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Year 10 CAIE Chemistry: Formulae & Theorems Quick Reference | Year 10 CAIE 化学：公式定理速查手册

2026-07-20 21:09 · 本文部分内容由AI辅助创作

📚 Year 10 CAIE Chemistry: Formulae & Theorems Quick Reference | Year 10 CAIE 化学：公式定理速查手册

This handbook provides a concise summary of the essential formulas and theorems in the Year 10 CAIE Chemistry syllabus. It is designed for quick revision and handy reference, so that you can recall each relationship, substitute the correct units and solve quantitative questions with confidence in both paper 2 (multiple choice) and paper 4 (theory).

本手册简明总结了 Year 10 CAIE 化学课程中的基本公式与定理，旨在方便快速复习和查阅。它帮助你快速回忆每个关系式、代入正确的单位，并在选择题（Paper 2）与理论题（Paper 4）中自信地解决定量计算问题。

Every formula below is written in the form used by Cambridge examiners. Where a symbol has a standard meaning (n for amount of substance in moles, m for mass, V for volume, c for concentration), the same symbol is kept throughout the whole handbook so that you never have to re-learn notation.

下文所有公式均采用剑桥考官的书写习惯。凡有标准含义的符号（n 表示物质的量，单位 mol；m 表示质量；V 表示体积；c 表示浓度），全篇保持一致，避免你在不同章节之间反复适应符号变化。

1. Relative Atomic Mass and Molar Mass | 相对原子质量与摩尔质量

The relative atomic mass (Aᵣ) is the ratio of the average mass of an atom of an element to 1/12 of the mass of a carbon-12 atom. It has no units, and its value is the weighted average of the masses of all naturally occurring isotopes of that element.

相对原子质量 (Aᵣ) 是某元素原子的平均质量与碳-12 原子质量 1/12 的比值，没有单位。它的数值等于该元素所有天然同位素质量的加权平均值。

The relative molecular mass (Mᵣ) is the sum of the Aᵣ values of all the atoms in a molecule. For ionic compounds, which exist as giant lattices rather than discrete molecules, the same calculation gives the relative formula mass, and the symbol Mᵣ is still used.

相对分子质量 (Mᵣ) 是分子中所有原子 Aᵣ 之和。对于以巨型晶格存在、并非独立分子的离子化合物，同样的计算得到的是相对式量，符号仍写作 Mᵣ。

he bridge between the microscopic world of atoms and the macroscopic world of the balance.

摩尔质量 (M) 是一摩尔物质的质量，单位为 g mol⁻¹。对原子，M = Aᵣ g mol⁻¹；对分子，M = Mᵣ g mol⁻¹。它是原子微观世界与天平宏观世界之间的桥梁。

To calculate Aᵣ from isotopic abundances:

根据同位素丰度计算 Aᵣ：

Aᵣ = (m₁ × %₁ + m₂ × %₂ + ...) / 100

where mᵢ is the isotopic mass of isotope i and % s its percentage abundance. For chlorine, with isotopes of mass 35 and 37 in abundances 75% and 25%, Aᵣ = (35 × 75 + 37 × 25) / 100 = 35.5.

其中 mᵢ 为第 i 种同位素的质量，%ᵢ 为其丰度百分比。以氯为例，质量数 35 与 37 的同位素丰度分别为 75% 和 25%，则 Aᵣ = (35 × 75 + 37 × 25) / 100 = 35.5。

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

cules, ions, electrons, formula units, and so on). This number is the Avogadro constant, NA = 6.02 × 10²³ mol⁻¹.

一摩尔是含有 6.02 × 10²³ 个指定微粒（原子、分子、离子、电子、式量单元等）的物质的量。这个数值称为阿伏伽德罗常数，NA = 6.02 × 10²³ mol⁻¹。

The number of particles is related to the amount in moles by a single equation, which is simply a definition rearranged:

微粒数与物质的量之间由一个方程联系，它其实就是定义的变形：

N = n × NA      n = N / NA

The word 'specified' f hydrogen molecules, H₂, contains 6.02 × 10²³ molecules and therefore 1.204 × 10²⁴ atoms.

