📚 Year 11 Cambridge Chemistry: Formula & Theorem Quick Reference Handbook | Year 11 Cambridge 化学：公式定理速查手册
This quick reference handbook compiles the essential formulae, key theorems and numerical relationships required for the Cambridge IGCSE / O‑Level Chemistry syllabus (Year 11). Each section gives the core equation in bold, followed by a concise explanation of its use and typical units. Mastering these tools will help you solve quantitative problems confidently in Paper 3 (Theory) and Paper 5 (Practical Test).
本速查手册汇编了剑桥 IGCSE / O‑Level 化学大纲（Year 11）所要求的核心公式、关键定理与数量关系。每一节以粗体给出核心方程，并简要说明其用途与常用单位。熟练掌握这些工具将帮助你自信地解答 Paper 3（理论）和 Paper 5（实验）中的定量问题。
1. Relative Atomic & Molecular Mass | 相对原子质量与相对分子质量
The relative atomic mass (Aᵣ) of an element is the average mass of its atoms compared to 1/12 of the mass of a carbon‑12 atom. It has no unit.
元素的相对原子质量 (Aᵣ) 是其原子的平均质量与一个碳‑12 原子质量的 1/12 之比，无单位。
The relative molecular mass (Mᵣ) is the sum of the Aᵣ values of all atoms in a molecule. For ionic compounds the term relative formula mass is used, but calculated in the same way.
相对分子质量 (Mᵣ) 是分子中所有原子 Aᵣ 值之和。对于离子化合物使用相对式量，但计算方法相同。
Mᵣ = Σ (Aᵣ of each atom)
Example: Mᵣ of H₂SO₄ = (2×1) + 32 + (4×16) = 98. Always use the Aᵣ values from the Periodic Table provided in the exam.
示例：H₂SO₄ 的 Mᵣ = (2×1) + 32 + (4×16) = 98。务必使用试卷提供的周期表上的 Aᵣ 值。
2. The Mole & Molar Mass | 摩尔与摩尔质量
One mole of a substance contains 6.02 × 10²³ particles (Avogadro’s constant). The molar mass (M) is the mass of one mole of the substance, expressed in g mol⁻¹. Numerically, M equals the relative atomic or molecular mass.
一摩尔物质含有 6.02 × 10²³ 个粒子（阿伏伽德罗常数）。摩尔质量 (M) 是一摩尔物质的质量，单位为 g mol⁻¹。数值上 M 等于相对原子质量或相对分子质量。
Amount (mol) n = mass (g) / molar mass (g mol⁻¹)
Rearrange to find mass: m = n × M. This relationship is the foundation of all quantitative chemistry.
变形求质量：m = n × M。这一关系是所有定量化学的基础。
3. Mass–Mole Conversions | 质量与摩尔转换
To calculate the number of moles from a known mass:
已知质量求摩尔数：
n = m / M
To calculate the mass of a known number of moles:
已知摩尔数求质量：
m = n × M
Always check that the units are consistent: mass in grams, molar mass in g mol⁻¹. For very small masses (e.g. in titrations) you may be given masses in milligrams; convert to grams first.
始终确保单位一致：质量用克，摩尔质量用 g mol⁻¹。对于极小质量（如滴定中），可能给出毫克单位，需先转换为克。
4. Gas Volume Calculations | 气体体积计算
At room temperature and pressure (r.t.p., 25 °C and 1 atm), one mole of any gas occupies 24 dm³ (24,000 cm³). This is the molar gas volume, Vₘ.
在常温常压（r.t.p., 25 °C 和 1 atm）下，一摩尔任何气体占据 24 dm³ (24,000 cm³)。这是气体摩尔体积 Vₘ。
Volume of gas (dm³) = n × 24 or Volume (cm³) = n × 24,000
Conversely, you can find moles from a measured gas volume:
反之，可由测得的气体体积求摩尔数：
n = Volume (dm³) / 24 or n = Volume (cm³) / 24,000
This relationship applies only to gases at r.t.p. If conditions are different, the ideal gas equation is not required at IGCSE, but you may be told to assume r.t.p. unless stated otherwise.
该关系仅适用于 r.t.p. 下的气体。若条件不同，IGCSE 不要求理想气体状态方程，但题目通常会说明可以假定为 r.t.p.。
5. Solution Concentration | 溶液浓度
The concentration of a solution tells you how many moles of solute are dissolved in 1 dm³ of solution. The unit is mol dm⁻³ (often written M).
