Year 11 WJEC Chemistry: Quick Revision Formula & Theorem Handbook | WJEC 化学公式定理速查手册

📚 Year 11 WJEC Chemistry: Quick Revision Formula & Theorem Handbook | WJEC 化学公式定理速查手册

This revision handbook brings together all the essential formulae and key theorems from the Year 11 WJEC Chemistry specification. It is designed as a quick-reference tool for last-minute revision, helping you consolidate the quantitative and conceptual foundations needed for your exam. Each section pairs the core relationships with worked-style explanations, so you can swiftly recall definitions, units and typical calculation steps.

本速查手册汇集了 WJEC 化学 Year 11 课程中所有核心公式和关键定理。它旨在作为考前快速回顾的工具，帮助你巩固考试所需的定量计算与概念基础。每个章节都将核心关系与解释配对呈现，让你快速回忆起定义、单位和典型计算步骤。

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1. Relative Atomic Mass (A_r) and Relative Formula Mass (M_r) | 相对原子质量与相对分子质量

Relative atomic mass, A_r, is the weighted average mass of an atom of an element compared to 1/12th the mass of a carbon‑12 atom. It has no units. For an element like chlorine, the A_r of 35.5 arises from the isotopic mixture of ³⁵Cl and ³⁷Cl.

相对原子质量（A_r）是元素一个原子的加权平均质量与碳‑12 原子质量的 1/12 相比的比值，没有单位。像氯这样的元素，其 A_r 为 35.5，来源于 ³⁵Cl 和 ³⁷Cl 同位素的混合。

The relative formula mass, M_r, for a compound is the sum of the A_r values of all atoms in its formula. For example, M_r of H₂O = (2 × 1) + 16 = 18. This is used directly in mole calculations.

对于化合物，相对分子质量（M_r）等于其化学式中所有原子的 A_r 总和。例如，H₂O 的 M_r = (2 × 1) + 16 = 18。此值直接用于摩尔计算。

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2. The Mole and Avogadro's Constant | 摩尔与阿伏伽德罗常数

One mole of any substance contains exactly 6.02 × 10²³ specified particles (atoms, molecules, ions or formula units). This number is Avogadro's constant, N_A. The mole allows chemists to count particles by weighing.

一摩尔的任何物质恰好含有 6.02 × 10²³ 个指定微粒（原子、分子、离子或化学式单元）。这个数值就是阿伏伽德罗常数，N_A。摩尔使化学家能够通过称量来“数”微粒。

The relationship between number of particles, N, and amount in moles, n, is:

N = n × N_A

微粒数 N 与摩尔数 n 的关系为：

N = n × N_A

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3. Calculating Moles from Mass | 质量与摩尔数的换算

The core mole‑mass equation links the mass of a substance to its molar mass:

n = m / M_r

where n is the amount in mol, m is the mass in grams (g), and M_r is the relative formula mass in g mol^-1.

n = m / M_r

其中 n 为物质的量（mol），m 为质量（g），M_r 为相对分子质量（g mol^-1）。

For example, to find the moles in 8 g of NaOH (M_r mol. This equation is fundamental to almost every quantitative chemistry problem in WJEC.

例如，计算 8 g NaOH (M_r = 40) 的摩尔数：n = 8 / 40 = 0.20 mol。该公式是 WJEC 中几乎所有化学定量问题的基础。

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4. Moles of Gases at Room Temperature and Pressure (RTP) | 室温常压下气体的摩尔体积

At room temperature (20 °C) and atmospheric pressure, one mole of any gas occupies 24 dm³ (24 000 cm³). This fixed molar volume, V_m, is invaluable for converting between moles and gas volumes.

在室温（20 °C）和常压下，1 mol 任何气体的体积为 24 dm³（24 000 cm³）。这个固定的摩尔体积 V_m 对于摩尔与气体体积之间的换算极为重要。

Volume (dm³) = n × 24

Volume (cm³) = n × 24 000

For instance, 0.5 mol of CO₂ dm³. This directly links stoichiometry to measurable gas volumes in reactants or products.

