Pre-U AQA Chemistry: Quick Reference Handbook of Formulas and Theorems | Pre-U AQA 化学：公式定理速查手册

📚 Pre-U AQA Chemistry: Quick Reference Handbook of Formulas and Theorems | Pre-U AQA 化学：公式定理速查手册

This quick reference handbook brings together the essential formulas, equations and theorems you will meet across the Pre-U AQA Chemistry course. It is arranged by topic to help you find what you need during revision, problem-solving or in the lead-up to examinations. Every entry is presented in paired English–Chinese explanations so that you can absorb the quantitative and conceptual links efficiently.

本手册集中整理了 Pre–U AQA 化学课程中的核心公式、方程与定理，按主题编排，方便你在复习、练习和考前快速查阅。每个条目均以英中对照的形式呈现，帮助你高效掌握定量关系和概念内涵。

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1. The Mole and Stoichiometric Relationships | 物质的量与化学计量关系

The amount of substance, n (mol), is the central counting unit in chemistry. It links mass, particle number and gas volume through the relations: n = m / M, where m is mass (g) and M is molar mass (g mol⁻¹).

物质的量 n (摩尔) 是化学计量的核心。它将质量、粒子数与气体体积关联起来：n = m / M，其中 m 是质量 (克)，M 为摩尔质量 (克每摩尔)。

For a pure substance, n = N / N_A, where N is the number of specified particles and N_A = 6.02 × 10²³ mol⁻¹ is the Avogadro constant.

对纯物质，n = N / N_A，其中 N 为指定粒子数，N_A = 6.02 × 10²³ mol⁻¹ 是阿伏伽德罗常数。

At standard temperature and pressure (STP: 0 °C, 100 kPa), the molar volume of an ideal gas is approximately V_m ≈ 22.4 dm³ mol⁻¹, giving n = V / V_m.

在标准状况 (STP: 0 °C，100 kPa) 下，理想气体的摩尔体积约为 V_m ≈ 22.4 dm³ mol⁻¹，于是 n = V / V_m。

Concentration of a solution is c = n / V, with units mol dm⁻³. This underpins all titrimetric calculations.

溶液的浓度 c = n / V，单位为 mol dm⁻³。这是所有滴定计算的依据。

Percentage yield = (actual yield / theoretical yield) × 100% tom economy = (molar mass of desired product / sum of molar masses of all reactants) × 100%.

产率 = (实际产量 / 理论产量) × 100%；原子经济性 = (目标产物的摩尔质量 / 所有反应物摩尔质量之和) × 100%。

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2. Gases: Ideal Gas Equation and Kinetic Theory | 气体：理想气体方程与分子运动论

The ideal gas equation is pV = nRT, where p is pressure (Pa), V is volume (m³), n is amount (mol), T is absolute temperature (K), and R = 8.31 J K⁻¹ mol⁻¹.

理想气体状态方程为 pV = nRT，其中 p 为压强 (帕)，V 为体积 (立方米)，n 为物质的量 (摩尔)，T 为热力学温度 (开尔文)，R = 8.31 J K⁻¹ mol⁻¹。

When the amount of gas is constant, the combined gas law applies: p₁V₁ / T₁ = p₂V₂ / T₂.

气体物质的量不变时，可用联合气体定律：p₁V₁ / T₁ = p₂V₂ / T₂。

From kinetic theory, the average translational kinetic energy of a mole of gas is E_k = (3/2) RT. For a single molecule, E_k = (3/2) k_BT, with k_B = R / N_A.

由分子运动论，每摩尔气体的平均平动动能 E_k = (3/2) RT。对一个分子，E_k = (3/2) k_BT，其中 k_B = R / N_A。

Graham's law of effusion states that the rate of effusion is inversely proportional to the square root of the molar mass: rate ∝ 1 / √M.

格雷姆扩散定律指出，扩散速率与摩尔质量的平方根成反比：rate ∝ 1 / √M。

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3. Energetics: Enthalpy, Hess's Law, and Bond Enthalpies | 能量学：焓变、盖斯定律与键焓

The heat transferred at constant pressure is the enthalpy change, ΔH. For a reaction in solution, q = m c ΔT, where m is mass, c is specific heat capacity, and ΔT is the temperature change. Then ΔH = –q / n (limiting reactant).

