SQA Chemistry Quick Reference: Formulas & Theorems | SQA 化学：公式定理速查手册

📚 SQA Chemistry Quick Reference: Formulas & Theorems | SQA 化学：公式定理速查手册

This quick reference guide brings together the essential formulas and theorems you need for Year 11 SQA Chemistry. It is designed to help you recall key relationships in quantitative chemistry, reaction rates, acids and bases, bonding and energy. Each entry is paired with a short explanation to show how it is used in problem‑solving and in understanding chemical principles.

本速查手册汇集了 Year 11 SQA 化学必备的核心公式与定理。手册帮助你快速回顾定量化学、反应速率、酸碱、化学键与能量变化中的关键关系。每一条公式都配有简短说明，展示如何在解题和理解化学原理中应用它们。

1. The Mole and Molar Mass | 物质的量与摩尔质量

The mole is the chemist’s counting unit, linking the mass of a substance to the number of particles it contains. The fundamental relationship is:

物质的量（摩尔）是化学家计数的单位，它将物质的质量与所含粒子的数目联系起来。基本关系为：

n = m / M

where n is the amount of substance in moles (mol), m is the mass in grams (g) and M is the molar mass in grams per mole (g mol⁻¹). Molar mass is numerically equal to the relative atomic mass (Aᵣ) or relative formula mass (Mᵣ) of the substance, taken from the Periodic Table.

其中 n 是物质的量（mol），m 是质量（g），M 是摩尔质量（g mol⁻¹）。摩尔质量在数值上等于该物质的相对原子质量 (Aᵣ) 或相对式量 (Mᵣ)，数据取自周期表。

2. Concentration of Solutions | 溶液的浓度

The concentration of a solution tells us how much solute is dissolved in a given volume of solvent. It is most often expressed in mol l⁻¹.

溶液的浓度表示在给定体积的溶剂中溶解了多少溶质，最常用的单位是 mol l⁻¹。

c = n / V

Here c is concentration (mol l⁻¹), n is the amount of solute (mol), and V is the volume of solution in litres (l). If the volume is given in cm³, divide by 1000 to convert to litres. This formula can be rearranged to n = c × V or V = n / c.

此处 c 是浓度（mol l⁻¹），n 是溶质的物质的量（mol），V 是溶液的体积（l）。如果体积以 cm³ 给出，需除以 1000 转换为升。此式可变形为 n = c × V 或 V = n / c。

3. Molar Volume of Gases | 气体的摩尔体积

oom temperature and pressure (≈20 °C, 1 atm), the molar volume of any gas is approximately 24.0 l mol⁻¹.

在相同温度和压强下，不同气体的相同物质的量占有相同的体积。在常温常压下（≈20 °C, 1 atm），任何气体的摩尔体积约为 24.0 l mol⁻¹。

V = n × 24.0 (at RTP)

where V is the volume of the gas in litres and n is the amount in moles. This relationship is used to calculate the number of moles from a gas volume or to find the volume from a known amount of gas. If conditions differ, an appropriate conversion may be required.

式中 V 是气体体积（l），n 是物质的量（mol）。此关系式用于由气体体积求物质的量，或由已知物质的量求体积。若条件不同，可能需要相应的换算。

4. Percentage Yield and Atom Economy | 产率与原子经济性

Chemists measure the efficiency of a reaction in two ways: percentage yield and atom economy. Percentage yield compares the actual mass of product obtained with the theoretical mass predicted by stoichiometry.

化学家用两种方法衡量反应的效率：产率和原子经济性。产率比较实际获得的产品质量与通过化学计量计算的理论质量。

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

Atom economy, on the other hand, considers how much of the starting materials ends up in the desired product, helping to design greener syntheses.

另一方面，原子经济性考察有多少起始原料进入了目标产物，有助于设计更绿色的合成路线。

% Atom Economy = (Mᵣ of desired product / total Mᵣ of all reactants) × 100

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

The empirical formula gives the simplest whole‑number ratio of atoms of each element in a compound. To determine it, convert the mass (or percentage) of each element to moles, divide by the smallest number of moles, and then multiply to obtain whole numbers.

