📚 GCSE WJEC Chemistry: Formula Summary Handbook | GCSE WJEC 化学：公式汇总手册
Mastering the essential formulas is the key to success in GCSE WJEC Chemistry. This handbook collects every quantitative relationship you need – from mole calculations and gas volumes to energy changes and atom economy – with clear explanations and paired Chinese translations to reinforce your understanding.
掌握核心公式是攻克 GCSE WJEC 化学的关键。本手册汇集了你所需的全部定量关系——从摩尔计算、气体体积到能量变化与原子经济性——并配有清楚的中英双语解释，帮助你巩固理解。
1. Relative Atomic Mass (Aᵣ) and Relative Formula Mass (Mᵣ) | 相对原子质量 (Aᵣ) 与相对式量 (Mᵣ)
Relative atomic mass (Aᵣ) is the weighted mean mass of an atom of an element compared to 1/12th of the mass of a carbon‑12 atom. It has no units.
相对原子质量 (Aᵣ) 是某元素一个原子的加权平均质量与一个碳‑12 原子质量的 1/12 的比值，没有单位。
The relative formula mass (Mᵣ) of a compound is the sum of the Aᵣ values of all the atoms in its formula unit. For ionic substances we use the term relative formula mass; for covalent molecules we often call it relative molecular mass, but the calculation is identical.
化合物的相对式量 (Mᵣ) 是其化学式单元中所有原子的 Aᵣ 之和。对于离子化合物我们使用相对式量；对于共价分子常称为相对分子质量，但计算方法完全相同。
Mᵣ = (number of atoms of element 1 × Aᵣ of element 1) + (number of atoms of element 2 × Aᵣ of element 2) + …
To calculate Mᵣ, multiply the Aᵣ of each element by the number of atoms of that element present in the formula, then add all the contributions together.
计算 Mᵣ 时，将每种元素的 Aᵣ 乘以其在化学式中的原子个数，再将所有结果相加。
2. The Mole and Molar Mass | 摩尔与摩尔质量
One mole of any substance contains 6.02 × 10²³ particles (Avogadro constant). The molar mass (M) of a substance is the mass of one mole of that substance, expressed in grams per mole (g/mol). Numerically, the molar mass equals the relative formula mass (Mᵣ) of the substance.
1 摩尔任何物质含有 6.02 × 10²³ 个微粒（阿伏伽德罗常数）。物质的摩尔质量 (M) 是指 1 摩尔该物质的质量，单位为 g/mol。摩尔质量的数值等于该物质的相对式量 (Mᵣ)。
M = Mᵣ g/mol
For example, the Mᵣ of water (H₂O) is 18, so the molar mass of water is 18 g/mol. This relationship allows you to convert between mass and number of moles seamlessly.
例如，水 (H₂O) 的 Mᵣ 为 18，因此水的摩尔质量为 18 g/mol。这一关系使你能够在质量与摩尔数之间自由转换。
3. Calculating Moles from Mass | 由质量计算摩尔数
The central equation connecting mass, moles and molar mass is used more than any other in quantitative chemistry. Always remember to work with mass in grams.
连接质量、摩尔数与摩尔质量的核心公式在定量化学中使用频率最高。务必始终使用克作为质量单位。
n = m ÷ M
Where n is the amount of substance (mol), m is the mass (g) and M is the molar mass (g/mol). You can rearrange this to m = n × M or M = m ÷ n as required by the question.
其中 n 为物质的量 (mol)，m 为质量 (g)，M 为摩尔质量 (g/mol)。可根据题意变形为 m = n × M 或 M = m ÷ n。
For a sample of 8.0 g of calcium carbonate (CaCO₃, M = 100 g/mol), the number of moles is n = 8.0 ÷ 100 = 0.080 mol. Always show the rearrangement step to secure full marks.
对于 8.0 g 碳酸钙 (CaCO₃, M = 100 g/mol)，摩尔数为 n = 8.0 ÷ 100 = 0.080 mol。务必展示变形步骤以获得满分。
4. Concentration of Solutions | 溶液浓度
Concentration can be expressed in grams per cubic decimetre (g/dm³) or in moles per cubic decimetre (mol/dm³). Both versions are tested in WJEC GCSE Chemistry.
浓度可以用克每立方分米 (g/dm³) 或摩尔每立方分米 (mol/dm³) 表示，WJEC GCSE 化学对两种表达都会考查。
Mass concentration (g/dm³) = mass (g) ÷ volume (dm³)
The mass concentration calculation is straightforward when a solid is dissolved and the final volume is known.
当溶质是固体且已知最终体积时，质量浓度的计算非常直接。
Molar concentration (mol/dm³) = n ÷ V
Where n is the number of moles of solute and V is the volume of the solution in dm³. This relationship is often written as c = n / V, where c represents molar concentration.
其中 n 是溶质的物质的量 (mol)，V 是溶液的体积 (dm³)。该关系常写作 c = n / V，c 表示物质的量浓度。
You can link the two by: mass concentration (g/dm³) = molar concentration (mol/dm³) × M (g/mol).
