IGCSE AQA Chemistry: Formula Handbook | IGCSE AQA 化学公式汇总手册

📚 IGCSE AQA Chemistry: Formula Handbook | IGCSE AQA 化学公式汇总手册

Formulae are the language of quantitative chemistry. In IGCSE AQA Chemistry, you need to be able to recall and apply a set of key equations that link mass, moles, concentration, gas volumes and energy changes. This handbook brings together every essential formula, explains how to use each one and provides worked examples to help you tackle calculations with confidence.

公式是定量化学的语言。在 IGCSE AQA 化学中，你需要记住并运用一系列关键方程式，它们把质量、摩尔、浓度、气体体积和能量变化联系起来。这本手册汇总了所有必背公式，解释每个公式如何使用，并配以实例，帮助你自信地应对计算题。

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1. Relative Masses & Percentage Composition | 相对质量与百分组成

The relative atomic mass (Aᵣ) is the weighted average mass of an atom of an element compared with 1/12 of the mass of a carbon‑12 atom. The relative formula mass (Mᵣ) is the sum of the Aᵣ values of all atoms in a formula unit.

相对原子质量（Aᵣ）是一个元素的原子质量与一个碳‑12 原子质量的 1/12 相比较的加权平均值。相对式量（Mᵣ）是化学式单元中所有原子的 Aᵣ 值之和。

You can calculate the percentage by mass of an element in a compound using:

你可以用下式计算某元素在化合物中的质量百分数：

% element = (Aᵣ × number of atoms / Mᵣ of compound) × 100%

For example, in water H₂O, Mᵣ = (2×1) + 16 = 18. The % of hydrogen = (2/18)×100% = 11.1%.

例如，在水中 H₂O，Mᵣ = (2×1)+16=18。氢的百分含量 = (2/18)×100% = 11.1%。

Always use the correct Aᵣ from the Periodic Table, and remember to multiply by the number of atoms present.

务必使用元素周期表中正确的 Aᵣ，并记住乘以原子个数。

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2. The Mole Concept & Molar Mass | 摩尔概念与摩尔质量

One mole of any substance contains 6.02 × 10²³ particles (Avogadro constant). The molar mass (M) is the mass of one mole and has units g mol⁻¹; numerically it equals the Mᵣ.

一摩尔任何物质含有 6.02 × 10²³ 个微粒（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；数值上与 Mᵣ 相等。

The central equation connecting mass and moles is:

联系质量与摩尔的核心方程式是：

n = m / M

where n = amount (mol), m = mass (g), M = molar mass (g mol⁻¹).

其中 n = 物质的量（mol），m = 质量（g），M = 摩尔质量（g mol⁻¹）。

Rearrange as needed: m = n × M or M = m / n. Always convert masses to grams before substituting into the equation.

根据需要变形：m = n × M 或 M = m / n。代入方程前一定要将质量转换为克。

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3. Empirical and Molecular Formulae | 经验式与分子式

An empirical formula shows the simplest whole‑number ratio of atoms in a compound. A molecular formula gives the actual number of atoms of each element in a molecule.

经验式表示化合物中各原子的最简整数比。分子式给出一个分子中每种原子的真实数目。

To find the empirical formula from mass or % composition:

从质量或百分组成求经验式的步骤：

• Write down the mass or % of each element present.

  列出每种元素所占的质量或百分数。

• Divide each by its Aᵣ to get moles.

  将每个数值除以它自己的 Aᵣ 得到摩尔数。

• Divide all mole values by the smallest number to obtain the simplest ratio.

  用最小的摩尔数去除所有摩尔值，得到最简比。

• Round carefully; ratios like 1.5 usually indicate a need to multiply all ratios by 2.

  谨慎取整；像 1.5 这样的比例通常需要将全部比例乘以 2。

If the empirical formula mass is known and the molecular mass is given, the multiplier is: n = molecular Mᵣ / empirical formula Mᵣ.