考试题干中"指定"二字非常关键。一摩尔氢原子 H 含 6.02 × 10²³ 个原子；而一摩尔氢分子 H₂ 含 6.02 × 10²³ 个分子，因此含 1.204 × 10²⁴ 个原子。

Always name the particle you are counting. In 1 mol of water, H₂O, there are 1 mol of oxygen atoms and 2 mol of hydrogen atoms, giving 3 mol of atoms in total. Avogadro's constant is only ever used to convert between a count of particles and moles, never directly to a mass.

务必写出你所数的微粒名称。1 mol 水 H₂O 中含 1 mol 氧原子和 2 mol 氢原子，共 3 mol 原子。阿伏伽德罗常数只用于"微粒数与物质的量"之间的换算，绝不能直接用于质量。

3. Mass, Concentration and Gas Volume | 质量、浓度与气体体积

Amount of substance is the central hub of Year 10 quantitative chemistry. Three different measured quantities can all be converted into moles, and once you are in moles every other calculation becomes possible.

物质的量是 Year 10 定量化学的核心枢纽。三种不同的可测量物理量都能换算成摩尔，而一旦进入"摩尔"，其余计算便水到渠成。

n = m / M      n = c × V      n = V / 24

In the first equation, m is the mass in grams and M is the molar mass in g mol⁻¹. In the second, c is the concentration in mol dm⁻³ and V is the volume of solution in dm³. In the third, V is the volume of gas in dm³ measured at room temperature and pressure (r.t.p.), where the molar gas volume is 24 dm³ mol⁻¹.

第一式中 m 为质量（g），M 为摩尔质量（g mol⁻¹）。第二式中 c 为浓度（mol dm⁻³），V 为溶液体积（dm³）。第三式中 V 为室温常压（r.t.p.）下气体的体积（dm³），此时摩尔气体体积为 24 dm³ mol⁻¹。

n quotes a volume in cm³ and a concentration in mol dm⁻³, you must divide the volume by 1000 before multiplying.

单位换算是失分最多的地方。记住 1 dm³ = 1000 cm³，因此 25.0 cm³ = 0.0250 dm³。若题目给出 cm³ 的体积和 mol dm⁻³ 的浓度，相乘之前必须先把体积除以 1000。

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

The empirical formula is the simplest whole-number ratio of atoms of each element in a compound. The molecular formula is the actual number of atoms in one molecule, and it is always a whole-number multiple of the empirical formula.

经验式（最简式）是化合物中各元素原子数的最简单整数比；分子式是一个分子中实际的原子数目，它总是经验式的整数倍。

The standard four-step method works whether the data is given as masses or as percentage composition:

无论题目给出的是质量还是质量分数，标准四步法都适用：

For a compound containing 40.0% carbon, 6.7% hydrogen and 53.3% gives C : H : O = 1 : 2 : 1, so the empirical formula is CH₂O and its formula mass is 30.

某化合物含 40.0% 碳、6.7% 氢、53.3% 氧：C = 40.0 / 12 = 3.33，H = 6.7 / 1 = 6.7，O = 53.3 / 16 = 3.33。同除以 3.33 得 C : H : O = 1 : 2 : 1，故经验式为 CH₂O，式量为 30。

n = Mᵣ (molecular) / formula mass (empirical)

₆H₁₂O₆. Always finish by multiplying every subscript in the empirical formula by that whole number.

若测得 Mᵣ = 180，则 n = 180 / 30 = 6，分子式为 C₆H₁₂O₆。最后一步务必把经验式中每个下标都乘以该整数。

5. Equations, Limiting Reagents and Percentage Yield | 方程式、限量试剂与产率

A balanced chemical equation is a statement of molar ratio. The coefficients tell you the ratio in which particles react, and the same ratio applies to moles, to gas volumes at the same temperature and pressure, and to the moles of ions in solution.

