📚 CAIE Year 11 Chemistry Formula & Theorem Quick Reference Handbook | CAIE 11年级化学公式定理速查手册
This quick reference handbook brings together all the essential formulas, relationships, and quantitative skills required for the CAIE IGCSE Chemistry course (Year 11). Use it to revise mole calculations, energy changes, rates, titration outcomes, and more. Each section presents a clear English explanation immediately followed by its Chinese equivalent, ensuring you can study confidently in both languages.
本速查手册汇集了CAIE IGCSE化学（11年级）课程所需的所有核心公式、定量关系与计算技能。涵盖摩尔运算、能量变化、反应速率、滴定结果等内容。每个知识点均以英文搭配中文的方式呈现，帮助你在双语环境中高效复习。
1. The Mole and Avogadro’s Number | 摩尔与阿伏伽德罗常数
The mole is the unit for amount of substance. One mole contains exactly 6.02 × 10²³ particles (atoms, molecules, ions or electrons). This number is called the Avogadro constant, symbol Nₐ.
摩尔是物质的量的单位。1摩尔物质恰好含有6.02 × 10²³个微粒（原子、分子、离子或电子），这个数值称为阿伏伽德罗常数，符号为Nₐ。
n = N / Nₐ
where n = number of moles, N = number of particles, Nₐ = 6.02 × 10²³ mol⁻¹. The formula connects the microscopic world to laboratory masses.
其中 n 为摩尔数，N 为微粒个数，Nₐ = 6.02 × 10²³ mol⁻¹。此公式将微观粒子数与宏观质量联系起来。
2. Molar Mass and Mass Conversions | 摩尔质量与质量换算
The molar mass (M) of a substance is the mass of one mole of its formula units, expressed in g mol⁻¹. It is numerically equal to the relative atomic mass (Aᵣ) or relative formula mass (Mᵣ).
物质的摩尔质量(M)是指1摩尔该物质的质量，单位为g mol⁻¹，数值上等于相对原子质量(Aᵣ)或相对式量(Mᵣ)。
n = m / M
where m is mass in grams, M is molar mass in g mol⁻¹, and n is amount in moles. Rearranging gives m = n × M, which is used for reacting mass calculations.
其中 m 为质量(g)，M 为摩尔质量(g mol⁻¹)，n 为物质的量(mol)。变形后 m = n × M 常用于反应质量计算。
3. Empirical and Molecular Formulae | 实验式与分子式
The empirical formula gives the simplest whole‑number ratio of atoms in a compound. It is found by converting the mass (or percentage) of each element to moles, then dividing by the smallest number of moles.
实验式表示化合物中原子个数的最简整数比。可通过将各元素的质量（或百分含量）换算为摩尔数，再除以最小的摩尔数得到。
The molecular formula shows the actual number of atoms of each element in a molecule. It is a whole‑number multiple of the empirical formula: Molecular formula = (Empirical formula) × n, where n = Mᵣ / empirical formula mass.
分子式表示一个分子中各原子的实际个数，它是实验式的整数倍：分子式 = (实验式) × n，其中 n = 相对分子质量(Mᵣ) ÷ 实验式量。
4. Reacting Mass Calculations | 反应质量计算
Using a balanced chemical equation, the mole ratio of reactants and products allows masses to be predicted. The steps are: write the balanced equation, convert known masses to moles, use the mole ratio to find moles of the unknown, then convert back to mass.
利用配平的化学方程式，通过反应物与生成物的摩尔比可以预测质量。步骤为：写出配平方程式，将已知质量换算为摩尔数，利用摩尔比求出未知物的摩尔数，再换算为质量。
Example: 2Mg + O₂ → 2MgO. If 48 g of Mg react, n(Mg) = 48/24 = 2.0 mol. Mole ratio Mg:MgO is 2:2, so n(MgO) = 2.0 mol. Mass MgO = 2.0 × 40 = 80 g.
示例：2Mg + O₂ → 2MgO。若48 g镁反应，n(Mg)=48/24=2.0 mol。Mg与MgO的摩尔比为2:2，因此n(MgO)=2.0 mol，MgO质量=2.0×40=80 g。
5. Concentration and Titrations | 浓度与滴定
Concentration expresses how much solute is dissolved in a given volume of solution. Two common units are g dm⁻³ and mol dm⁻³.
浓度表示一定体积溶液中溶质的量。常用单位为g dm⁻³和mol dm⁻³。
c = n / V
where c = concentration (mol dm⁻³), n = moles of solute, V = volume of solution (dm³). If volume is in cm³, divide by 1000: V(dm³) = V(cm³) / 1000.