经验式给出化合物中各元素原子的最简整数比。确定经验式时，将各元素的质量（或百分含量）换算为物质的量，除以最小物质的量，再乘以适当的系数得到整数比。

The molecular formula is a multiple of the empirical formula. The magnitude of the multiple is found by dividing the relative molecular mass (Mᵣ) of the compound by the relative formula mass of its empirical formula.

分子式是经验式的整数倍。该倍数由化合物的相对分子质量 (Mᵣ) 除以其经验式的相对式量得到。

6. Rate of Reaction | 反应速率

The average rate of a chemical reaction is defined as the change in quantity of a reactant or product per unit time. It can be followed by measuring mass loss, gas volume produced, colour change, or other suitable variable.

化学反应的平均速率定义为单位时间内反应物或产物的变化量。可通过测量质量损失、气体生成体积、颜色变化或其他合适的变量来跟踪。

Average rate = Δ quantity / Δ time

For example, if the reaction produces a gas, rate = Δ volume of gas / Δ time (cm³ s⁻¹). For a change in mass, rate = Δ mass / Δ time (g s⁻¹). The instantaneous rate at a particular time is given by the slope of the tangent to the curve on a progress‑time graph.

例如，若反应生成气体，速率 = 气体体积变化 / 时间变化 (cm³ s⁻¹)。对于质量变化，速率 = 质量变化 / 时间变化 (g s⁻¹)。某一时刻的瞬时速率由进度‑时间曲线切线的斜率给出。

7. pH and the Hydrogen Ion Concentration | pH 与氢离子浓度

The pH scale is a logarithmic measure of the acidity of an aqueous solution. It is related to the concentration of hydrogen ions, H⁺(aq).

pH 值是对水溶液酸度的一种对数度量。它与氢离子 H⁺(aq) 的浓度有关。

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pH = −log₁₀ [H⁺]

ns [H⁺] > 1 × 10⁻⁷ mol l⁻¹ so pH < 7; in alkaline solutions [H⁺] < 1 × 10⁻⁷ mol l⁻¹ so pH > 7. For a strong monoprotic acid, [H⁺] is equal to the concentration of the acid.

式中 [H⁺] 是氢离子浓度，单位为 mol l⁻¹。在纯水和中性溶液中，[H⁺] = 1 × 10⁻⁷ mol l⁻¹，对应 pH = 7。在酸性溶液中 [H⁺] > 1 × 10⁻⁷ mol l⁻¹，因此 pH < 7；在碱性溶液中 [H⁺] < 1 × 10⁻⁷ mol l⁻¹，所以 pH > 7。对于强一元酸，[H⁺] 等于该酸的浓度。

8. Enthalpy Change and Energy in Reactions | 焓变与反应热

The enthalpy change, ΔH, is the heat energy transferred in a reaction at constant pressure. Exothermic reactions release heat (ΔH negative); endothermic reactions absorb heat (ΔH positive).

焓变 ΔH 是恒压下反应中传递的热量。放热反应释放热量（ΔH 为负值）；吸热反应吸收热量（ΔH 为正值）。

For reactions in solution, the heat absorbed or released can be calculated using:

对于溶液中的反应，吸收或释放的热量可用以下公式计算：

q = c × m × ΔT

where q is the heat energy (J), c is the specific heat capacity of the solution (for water, 4.18 J g⁻¹ °C⁻¹), m is the mass of the solution (g), and ΔT is the temperature change (°C). To find the enthalpy change per mole, divide q by the number of moles of the limiting reactant: ΔH = −q / n (the negative sign indicates that when the surroundings gain heat, the system loses heat).

其中 q 是热量（J），c 是溶液的比热容（水的为 4.18 J g⁻¹ °C⁻¹），m 是溶液的质量（g），ΔT 是温度变化（°C）。要计算每摩尔的焓变，用 q 除以限制反应物的物质的量：ΔH = −q / n（负号表示当环境获得热量时，系统失去热量）。

9. Avogadro's Law and Gas Calculations | 阿伏伽德罗定律与气体计算

Avogadro's law states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. This principle allows us to use volume ratios directly from a balanced chemical equation when the reactants and products are gases under identical conditions.