如果已知经验式质量并且给出了分子质量，则倍数为：n = 分子 Mᵣ / 经验式 Mᵣ。

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4. Mass Calculations in Reactions | 反应中的质量计算

Reacting mass questions always start with a balanced chemical equation. The coefficients give the mole ratio in which substances react and form.

反应质量的问题总是从配平的化学方程式开始。各系数给出了物质反应和生成的摩尔比。

The general steps are:

一般步骤如下：

• Write the balanced equation and highlight the two substances you are comparing.

  写出配平的方程式，并标出你要比较的两种物质。

• Convert the given mass to moles using n = m / M.

  用 n = m / M 将已知质量换算成摩尔。

• Use the mole ratio from the equation to find the moles of the unknown substance.

  利用方程式中的摩尔比求出未知物质的摩尔数。

• Finally convert moles of the unknown back to mass with m = n × M.

  最后用 m = n × M 将未知物质的摩尔换算为质量。

Check that the final answer is sensible and includes the unit (g or tonnes, etc.).

检查最终答案是否合理，并带上单位（g 或 tonnes 等）。

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5. Gas Volumes (RTP) | 气体体积（室温常压）

At room temperature and pressure (RTP, around 20 °C and 1 atm), one mole of any gas occupies 24.0 dm³. This is the molar gas volume, Vₘ.

在室温常压（RTP，约 20 °C 和 1 atm）下，一摩尔任何气体的体积为 24.0 dm³。这就是摩尔气体体积 Vₘ。

The relationship is:

关系式为：

volume (dm³) = n × 24.0 dm³ mol⁻¹

or n = volume / 24.0.

或 n = 体积 / 24.0。

If a volume is given in cm³, divide by 1000 to convert to dm³. This formula is often combined with mass‑to‑mole conversions in reacting gas problems.

如果给出体积单位为 cm³，除以 1000 转换为 dm³。在处理气体反应的题目中，这一公式常与质量‑摩尔换算结合使用。

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6. Concentration of Solutions | 溶液浓度

Concentration can be expressed in mol dm⁻³ or g dm⁻³. The key molarity equation is:

浓度可用 mol dm⁻³ 或 g dm⁻³ 表示。关键的摩尔浓度方程是：

c = n / V

where c = concentration (mol dm⁻³), n = amount (mol) and V = volume (dm³).

其中 c = 浓度（mol dm⁻³），n = 物质的量（mol），V = 体积（dm³）。

If the volume is in cm³, you must convert to dm³ (÷ 1000) before using the equation. Rearranged forms are n = c × V and V = n / c.

如果体积的单位是 cm³，使用公式前必须转换为 dm³（除以 1000）。变形公式有 n = c × V 和 V = n / c。

Mass concentration (g dm⁻³) is simply mass of solute / volume of solution (dm³).

质量浓度（g dm⁻³）就是溶质质量 / 溶液体积（dm³）。

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7. Titration and Volumetric Analysis | 滴定与容量分析

Titration results give the volumes of two reacting solutions. For a simple acid–base reaction A + B → products, the mole ratio is used to find an unknown concentration.

滴定结果给出两种反应溶液的体积。对于简单的酸碱反应 A + B → 产物，用摩尔比来求未知浓度。

The general titration formula is:

通用的滴定公式为：

c₁V₁ / n₁ = c₂V₂ / n₂

where c₁, V₁, n₁ refer to the concentration, volume and mole coefficient of the first reactant, and c₂, V₂, n₂ refer to the second.

其中 c₁、V₁、n₁ 是第一个反应物的浓度、体积和化学方程式中的系数，c₂、V₂、n₂ 是第二个反应物的对应值。

Always convert volumes to dm³. For example, if 25.0 cm³ of NaOH is titrated with HCl of known concentration, use the 1:1 ratio to find [NaOH].

始终将体积转换为 dm³。例如，若 25.0 cm³ 的 NaOH 用已知浓度的 HCl 滴定，利用 1:1 的摩尔比即可求出 NaOH 的浓度。

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8. Yield and Atom Economy | 产率与原子经济性

Percentage yield compares the mass of product actually made with the theoretical maximum.

