常数 (NA = 6.02 × 10²³ mol⁻¹) 计数：
Number of particles = n × NA
In stoichiometry, the mole ratio from a balanced equation allows conversion between reactants and products. Percentage yield and atom economy are critical for evaluating reaction efficiency.
在化学计量中，平衡方程式中的摩尔比可用于反应物和产物之间的转换。产率和原子经济性是评估反应效率的重要指标。
% yield = (actual yield ÷ theoretical yield) × 100%
Atom economy = (molar mass of desired product ÷ total molar mass of reactants) × 100%
2. Empirical and Molecular Formulae | 经验式与分子式
The empirical formula gives the simplest whole-number ratio of atoms in a compound, while the molecular formula shows the actual number of atoms. The empirical formula mass (ME) relates the two:
经验式表示化合物中原子的最简整数比，而分子式表示实际原子数。经验式质量 (ME) 将两者联系起来：
n = Mr ÷ ME
where n is an integer multiplier, and Mr is the relative molecular mass.
其中 n 是整数乘数，Mr 是相对分子质量。
Combustion analysis data or composition by mass is used to find empirical formulae. Always convert mass to moles, divide by the smallest value, and multiply to obtain whole numbers.
燃烧分析数据或质量组成用于求经验式。始终将质量转化为摩尔数，除以最小值，并相乘得到整数比。
3. Gas Laws and Ideal Gas Equation | 气体定律与理想气体方程
The ideal gas equation unites pressure (P), volume (V), amount (n), and temperature (T) with the gas constant (R):
理想气体方程将压力 (P)、体积 (V)、物质的量 (n) 和温度 (T) 与气体常数 (R) 结合起来：
PV = nRT
In IB and CIE examinations, R = 8.31 J K⁻¹ mol⁻¹ if pressure is in kPa and volume in dm³, or 0.0821 L atm K⁻¹ mol⁻¹ in other units. Temperature must be in Kelvin: T(K) = t(°C) + 273.
在 IB 和 CIE 考试中，如果压力用 kPa、体积用 dm³，则 R = 8.31 J K⁻¹ mol⁻¹；若用其他单位，R = 0.0821 L atm K⁻¹ mol⁻¹。温度必须用开尔文：T(K) = t(°C) + 273。
For a fixed mass of gas, combined gas law:
对于一定质量的气体，联合气体定律：
(P₁V₁) ÷ T₁ = (P₂V₂) ÷ T₂
At room temperature and pressure (RTP) or standard temperature and pressure (STP), molar volume is often taken as 24 dm³ mol⁻¹ or 22.7 dm³ mol⁻¹ respectively.
在室温常压 (RTP) 或标准温压 (STP) 下，摩尔体积通常分别取 24 dm³ mol⁻¹ 或 22.7 dm³ mol⁻¹。
4. Concentration, Dilution, and Titration | 浓度、稀释与滴定
Concentration (c) links moles of solute and volume of solution. Standard formula:
浓度 (c) 关联溶质的物质的量和溶液的体积。标准公式：
c = n ÷ V (in mol dm⁻³)
Dilution calculations follow the principle of conservation of moles:
稀释计算遵循物质的量守恒原则：
c₁V₁ = c₂V₂
In acid-base titrations, the equivalence point allows determination of unknown concentration:
在酸碱滴定中，等当点可用于求未知浓度：
nacid : nbase ratio from balanced equation
Back titration and redox titration formulae extend the same mole concept.
返滴定和氧化还原滴定公式延伸了相同的摩尔概念。
5. Energetics and Thermochemistry | 化学热力学
Enthalpy change (ΔH) is calculated from temperature change during a reaction using specific heat capacity (c) and mass (m):
焓变 (ΔH) 通过反应过程中的温度变化、比热容 (c) 和质量 (m) 计算：
q = mcΔT
Then ΔH = −q ÷ n (for exothermic reactions q is negative by convention). Calorimetry experiments rely on this principle.