阿伏伽德罗定律指出，在相同温度和压强下，同体积的任何气体含有相同数目的分子。利用这一原理，当反应物和产物在相同条件下均为气体时，可直接由配平的化学方程式得到体积比。

For example, in the reaction N₂(g) + 3H₂(g) → 2NH₃(g), 1 volume of nitrogen reacts with 3 volumes of hydrogen to produce 2 volumes of ammonia, assuming all gases are measured at the same temperature and pressure.

例如，在反应 N₂(g) + 3H₂(g) → 2NH₃(g) 中，假设所有气体在相同温度和压强下测量，1 体积氮气与 3 体积氢气反应生成 2 体积氨气。

10. Neutralisation and Titration Calculations | 中和反应与滴定计算

In a titration, a known volume of a standard solution is reacted with the analyte. The point at which the reaction is just complete is called the equivalence point. The relationship used is:

在滴定中，已知体积的标准溶液与待测溶液反应。反应恰好完成的一点称为等当点。所用的关系式为：

c₁ × V₁ / n₁ = c₂ × V₂ / n₂

where c₁ and c₂ are the concentrations of the two solutions, V₁ and V₂ are their reacting volumes (in the same units), and n₁ and n₂ balanced equation. For a 1:1 reaction (e.g., HCl + NaOH → NaCl + H₂O), this simplifies to c₁V₁ = c₂V₂. Always ensure the volumes are in the same units (usually cm³).

其中 c₁ 和 c₂ 是两种溶液的浓度，V₁ 和 V₂ 是它们反应所需的体积（单位一致），n₁ 和 n₂ 是配平方程式中反应的摩尔数。对于 1:1 反应（如 HCl + NaOH → NaCl + H₂O），可简化为 c₁V₁ = c₂V₂。务必确保体积单位一致（通常为 cm³）。

11. Ionic Bonding and Stoichiometry of Salts | 离子键与盐的化学计量

In ionic compounds, the total positive charge must balance the total negative charge. This principle dictates the formula of a salt. For example, sodium chloride is NaCl (Na⁺ and Cl⁻), magnesium chloride is MgCl₂ (Mg²⁺ and 2Cl⁻), and aluminium oxide is Al₂O₃ (2Al³⁺ and 3O²⁻).

在离子化合物中，正电荷总数必须与负电荷总数相等。这一原则决定了盐的化学式。例如，氯化钠为 NaCl（Na⁺ 与 Cl⁻），氯化镁为 MgCl₂（Mg²⁺ 与 2Cl⁻），氧化铝为 Al₂O₃（2Al³⁺ 与 3O²⁻）。

The concept of charge balance also helps in working out the ratios in which solutions react. Understanding ion charges allows you to predict the products of precipitation reactions and to write balanced ionic equations.

电荷平衡的概念也有助于确定溶液反应的化学计量比。理解离子电荷可以让你预测沉淀反应的产物，并书写配平的离子方程式。

12. Summary of Key Equation Rearrangements | 核心公式变形汇总

In SQA Chemistry, you are frequently required to rearrange simple equations. The triangular relationship is a useful memory aid for n = m / M, c = n / V, and n = V / 24.0. For instance, if you cover the quantity you want to find, the remaining two symbols show you how to calculate it: in the 'mole triangle', m on top, n and M on the bottom, giving n = m / M, m = n × M, and M = m / n. The same logic applies to the concentration and gas volume relationships.

在 SQA 化学中，你经常需要变形简单的公式。三角关系是记忆 n = m / M、c = n / V 和 n = V / 24.0 的好方法。例如，在“摩尔三角”中，m 在上方，n 和 M 在下方，可以得到 n = m / M、m = n × M 和 M = m / n。同样的逻辑适用于浓度和气体体积关系。记住，检查单位的一致性可以避免许多常见错误。

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