百分产率将实际得到的产物质量与理论最大产量进行比较。

% yield = (actual mass / theoretical mass) × 100%

Atom economy measures how well the reactant atoms end up in the desired product.

原子经济性衡量反应物原子成为期望产物的效率。

atom economy = (Mᵣ of desired product / total Mᵣ of all reactants) × 100%

A high atom economy means less waste and is an important principle of green chemistry. In calculations, remember that total Mᵣ of all reactants means the sum over all reactants used, multiplied by their coefficients.

原子经济性高意味着废物少，是绿色化学的一项重要原则。计算时，所有反应物的总 Mᵣ 是指所使用的所有反应物按系数加和。

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9. Energy Transfer (Calorimetry) | 能量传递（量热法）

When a reaction takes place in solution, the heat change can be measured using the equation:

当反应在溶液中发生时，可以用下式测定热量变化：

q = m c ΔT

where q = heat energy (J), m = mass of solution (g), c = specific heat capacity (J g⁻¹ °C⁻¹, usually 4.18 for water) and ΔT = temperature change (°C).

其中 q = 热能（J），m = 溶液质量（g），c = 比热容（J g⁻¹ °C⁻¹，水通常为 4.18），ΔT = 温度变化（°C）。

To find the molar enthalpy change (ΔH) in kJ mol⁻¹:

求摩尔焓变（ΔH）单位为 kJ mol⁻¹ 时：

ΔH = –q / n

where n is the moles of the limiting reactant. Divide by 1000 to convert J to kJ. The negative sign indicates that heat is released in exothermic reactions.

其中 n 是限制试剂的摩尔数。除以 1000 将 J 转换为 kJ。负号表示放热反应中热量被释放。

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10. Rate of Reaction | 反应速率

The mean rate of a reaction is calculated from the change in a measurable quantity over time:

反应的平均速率由某一可测量量随时间的变化来计算：

mean rate = Δquantity / Δtime

Quantities can include mass of a reactant, volume of gas produced, or concentration. The unit depends on the quantity used, e.g. cm³ s⁻¹ or g s⁻¹.

可测量量包括反应物的质量、生成的气体体积或浓度。单位取决于所用的量，例如 cm³ s⁻¹ 或 g s⁻¹。

At a specific point, the instantaneous rate can be found as the gradient of a tangent to a concentration‑time or volume‑time graph.

在某一特定时刻，瞬时速率可以通过浓度‑时间或体积‑时间曲线的切线斜率求得。

Drawing a tangent and calculating its slope gives the rate with appropriate units.

画切线并计算其斜率，可得到带有合适单位的速率。

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11. Formula Summary Table | 公式汇总表

The table below collects all the key formulae you must memorise for the IGCSE AQA Chemistry exam. Practise rearranging each one and applying it to different problems.

下表汇集了 IGCSE AQA 化学考试中你必须牢记的所有关键公式。请练习变形每个公式，并将其应用于不同习题。

Formula / 公式	Description / 说明
n = m / M	mol = mass ÷ molar mass | 摩尔 = 质量 ÷ 摩尔质量
% element = (Aᵣ × atoms / Mᵣ) × 100%	Percentage composition by mass | 质量百分组成
c = n / V	Concentration (mol dm⁻³) | 摩尔浓度
c₁V₁ / n₁ = c₂V₂ / n₂	Titration formula | 滴定公式
volume (dm³) = n × 24.0	Gas volume at RTP | 室温常压下气体体积
% yield = (actual / theoretical) × 100%	Percentage yield | 百分产率
atom economy = (Mᵣ(desired) / total Mᵣ(reactants)) × 100%	Atom economy | 原子经济性
q = m c ΔT	Heat energy change | 热量变化
ΔH = –q / n	Molar enthalpy change | 摩尔焓变
mean rate = Δquantity / Δtime	Average rate of reaction | 平均反应速率

For each calculation, write down the formula, identify the data and substitute carefully. Always check that units are consistent and that your final answer is given to an appropriate number of significant figures.

每做一道计算题时，先写出公式，找出数据，再仔细代入。务必检查单位是否一致，最终答案要保留合适位数。

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