然后 ΔH = −q ÷ n (对于放热反应，按惯例 q 为负)。量热实验依赖这一原理。
Hess’s Law states that the total enthalpy change for a reaction is independent of the route taken:
盖斯定律指出，反应的总焓变与途径无关：
ΔHreaction = Σ ΔHf°(products) − Σ ΔHf°(reactants)
Bond enthalpy calculations (all gaseous species):
键焓计算（全部为气态物种）：
ΔH ≈ Σ (bond enthalpies broken) − Σ (bond enthalpies formed)
6. Chemical Equilibrium | 化学平衡
The equilibrium constant (Kc) expresses the ratio of product to reactant concentrations at equilibrium, each raised to the power of its stoichiometric coefficient:
平衡常数 (Kc) 表示平衡时产物浓度与反应物浓度之比，各浓度以其化学计量数为指数：
For aA + bB ⇌ cC + dD: Kc = [C]c[D]d ÷ [A]a[B]b
The reaction quotient (Q) uses the same expression but with initial concentrations, predicting the direction of shift.
反应商 (Q) 使用相同表达式但用初始浓度，可预测平衡移动方向。
For gaseous equilibria, Kp uses partial pressures:
对于气相平衡，Kp 使用分压：
Kp = (PCc × PDd) ÷ (PAa × PBb)
Relationship between Kp and Kc: Kp = Kc(RT)Δn, where Δn = moles of gaseous products − moles of gaseous reactants.
Kp 与 Kc 的关系：Kp = Kc(RT)Δn，其中 Δn = 气态产物摩尔数 − 气态反应物摩尔数。
7. Acids, Bases, and pH | 酸、碱与 pH
The pH scale is defined by the hydrogen ion concentration:
pH 标度由氢离子浓度定义：
pH = −log₁₀[H⁺]
Similarly, pOH = −log₁₀[OH⁻] and pH + pOH = 14 at 298 K for aqueous solutions.
类似地，pOH = −log₁₀[OH⁻]，在 298 K 的水溶液中 pH + pOH = 14。
For strong acids and bases, complete dissociation is assumed. For weak acids, the acid dissociation constant Ka applies:
对于强酸强碱，假定完全电离。对于弱酸，使用酸解离常数 Ka：
HA ⇌ H⁺ + A⁻ : Ka = [H⁺][A⁻] ÷ [HA]
The Henderson-Hasselbalch equation for buffer solutions:
缓冲溶液的亨德森-哈塞尔巴尔赫方程：
pH = pKa + log₁₀([salt] ÷ [acid])
pKa = −log₁₀Ka. Similar expressions exist for bases using Kb and pKb.
pKa = −log₁₀Ka。碱也有类似表达式，使用 Kb 和 pKb。
8. Electrochemistry | 电化学
The standard cell potential (E°cell) determines the driving force of a redox reaction:
标准电池电动势 (E°cell) 决定氧化还原反应的驱动力：
E°cell = E°cathode − E°anode
The relationship between Gibbs free energy change and cell potential:
吉布斯自由能变与电池电动势的关系：
ΔG° = −nFE°cell
where n is the number of electrons transferred, and F is the Faraday constant (96 500 C mol⁻¹).
其中 n 是转移电子数，F 是法拉第常数 (96 500 C mol⁻¹)。
The Nernst equation for non-standard conditions:
非标准条件下的能斯特方程：
E = E° − (RT ÷ nF) ln Q
At 298 K, this simplifies to: E = E° − (0.0592 ÷ n) log₁₀ Q.
在 298 K 时，可简化为：E = E° − (0.0592 ÷ n) log₁₀ Q。
In electrolysis, the quantity of electric charge (Q = It) relates to moles of substance via Faraday’s laws:
在电解中，电荷量 (Q = It) 通过法拉第定律与物质的量相关：
Q = It and n = Q ÷ (zF)
where z is the number of electrons per ion.