配平后的化学方程式本质上是"摩尔比"的陈述。系数表示微粒反应的比，同样的比例也适用于物质的量、同温同压下的气体体积，以及溶液中离子的物质的量。

les of hydrogen react with one mole of oxygen to give two moles of water. Note that 2 mol of H₂ (4 g) and 1 mol of O₂ (32 g) give 2 mol of H₂O (36 g), which confirms conservation of mass.

对于反应 2H₂ + O₂ → 2H₂O，2 mol 氢与 1 mol 氧反应生成 2 mol 水。注意 2 mol H₂（4 g）与 1 mol O₂（32 g）生成 2 mol H₂O（36 g），验证了质量守恒。

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The limiting reagent is the reactant that is used up first; it determines the maximum amount of product. To identify it, divide the amount of each reactant by its coefficient in the balanced equation. The smallest value belongs to the limiting reagent.

限量试剂是最先被消耗完的反应物，它决定产物的最大量。判断方法：将各反应物的物质的量除以其在方程式中的系数，所得最小值对应的即为限量试剂。

Percentage yield = (actual yield / predicted yield) × 100%

The predicted yield is the maximum mass calculated from the limiting reagent using the molar ratio. The actual yield is the mass you really obtain, always the smaller value, because of incomplete reactions, side reactions, transfer losses and impurities.

理论产量是根据限量试剂与摩尔比算出的最大质量；实际产量是实验中真实得到的质量，它总是更小，原因包括反应不完全、副反应、转移损失和杂质等。

6. Atom Economy and Reacting Mass Calculations | 原子经济性与反应质量计算

Atom economy measures how much of the reactant atoms end up in the desired product. It is a green-chemistry concept and a favourite in structured questions, because it compares the efficiency of competing routes rather than the skill of the experimenter.

原子经济性衡量有多少反应物原子最终进入目标产物。它属于绿色化学概念，也是简答题中的常客，因为它比较的是不同合成路线的效率，而非实验者的操作水平。

Atom economy = (Mᵣ of desired product / Σ Mᵣ of all reactants) × 100%

Remember that the denominator includes every reactant, even cheap or 'unimportant' ones, and that coefficients must be included when the equation is not 1 : 1. A reaction with only one product, such as an addition reaction, always has 100% atom economy.

注意：分母必须包含全部反应物，哪怕是廉价或"不重要"的试剂；当方程式不是 1 : 1 时，还要乘上系数。只有一种产物的反应（如加成反应）原子经济性恒为 100%。

Reacting mass calculations follow a reliable four-step route: convert the given mass to moles, apply the molar ratio from the equation, convert back to moles of the required substance, and finally multiply by its molar mass. Percentage yield and atom economy are separate quantities and must not be confused.

反应质量计算遵循可靠的"四步法"：把已知质量换算为物质的量 → 按方程式摩尔比换算 → 换算为目标物质的物质的量 → 乘以目标物质的摩尔质量。产率与原子经济性是两回事，切勿混淆。

7. Concentration, Dilution and Titration | 浓度、稀释与滴定

Concentration is the amount of solute per unit volume of solution. Cambridge uses mol dm⁻³ as the standard unit, but g dm⁻³ also appears, especially in rates experiments.

浓度是单位体积溶液中所含溶质的量。剑桥以 mol dm⁻³ 为标准单位，但 g dm⁻³ 也会出现，尤其在反应速率实验中。

c = n / V      concentration in g dm⁻³ = concentration in mol dm⁻³ × M

When a solution is diluted with water, the amount of solute does not change, only the volume. This gives the dilution equation, which is extremely quick to use in multi-step questions.

用水稀释溶液时，溶质的物质的量不变，改变的只有体积。由此得到稀释公式，在多步计算中非常高效。

c₁ × V₁ = c₂ × V₂

In a titration, a solution of known concentration is added from a burette to a measured volume of the unknown solution until the indicator changes colour. The calculation uses the molar ratio from the balanced equation:

滴定中，用滴定管把已知浓度的溶液滴入已量取体积的待测溶液中，直至指示剂变色。计算依据配平方程式的摩尔比：

n(A) / n(B) = a / b      cA × VA / a = cB × VB / b

Here a and b are the coefficients of A and B in the equation. Always convert the burette reading from cm³ to dm³, and always use the average of concordant titres, which normally agree to within 0.10 cm³.