其中 c 为浓度(mol dm⁻³)，n 为溶质的摩尔数，V 为溶液体积(dm³)。若体积单位为cm³，需除以1000换算：V(dm³) = V(cm³) / 1000。
In a titration, the point where the indicator changes colour is the end‑point. The formula c₁V₁/n₁ = c₂V₂/n₂ relates the two solutions, where n₁ and n₂ are the balancing numbers from the equation.
滴定中指示剂变色时为终点。两种溶液的浓度与体积关系为 c₁V₁/n₁ = c₂V₂/n₂，其中 n₁、n₂ 为配平方程式中相应物质的系数。
6. Gas Volume at Room Temperature and Pressure | 室温常压下气体体积
At room temperature and pressure (r.t.p., 20 °C and 1 atmosphere), one mole of any gas occupies a volume of 24 dm³ (24 000 cm³). This is the molar gas volume.
在室温常压条件下（r.t.p.，20 °C，1 atm），1摩尔任何气体的体积为24 dm³（即24 000 cm³），此为气体的摩尔体积。
V = n × 24
where V is the volume of gas in dm³ at r.t.p., and n is the number of moles. The same relationship holds for mixtures of gases as long as conditions are constant.
其中 V 为r.t.p.下气体体积(dm³)，n 为摩尔数。只要条件不变，该关系同样适用于混合气体。
7. Percentage Yield and Atom Economy | 百分产率与原子经济
The percentage yield compares the actual mass of product obtained to the theoretical mass predicted from the balanced equation.
百分产率将实际得到的产物质量与根据配平方程式计算的理论产量进行比较。
% Yield = (actual mass / theoretical mass) × 100
Atom economy measures how efficiently reactants are converted into the desired product in a chemical reaction.
原子经济衡量反应物转化为目标产物的效率。
% Atom Economy = (Mᵣ of desired product / sum of Mᵣ of all reactants) × 100
Reactions with high atom economy produce less waste and are more sustainable.
原子经济高的反应废物更少，更符合绿色化学原则。
8. Energy Changes: Calorimetry | 能量变化：量热法
The heat absorbed or released in a reaction can be measured using a calorimeter. For aqueous reactions, the formula relates temperature change to heat energy.
反应中吸收或放出的热量可用量热计测量。对于水溶液反应，可通过温度变化计算热量。
Q = m × c × ΔT
where Q = heat energy (J), m = mass of water or solution (g), c = specific heat capacity (4.18 J g⁻¹ °C⁻¹ for water), ΔT = temperature change (°C).
其中 Q 为热量(J)，m 为水或溶液的质量(g)，c 为比热容(水的比热容为4.18 J g⁻¹ °C⁻¹)，ΔT 为温度变化(°C)。
The molar enthalpy change (ΔH) is then ΔH = –Q / n, where n is the moles of the limiting reactant. The negative sign indicates exothermic reactions.
摩尔焓变 ΔH = –Q / n，其中 n 为限制反应物的摩尔数。负号表示放热反应。
9. Bond Energy Calculations | 键能计算
Bond energy (bond enthalpy) is the energy required to break one mole of a particular covalent bond in gaseous molecules. Energy changes for a reaction can be estimated using average bond energies.
键能（键焓）是断裂气态分子中1摩尔某特定共价键所需的能量。利用平均键能可估算反应的能量变化。
ΔH = Σ (bond energies of bonds broken) – Σ (bond energies of bonds formed)
Bond breaking is endothermic (requires energy, positive), bond making is exothermic (releases energy, negative). If the overall ΔH is negative, the reaction is exothermic.
断键吸收热量（正值），成键放出热量（负值）。若总ΔH为负，反应为放热反应。
10. Rate of Reaction (Expressions) | 反应速率（表达式）
The rate of a reaction is the change in concentration (or mass or volume) of a reactant or product per unit time. It is often expressed with reference to a gas produced or a colour change.
反应速率指单位时间内反应物或生成物浓度（或质量、体积）的变化，常通过气体产生量或颜色变化来测量。
Average rate = Δ(quantity) / Δt
For example, if 60 cm³ of hydrogen gas is produced in 30 seconds, the average rate = 60/30 = 2.0 cm³ s⁻¹. The instantaneous rate can be obtained from the gradient of a tangent to the curve on a progress graph.
例如，若30秒内产生60 cm³氢气，平均速率 = 60/30 = 2.0 cm³ s⁻¹。瞬时速率可从变化曲线切线的斜率求得。
Factors affecting rate—concentration, temperature, surface area, catalysts—are explained by collision theory, which states that particles must collide with sufficient energy and correct orientation.
影响速率的因素（浓度、温度、表面积、催化剂）可由碰撞理论解释：微粒必须发生有效碰撞（能量足够且取向正确）才能反应。
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