两者可通过下式联系：质量浓度 (g/dm³) = 物质的量浓度 (mol/dm³) × M (g/mol)。
5. Gas Volumes | 气体体积
At room temperature and pressure (RTP), usually taken as 20 °C and 1 atmosphere, one mole of any gas occupies a volume of 24 dm³. This molar gas volume is a fundamental constant in WJEC GCSE calculations.
在常温常压 (RTP，通常取 20 °C 和 1 大气压) 下，1 摩尔任何气体的体积为 24 dm³。该气体摩尔体积是 WJEC GCSE 计算中的一个基本常数。
Volume of gas (dm³) = number of moles × 24
If the question provides a gas volume in cm³, convert to dm³ by dividing by 1000 before using the formula. Equally, you may be required to convert the final answer from dm³ to cm³ by multiplying by 1000.
如果题目给出的气体体积单位是 cm³，使用公式前先除以 1000 转换为 dm³。同样，最后可能需要将 dm³ 乘以 1000 转换为 cm³。
For example, 0.50 mol of hydrogen gas occupies 0.50 × 24 = 12 dm³. Conversely, if 6 dm³ of oxygen is produced, the amount of oxygen is 6 ÷ 24 = 0.25 mol.
例如，0.50 mol 氢气体积为 0.50 × 24 = 12 dm³。反之，如果产生 6 dm³ 氧气，则氧气的物质的量为 6 ÷ 24 = 0.25 mol。
6. Percentage Yield | 百分产率
The percentage yield compares the mass of product actually obtained from an experiment to the maximum theoretical mass predicted by stoichiometry. It is a measure of the efficiency of a reaction.
百分产率将实验实际得到的产品质量与通过化学计量学预测的最大理论质量进行比较，是衡量反应效率的指标。
Percentage yield = (actual yield ÷ theoretical yield) × 100%
Actual yield comes from experimental data, while theoretical yield is calculated from the mole ratio in the balanced equation and the limiting reactant. The value is usually less than 100% due to incomplete reactions, side reactions and losses during purification.
实际产率来自实验数据，理论产率则根据配平方程式和限量反应物的摩尔比计算得出。由于反应不完全、副反应以及提纯过程中的损失，百分产率通常小于 100%。
Always make sure both yields have the same units (grams or moles) before dividing. The percentage yield never exceeds 100% in valid experimental reporting.
务必确保实际产率与理论产率单位相同（同为克或同为摩尔）后再相除。在有效的实验报告中百分产率不会超过 100%。
7. Atom Economy | 原子经济性
Atom economy measures the proportion of reactant atoms that end up in the desired product. It is a critical concept in green chemistry and is frequently assessed in WJEC papers.
原子经济性衡量有多少比例的反应物原子进入了目标产物。它是绿色化学中的关键概念，在 WJEC 试题中经常涉及。
Atom economy = (Mᵣ of desired product ÷ sum of Mᵣ of all reactants) × 100%
All reactants in the balanced equation must be included in the denominator. A higher atom economy means less waste and more sustainable industrial processes.
分母必须包含配平方程式中所有反应物的相对式量。原子经济性越高，意味着废物越少、工业过程更可持续。
For example, in the production of iron from iron(III) oxide: Fe₂O₃ + 3CO → 2Fe + 3CO₂, the desired product is Fe. Atom economy = (2 × 56) ÷ [(2×56 + 3×16) + 3×(12+16)] × 100%. Practice with different reactions to become fluent at extracting Mᵣ values from the equation.
例如，用氧化铁炼铁：Fe₂O₃ + 3CO → 2Fe + 3CO₂，目标产物是 Fe。原子经济性 = (2×56) ÷ [(2×56+3×16) + 3×(12+16)] × 100%。多练习不同反应，熟练从方程式中提取 Mᵣ 值。
8. Energy Changes (Calorimetry) | 能量变化（量热法）
When reactions are carried out in solution, the heat exchanged can be measured using a simple calorimeter. The thermal energy transferred, Q, is calculated from the mass of the solution, its specific heat capacity and the temperature change.
当反应在溶液中进行时，热量变化可用简易量热计测量。传递的热能 Q 可根据溶液质量、比热容和温度变化计算。
Q = m × c × ΔT
where m is the mass of the solution (g), c is the specific heat capacity of water (4.18 J/g°C) and ΔT is the temperature change (°C). Q is obtained in joules (J).
其中 m 为溶液的质量 (g)，c 为水的比热容 (4.18 J/g°C)，ΔT 为温度变化 (°C)。Q 的单位为焦耳 (J)。
ΔH = − Q ÷ (1000 × n) or ΔH = − Q ÷ n (with Q in kJ)
The molar enthalpy change ΔH is found by dividing the energy by the number of moles of the limiting reactant that reacted. The negative sign is placed for exothermic reactions (temperature rises) to give a negative ΔH; endothermic reactions give a positive ΔH. Remember to convert Q to kJ by dividing by 1000 if your ΔH is required in kJ/mol.