例如，0.5 mol CO₂ 的体积为 0.5 × 24 = 12 dm³。这将化学计量比与可测的气体体积直接联系起来。

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5. Concentration of Solutions | 溶液浓度

Concentration in mol dm^-3 relates the amount of solute to total solution volume:

c = n / V

where c is concentration (mol dm^-3), n is moles of solute, and V is volume in dm³ (1 dm³ = 1 000 cm³).

c = n / V

其中 c 为浓度（mol dm^-3），n 为溶质的摩尔数，V 为溶液体积（dm³，1 dm³ = 1 000 cm³）。

You may also see mass concentration in g dm^-3. To convert: concentration (mol dm^-3) = concentration (g dm^-3) / M_r. This becomes crucial when preparing standard solutions.

你也可能遇到质量浓度（g dm^-3）。换算关系为：浓度（mol dm^-3）= 浓度（g dm^-3）/ M_r。这在配制标准溶液时至关重要。

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6. Titration Calculations | 滴定计算

e unknown concentration to a standard solution. For a general reaction aA + bB → products,

c_AV_A / a = c_BV_B / b

where c_A and V_A are the concentration and volume of acid, and c_B, V_B those of base, with a and b the stoichiometric coefficients.

c_AV_A / a = c_BV_B / b

其中 c_A 和 V_A 为酸的浓度和体积，c_B、V_B 为碱的浓度和体积，a 与 b 为计量系数。

For a simple 1:1 neutralisation, such as HCl + NaOH → NaCl + H₂O, the equation simplifies to:

c_acidV_acid = c_baseV_base

Always ensure volumes are in dm³ (or cm³ consistently) and use the average titre from concordant results.

对于简单的 1:1 中和反应，如 HCl + NaOH → NaCl + H₂O，公式简化为：

c_酸V_酸 = c_碱V_碱

务必确保体积单位统一（dm³ 或一致使用 cm³），并使用几次吻合读数的平均滴定体积。

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7. Percentage Yield | 百分产率

Percentage yield compares the mass of product actually obtained with the maximum theoretical mass predicted from stoichiometry:

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

Reasons for a yield below 100% include incomplete reaction, side reactions, or product lost during purification (filtration, evaporation, transferring). A yield above 100% usually indicates an impurity or weighing error.

% 产率 = (实际产量 / 理论产量) × 100

产率低于 100% 的原因包括反应不完全、副反应发生，或产物在纯化（过滤、蒸发、转移）中损失。产率高于 100% 通常意味着产物不纯或称量错误。

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8. Atom Economy | 原子经济性

Atom economy measures how efficiently reactant atoms end up in the desired product. A higher atom economy indicates a greener process with less waste.

Atom Economy = (M_r of desired product / sum of M_r of all reactants) × 100

For the reaction A + B → product + by‑ nts for all reactants. Improving atom economy is a key principle in sustainable chemistry.

原子经济性 = (目标产物的 M_r / 所有反应物的 M_r 总和) × 100

对于 A + B → 产物 + 副产物 的反应，只有目标产物出现在分子中，而分母包含所有反应物的 M_r。提高原子经济性是可持续化学的一个核心原则。

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9. Empirical and Molecular Formulae | 实验式与分子式

The empirical formula shows the simplest whole‑number ratio of atoms in a compound. It is determined from the percentage composition by mass or from directly measured masses. The steps are:

• Divide each element's mass (or %) by its A_r to obtain relative moles.
• Divide all mole values by the smallest to find the simplest ratio.
• If necessary, multiply to convert fractions into whole numbers.

分子式表示化合物中各原子的最简整数比。它可以通过质量百分组成或直接测量的质量推导得出。步骤如下：

• 将每种元素的质量（或百分比）除以其 A_r，得到相对摩尔数。
• 将所有摩尔值除以其中最小值，求出最简比。
• 必要时通过乘法将分数化为整数。

To find the molecular formula, you need the compound's M_r:

n = M_r / (empirical formula mass)

then multiply the empirical formula subscripts by n. For example, a compound with empirical formula CH₂ and M_r of 56 has n = 56/14 = 4, giving the molecular formula C₄H₈.