溶液的浓度表示 1 dm³ 溶液中溶解了多少摩尔溶质。单位是 mol dm⁻³（常写作 M）。
Concentration (mol dm⁻³) = amount of solute (mol) / volume of solution (dm³)
Symbolically: c = n / V. You can also calculate the mass concentration (g dm⁻³) by multiplying by the molar mass: mass concentration = c × M.
符号表达：c = n / V。你也可以乘以摩尔质量得到质量浓度 (g dm⁻³)：质量浓度 = c × M。
For dilution calculations, use the fact that the number of moles stays the same:
稀释计算利用溶质摩尔数不变的事实：
c₁ V₁ = c₂ V₂
Where c₁ and V₁ are the initial concentration and volume, and c₂ and V₂ the final ones. Ensure both volumes are in the same unit.
其中 c₁ 和 V₁ 是初始浓度和体积，c₂ 和 V₂ 是最终浓度和体积。确保两个体积单位相同。
6. Chemical Equations & Stoichiometry | 化学方程式与计量关系
A balanced chemical equation gives the mole ratio of reactants and products. Use this ratio to convert between moles of different substances.
配平的化学方程式给出了反应物与产物的摩尔比。利用该比率在不同物质的摩尔数间进行转换。
Steps for stoichiometric calculations:
化学计量计算步骤：
- Write the balanced equation.
- 写出配平的方程式。
- Convert given mass/volume to moles.
- 将已知的质量/体积转换为摩尔数。
- Use the mole ratio from the equation to find moles of the required substance.
- 利用方程式中的摩尔比求所需物质的摩尔数。
- Convert moles back to mass, volume or concentration as needed.
- 根据需要将摩尔数转换回质量、体积或浓度。
Example: Mg + 2HCl → MgCl₂ + H₂. If 2 mol of Mg react, 2 mol of H₂ are produced (1:1 ratio). For every 2 mol of HCl consumed, 1 mol of H₂ is produced.
示例：Mg + 2HCl → MgCl₂ + H₂。若 2 mol Mg 反应，生成 2 mol H₂ (1:1 比)。每消耗 2 mol HCl，生成 1 mol H₂。
7. Energy Changes & Enthalpy | 能量变化和焓变
The heat energy transferred in a reaction is often measured by a temperature change in water or a solution.
反应中传递的热量常通过水或溶液的温度变化来测定。
Heat energy (J) q = m c ΔT
Where m = mass of water/solution (g), c = specific heat capacity (4.2 J g⁻¹ °C⁻¹ for water), ΔT = temperature change (°C).
其中 m = 水/溶液的质量 (g)，c = 比热容（水为 4.2 J g⁻¹ °C⁻¹），ΔT = 温度变化 (°C)。
The enthalpy change per mole (ΔH) is found by dividing q by the number of moles of the limiting reactant.
每摩尔的焓变 (ΔH) 由 q 除以限制反应物的摩尔数得到。
ΔH (J mol⁻¹) = q / n or ΔH (kJ mol⁻¹) = (q / 1000) / n
For exothermic reactions ΔH is negative; for endothermic reactions ΔH is positive. Always convert q to kJ when reporting final ΔH.
放热反应 ΔH 为负值；吸热反应 ΔH 为正值。报告最终 ΔH 时务必先将 q 转换为 kJ。
8. Rate of Reaction | 反应速率
The rate of a chemical reaction measures how quickly a reactant is used up or a product is formed.
化学反应速率衡量反应物消耗或产物生成的快慢。
Average rate = change in quantity / time taken
Quantity can be: mass of a reactant/product (g), volume of gas produced (cm³), concentration (mol dm⁻³), or colour intensity. The units of rate vary accordingly, e.g. g s⁻¹, cm³ s⁻¹.
物理量可以是：反应物/产物的质量 (g)、生成气体的体积 (cm³)、浓度 (mol dm⁻³) 或颜色强度。速率的单位相应不同，如 g s⁻¹、cm³ s⁻¹。
For a reaction involving a gas, you may plot volume of gas against time; the gradient of the curve at any point gives the instantaneous rate.
对于产生气体的反应，可绘制气体体积-时间图；曲线上任一点的斜率即为瞬时速率。
Factors affecting rate (collision theory): concentration, temperature, surface area, catalyst. Increasing any of these (except catalyst) increases the frequency and/or energy of collisions.
影响速率的因素（碰撞理论）：浓度、温度、表面积、催化剂。除催化剂外，增大任一因素都会增加碰撞频率和/或能量。
9. Chemical Equilibrium & Kc | 化学平衡与 Kc
Many reactions are reversible. At equilibrium the rates of the forward and reverse reactions are equal, and the concentrations of reactants and products remain constant.