摩尔焓变 ΔH 通过将热能除以发生反应的限量反应物的物质的量得到。放热反应（温度升高）取负值，使 ΔH 为负；吸热反应 ΔH 为正。注意若 ΔH 要求以 kJ/mol 表示，需将 Q 除以 1000 转换为 kJ。
9. Rates of Reaction | 反应速率
The rate of a chemical reaction can be measured by monitoring how quickly a reactant is used up or how quickly a product is formed. Quantitative rates appear regularly in WJEC data analysis questions.
化学反应速率可通过监测反应物消耗的快慢或产物生成的快慢来测量。定量的速率计算常出现在 WJEC 的数据分析题中。
Mean rate = quantity of product formed ÷ time taken
Mean rate = quantity of reactant used ÷ time taken
The quantity can be measured in various units: mass (g), volume of gas (cm³), concentration (mol/dm³) or even color intensity. The unit of rate then becomes g/s, cm³/s, mol/dm³/s accordingly.
量的单位可以是质量 (g)、气体体积 (cm³)、浓度 (mol/dm³) 甚至颜色深浅，速率的单位随之变为 g/s、cm³/s、mol/dm³/s 等。
For a graph, the rate at a specific point (instantaneous rate) is found by drawing a tangent and calculating its gradient. Gradient = change in y ÷ change in x.
对于曲线图，某一时刻的速率（瞬时速率）通过作切线并计算切线斜率求得：斜率 = y 的变化量 ÷ x 的变化量。
10. Titration Calculations | 滴定计算
Titration allows the determination of an unknown concentration by reacting it with a solution of known concentration. The key relationship uses the mole ratio from the balanced equation.
滴定通过与已知浓度的溶液反应来测定未知浓度。关键关系来自配平方程式中的摩尔比。
n = c × V
where c is the concentration in mol/dm³ and V is the volume in dm³. Since burette readings are usually given in cm³, you must first convert volume to dm³ by dividing by 1000.
其中 c 为物质的量浓度 (mol/dm³)，V 为体积 (dm³)。由于滴定管读数通常以 cm³ 为单位，必须先除以 1000 转换成 dm³。
The titration calculation steps:
1. Calculate moles of the known solution using n = c × V (dm³).
2. Use the balanced equation to find the mole ratio and determine moles of the unknown solute.
3. Calculate the unknown concentration using c = n ÷ V (dm³) or mass using m = n × M.
滴定计算步骤：
1. 用 n = c × V (dm³) 计算已知溶液中溶质的物质的量。
2. 利用配平方程式中的摩尔比，求出未知溶质的物质的量。
3. 通过 c = n ÷ V (dm³) 计算未知浓度，或通过 m = n × M 计算质量。
Always check that the volumes in dm³ match the titration volumes. Concordant titres (within 0.10 cm³) are used to obtain an average volume for accurate results.
务必确保 dm³ 体积与滴定体积对应。使用吻合的滴定值（相差不超过 0.10 cm³）来计算平均体积，以获得准确结果。
11. Converting Units | 单位换算
Unit errors are among the most common mistakes in GCSE Chemistry calculations. Becoming fluent in these conversions will prevent loss of marks throughout the paper.
单位换算是 GCSE 化学计算中最常见的错误之一。熟练掌握这些换算能避免整卷失分。
Volume: 1 dm³ = 1000 cm³
Mass: 1 kg = 1000 g; 1 tonne = 10⁶ g
Energy: 1 kJ = 1000 J
When using gas volumes, ensure you have converted cm³ to dm³ before applying the 24 dm³/mol rule. If a question gives a volume of 240 cm³, convert to 0.240 dm³ first.
使用气体体积时，先确认已将 cm³ 转换为 dm³ 再应用 24 dm³/mol 规则。若题目给出 240 cm³，先转换为 0.240 dm³。
In calorimetry, the mass of the solution is often taken as equal to its volume in cm³ because the density of dilute aqueous solutions is approximately 1 g/cm³.
在量热法中，溶液质量常直接取用其体积数值 (cm³)，因为稀水溶液的密度约为 1 g/cm³。
12. Summary of Key Equations | 关键方程式总结
The table below brings together all the essential formulas you need to memorise for the WJEC GCSE Chemistry examination. Use it as a quick reference while practising past paper questions.
下表汇总了你为 WJEC GCSE 化学考试需要记忆的所有核心公式。可在练习真题时用作快速查阅。
| Quantity | Equation | Units |
| Moles from mass | n = m / M | mol, g, g/mol |
| Mass concentration | Conc. (g/dm³) = mass / volume | g/dm³, g, dm³ |
| Molar concentration | c = n / V | mol/dm³, mol, dm³ |
| Gas volume (RTP) | V (dm³) = n × 24 | dm³, mol |
| Percentage yield | (actual / theoretical) × 100% | % |
| Atom economy | (Mᵣ desired / Σ Mᵣ reactants) × 100% | % |
| Heat energy (calorimetry) | Q = m × c × ΔT | J, g, J/g°C, °C |
| Molar enthalpy change | ΔH = − Q / (1000 × n) | kJ/mol, J, mol |
| Mean rate of reaction | rate = quantity / time | 更多咨询请联系16621398022（同微信）
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