要得到分子式，需要知道化合物的 M_r：

n = M_r / (实验式的相对质量)

然后将实验式角标乘以 n。例如，实验式为 CH₂、M_r 为 56 的化合物，n = 56/14 = 4，分子式为 C₄H₈。

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10. Energy Changes in Reactions | 反应中的能量变化

For reactions carried out in solution, the energy transferred to the surroundings (or absorbed) can be calculated using:

Q = m c ΔT

where Q is the heat energy (J), m is the mass of water or solution (g), c is the specific heat capacity (4.18 J g^-1 °C^-1 for water), and ΔT is the temperature change.

对于在溶液中进行的反应，传递到环境（或吸收）的能量可用下式计算：

Q = m c ΔT

其中 Q 为热能（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。

To find the molar enthalpy change, ΔH, divide the energy by the moles of limiting reactant:

ΔH = −Q / n

The negative sign is used for exothermic reactions (ΔH negative) so that the calculated value reflects energy lost to the surroundings. For endothermic reactions, ΔH is positive. In WJEC, you are usually expected to calculate the energy change per mole without sign conventions for simple experiments, but understanding the sign strengthens your answer.

要得到摩尔焓变 ΔH，将能量除以限制反应物的摩尔数：

ΔH = −Q / n

放热反应（ΔH 为负值）中使用负号，使计算值反映释放到环境中的能量。吸热反应 ΔH 为正值。在 WJEC 中，简单实验通常只要求计算每摩尔的能量变化而不强调符号，但理解符号会使你的答案更严谨。

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11. Rate of Reaction | 反应速率

The average rate of a chemical reaction measures how quickly a reactant is consumed or a product is formed over a time interval:

Rate = change in concentration (or mass, volume) / time taken

Units depend on what is measured, e.g. cm³ s^-1 or g s^-1. The rate can be obtained from the gradient of a concentration–time or volume–time graph.

平均反应速率衡量在一段时间内反应物消耗或产物生成的快慢：

速率 = 浓度（或质量、体积）的变化量 / 所用时间

单位取决于测量对象，例如 cm³ s^-1 或 g s^-1。速率可通过浓度–时间或体积–时间曲线的切线斜率求得。

Collision theory explains that for a reaction to occur, particles must collide with sufficient energy (activation energy) and correct orientation. Increasing temperature, concentration, surface area or the use of a catalyst all increase the frequency and/or effectiveness of collisions, thereby raising the rate.

碰撞理论解释：反应发生的条件是微粒必须发生碰撞，且具有足够的能量（活化能）和正确的取向。升高温度、增大浓度、增加固体表面积或使用催化剂，都能提高碰撞频率和/或碰撞有效性，从而提高反应速率。

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12. Reversible Reactions and Dynamic Equilibrium | 可逆反应与动态平衡

Many chemical reactions are reversible, indicated by the symbol ⇌. At dynamic equilibrium, the forward and reverse reactions proceed at equal rates, so the macroscopic concentrations of reactants and products remain constant. Equilibrium can only be achieved in a closed system.

许多化学反应是可逆的，用符号 ⇌ 表示。在动态平衡状态下，正反应和逆反应速率相等，因此反应物和产物的宏观浓度保持恒定。只有在封闭体系中才能达到平衡。

Le Chatelier's principle states: if a system at equilibrium experiences a change in concentration, temperature or pressure, the position of equilibrium shifts to counteract that change. For example, increasing the concentration of a reactant shifts equilibrium to the right; raising temperature favours the endothermic direction; increasing pressure favours the side with fewer gas molecules.

勒夏特列原理指出：如果处于平衡的体系受到浓度、温度或压力的影响，平衡位置将移动以抵消该影响。例如，增加反应物浓度会使平衡向右移动；升高温度有利于吸热方向；增大压强有利于气体分子数较少的一侧。

In the WJEC course, understanding these qualitative shifts is essential for interpreting industrial processes such as the Haber process and the Contact process, where conditions are chosen to optimise yield, rate and economic factors.

在 WJEC 课程中，理解这些定性移动对于解释哈伯法、接触法等工业过程至关重要，这些过程的工艺条件正是为了在产率、速率和经济性之间取得最佳平衡。

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