其中 z 是每个离子的电子数。
9. Rate of Reaction and Kinetics | 反应速率与动力学
The rate of a reaction is defined as the change in concentration of a reactant or product per unit time:
反应速率定义为单位时间内反应物或产物浓度的变化：
Rate = −Δ[A] ÷ Δt (for reactant A)
The rate law (rate equation) links rate to concentrations raised to some power:
速率定律（速率方程）将速率与浓度的某次方联系起来：
Rate = k[A]m[B]n
where k is the rate constant, and m, n are orders of reaction determined experimentally, not from the stoichiometric coefficients.
其中 k 是速率常数，m、n 是反应级数，由实验确定，而非根据化学计量系数。
The Arrhenius equation describes the temperature dependence of the rate constant:
阿伦尼乌斯方程描述速率常数与温度的关系：
k = Ae−Ea / RT
Or in logarithmic form: ln k = −Ea ÷ RT + ln A
或对数形式：ln k = −Ea ÷ RT + ln A
where Ea is activation energy, A is the pre-exponential factor.
其中 Ea 是活化能，A 是指前因子。
10. Organic Chemistry and Spectroscopy | 有机化学与光谱
While organic chemistry is more qualitative, index of hydrogen deficiency (IHD) is a key formula for structural determination:
虽然有机化学更偏重定性，但氢缺失指数 (IHD) 是结构鉴定的关键公式：
IHD = (2C + 2 + N − H − X) ÷ 2
where C, N, H, X are the numbers of carbon, nitrogen, hydrogen, and halogen atoms respectively.
其中 C、N、H、X 分别代表碳、氮、氢和卤素原子的数量。
In mass spectrometry, the relative atomic/molecular mass is calculated from isotopic abundances:
在质谱中，相对原子/分子质量由同位素丰度计算：
Ar = Σ (isotopic mass × % abundance) ÷ 100
Infrared (IR) and NMR spectroscopy focus on structural features rather than calculations, but the integration of signals in ¹H NMR relates to the ratio of protons in different environments.
红外 (IR) 和核磁共振 (NMR) 光谱侧重于结构特征而非计算，但 ¹H NMR 中信号的积分与不同环境中质子的比例相关。
11. Phase Changes and Solutions | 相变与溶液
Raoult’s law for ideal solutions gives the vapour pressure of a solvent above a solution:
拉乌尔定律用于理想溶液，给出溶液上方溶剂的蒸气压：
Psolution = χsolvent × P°solvent
Colligative properties such as boiling point elevation and freezing point depression follow:
依数性质如沸点升高和凝固点降低遵循：
ΔTb = iKbm and ΔTf = iKfm
where i is the van ‘t Hoff factor, Kb and Kf are ebullioscopic and cryoscopic constants, and m is molality (mol solute per kg solvent). Though less common in IB/CIE, these formulae occasionally appear in higher-level problems.
其中 i 是范特霍夫因子，Kb 和 Kf 是沸点升高常数和凝固点降低常数，m 是质量摩尔浓度（每千克溶剂中溶质的物质的量）。虽然这些公式在 IB/CIE 中不常见，但有时会出现在较高难度的问题中。
12. Thermodynamics and Spontaneity | 热力学与自发性
The Gibbs free energy change determines whether a reaction is spontaneous under constant temperature and pressure:
吉布斯自由能变决定在恒温恒压下反应是否自发：
ΔG = ΔH − TΔS
At standard conditions: ΔG° = −RT ln K, linking equilibrium constant and thermodynamic spontaneity.
在标准条件下：ΔG° = −RT ln K，将平衡常数与热力学自发性联系起来。
For non-standard conditions: ΔG = ΔG° + RT ln Q.
对于非标准条件：ΔG = ΔG° + RT ln Q。
These equations are vital in the IB and CIE syllabi, particularly in topics linking energetics and equilibrium.
这些方程在 IB 和 CIE 教学大纲中至关重要，尤其是连接热力学和平衡的主题。
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