其中 a、b 为 A、B 在方程式中的系数。务必把滴定管读数由 cm³ 换算为 dm³，并使用相互吻合的滴定体积平均值，通常要求彼此相差不超过 0.10 cm³。

8. Bond Energies and Enthalpy Change | 键能与焓变

Energy is absorbed when bonds are broken and released when bonds are formed. The overall enthalpy change of a reaction is therefore the difference between these two quantities.

断键吸收能量，成键放出能量。因此反应的总焓变就是这两个量之差。

ΔH = Σ bond energies broken − Σ bond energies formed

Bond energies are quoted in kJ mol⁻¹ and are always positive numbers, because breaking a bond requires energy. If the energy released in forming new bonds is greater than the energy absorbed in breaking old ones, ΔH is negative and the reaction is exothermic.

键能以 kJ mol⁻¹ 表示，且恒为正数，因为断键需要吸收能量。若成键放出的能量大于断键吸收的能量，则 ΔH 为负值，反应放热。

s − energy of reactants when using an energy level diagram. Exothermic reactions have a negative ΔH and the products sit lower than the reactants; endothermic reactions have a positive ΔH and the products sit higher.

等价地，用能量图表示时 ΔH = 产物能量 − 反应物能量。放热反应 ΔH 为负，产物能量低于反应物；吸热反应 ΔH 为正，产物能量高于反应物。

9. Rates of Reaction | 反应速率

Rate of reaction is the change in the amount of a reactant or product per unit time. In practical work this is measured as the loss of mass of a flask, the volume of gas collected, or the time taken for a cross to disappear.

反应速率是单位时间内反应物或产物数量的变化。实验上常以锥形瓶质量减少、收集到的气体体积，或"十字消失"所需时间来测量。

rate = change in amount / time taken

On a graph of volume of gas against time, the rate at any instant is the gradient of the curve at that point. Because the gradient steadily decreases for most reactions, it should be found by drawing a tangent, not by dividing the total volume by the total time.

在"气体体积—时间"图像上，任意时刻的速率等于该点曲线的斜率。由于大多数反应斜率逐渐减小，必须通过画切线求得，而不能用总体积除以总时间。

The four factors that increase the rate are all explained by collision theory: a higher concentration or pressure, a higher temperature, a larger surface area of solid, and the presence of a catalyst. Each one increases either the frequency of collisions or the fraction of collisions that have energy greater than the activation energy.

提高速率的四个因素都可用碰撞理论解释：更高的浓度或压强、更高的温度、更大的固体表面积，以及使用催化剂。它们分别提高了碰撞频率，或提高了能量大于活化能的碰撞所占的比例。

10. Electrolysis: Charge and Amount | 电解：电荷与物质的量

In electrolysis, the amount of substance produced at an electrode is proportional to the quantity of charge passed. Charge is the product of current and time, and one mole of electrons carries a charge of 96500 C.

在电解中，电极上析出物质的量与通过的电量成正比。电量等于电流与时间的乘积，而一摩尔电子所带电荷为 96500 C。

Q = I × t      n(e⁻) = Q / 96500

Q is measured in coulombs, I in amperes and t in seconds. If the current is given in amperes and the time in minutes, convert the time to seconds before multiplying, otherwise every subsequent step will be wrong.

Q 的单位为库仑（C），I 为安培（A），t 为秒（s）。若时间以分钟给出，必须先换算为秒再相乘，否则后续每一步都会出错。

electrons deposit 1 mol of copper, so the mass deposited is found from mass = n(Cu) × Aᵣ.

半反应式告诉你每生成 1 mol 产物需要多少摩尔电子。例如 Cu²⁺ + 2e⁻ → Cu，表示 2 mol 电子析出 1 mol 铜，故析出质量由 质量 = n(Cu) × Aᵣ 求得。