许多反应是可逆的。平衡时正逆反应速率相等，反应物和产物的浓度保持不变。
For a general reaction: a A + b B ⇌ c C + d D, the equilibrium constant in terms of concentration is:
对于一般反应：a A + b B ⇌ c C + d D，以浓度表示的平衡常数为：
Kc = ([C]ᶜ [D]ᵈ) / ([A]ᵃ [B]ᵇ)
Only aqueous and gaseous species appear in the Kc expression; solids and pure liquids have constant concentration and are omitted. Kc is temperature‑dependent; a change in temperature shifts the equilibrium position and alters the Kc value.
只有溶液和气体物种出现在 Kc 表达式中；固体和纯液体浓度恒定，不写入。Kc 与温度有关；温度变化会移动平衡位置并改变 Kc 值。
Le Chatelier’s principle states that if a system at equilibrium is disturbed, it will shift to counteract the change. Knowing how concentration, pressure and temperature affect equilibrium is essential for the industrial processes (e.g. Haber process, Contact process).
勒夏特列原理指出，若平衡体系受到扰动，体系将朝着减弱该变化的方向移动。理解浓度、压强和温度如何影响平衡对工业过程（如哈柏法、接触法）至关重要。
10. Acids, Bases & pH | 酸、碱与 pH
pH is a measure of the hydrogen ion concentration in a solution. A low pH (0–6) indicates an acidic solution; a high pH (8–14) indicates a basic solution; pH 7 is neutral.
pH 是溶液氢离子浓度的量度。低 pH (0–6) 表示酸性溶液；高 pH (8–14) 表示碱性溶液；pH 7 为中性。
pH = –log₁₀[H⁺]
Where [H⁺] is in mol dm⁻³. For a monoprotic strong acid, [H⁺] equals the acid concentration. Each unit decrease in pH represents a ten‑fold increase in [H⁺].
其中 [H⁺] 以 mol dm⁻³ 为单位。对于一元强酸，[H⁺] 等于酸的浓度。pH 每降低 1，[H⁺] 增大 10 倍。
During a neutralisation reaction, H⁺ ions from the acid react with OH⁻ ions from the base to form water: H⁺(aq) + OH⁻(aq) → H₂O(l). The ionic equation for neutralisation is always this.
在中和反应中，酸中的 H⁺ 离子与碱中的 OH⁻ 离子反应生成水：H⁺(aq) + OH⁻(aq) → H₂O(l)。中和的离子方程式总是这个。
Titration calculations use the relationship c₁V₁ = c₂V₂ after accounting for the mole ratio from the balanced equation. Indicators like phenolphthalein and methyl orange are used to detect the endpoint.
滴定计算在根据配平方程式考虑摩尔比后，使用 c₁V₁ = c₂V₂ 关系式。酚酞和甲基橙等指示剂用于检测终点。
11. Electrolysis & Faraday’s Laws | 电解与法拉第定律
The amount of substance produced at an electrode during electrolysis depends on the quantity of electric charge passed.
电解过程中电极上产物的量取决于通过的电量。
Charge (C) Q = current (A) × time (s) → Q = I t
One mole of electrons carries a charge of 96,500 coulombs (C mol⁻¹). This is the Faraday constant, F.
一摩尔电子携带 96,500 库仑的电量 (C mol⁻¹)。这是法拉第常数 F。
Moles of electrons n(e⁻) = Q / F = I t / 96,500
To find the mass of a substance deposited, you need the half‑equation to relate electrons to moles of product. For example, Cu²⁺ + 2e⁻ → Cu means 2 moles of electrons deposit 1 mole of copper.
求析出物质的质量时，需利用半反应式将电子与产物摩尔数关联。例如，Cu²⁺ + 2e⁻ → Cu 表示 2 mol 电子析出 1 mol 铜。
Mass deposited (g) = (M × I × t) / (n × F)
Where M = molar mass of the substance, I = current (A), t = time (s), n = number of electrons transferred per formula unit, and F = 96,500 C mol⁻¹.
其中 M = 物质的摩尔质量，I = 电流 (A)，t = 时间 (s)，n = 每个化学式单元转移的电子数，F = 96,500 C mol⁻¹。
For gas produced (e.g. H₂, O₂), you can first calculate the moles of gas and then find the volume: Volume (dm³) = n(gas) × 24 at r.t.p.
对于生成的气体（如 H₂、O₂），可先计算气体摩尔数，再求体积：体积 (dm³) = n(气体) × 24（r.t.p. 下）。
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