恒压下的热量变化即焓变 ΔH。对溶液中的反应，q = m c ΔT，其中 m 为质量，c 为比热容，ΔT 为温度变化。则 ΔH = –q / n (以限量反应物计)。

Hess's law: the enthalpy change for a reaction is the same regardless of the route taken, provided the initial and final conditions are the same.

盖斯定律：反应焓变只与始态和终态有关，与途径无关。

Standard enthalpy of formation ΔH_f⁰ is used to calculate reaction enthalpy: ΔH⁰ = Σ ΔH_f⁰ (products) – Σ ΔH_f⁰ (reactants).

标准生成焓 ΔH_f⁰ 用于计算反应焓：ΔH⁰ = Σ ΔH_f⁰ (产物) – Σ ΔH_f⁰ (反应物)。

Mean bond enthalpies give an estimate: ΔH ≈ Σ (bond enthalpies broken) – Σ (bond enthalpies made).

平均键焓提供估算值：ΔH ≈ Σ (断裂键的键焓) – Σ (生成键的键焓)。

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4. Entropy, Gibbs Free Energy, and Feasibility | 熵、吉布斯自由能与反应可行性

Entropy, S, measures disorder. The total entropy change of the universe is ΔS_total = ΔS_system + ΔS_surroundings. The entropy change of the surroundings is ΔS_surroundings = –ΔH / T (T in K).

熵 S 度量混乱度。宇宙的总熵变 ΔS_total = ΔS_system + ΔS_surroundings。环境的熵变 ΔS_surroundings = –ΔH / T (T 单位 K)。

Gibbs free energy change combines the system's enthalpy and entropy: ΔG = ΔH – TΔS. A reaction is thermodynamically feasible when ΔG < 0.

吉布斯自由能变综合了系统的焓变与熵变：ΔG = ΔH – TΔS。当 ΔG < 0 时，反应在热力学上可行。

For an equilibrium system, ΔG = –RT ln K, where K is the equilibrium constant. This links thermodynamics and equilibrium position.

对平衡系统，ΔG = –RT ln K，其中 K 为平衡常数，它把热力学与平衡位置结合起来。

At the temperature where a reaction just becomes feasible, ΔG = 0, so T = ΔH / ΔS.

在反应刚好可行的温度，ΔG = 0，因此 T = ΔH / ΔS。

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5. Chemical Equilibrium: K_c, K_p and Le Chatelier's Principle | 化学平衡：K_c、K_p 与勒沙特列原理

For a general reaction aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration is K_c = [C]^c[D]^d / [A]^a[B]^b. Only gases and aqueous species appear in the expression.

对于一般反应 aA + bB ⇌ cC + dD，浓度平衡常数 K_c = [C]^c[D]^d / [A]^a[B]^b。只有气体和溶液物种才出现在表达式中。

In terms of partial pressures: K_p = (p_C^c p_D^d) / (p_A^a p_B^b), each pressure expressed relative to standard pressure (1 bar).

以分压表示：K_p = (p_C^c p_D^d) / (p_A^a p_B^b)，各分压均相对于标准压力 (1 bar)。

The relationship between K_p and K_c is K_p = K_c (RT)^Δn, where Δn = (moles of gaseous products) – (moles of gaseous reactants).

K_p 与 K_c 的关系为 K_p = K_c (RT)^Δn，其中 Δn = (气体产物物质的量) – (气体反应物物质的量)。

Le Chatelier’s principle: when a system at equilibrium is subjected to a change in concentration, pressure or temperature, the position of equilibrium shifts to counteract the change.

勒沙特列原理：当平衡系统受到浓度、压强或温度变化的影响时，平衡会向减弱该变化的方向移动。

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6. Acids, Bases, and pH Calculations | 酸、碱与 pH 计算

The pH scale: pH = –log [H⁺] and pOH = –log [OH⁻]. At 298 K, K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴, and pH + pOH = 14.

pH 标度：pH = –log [H⁺]，pOH = –log [OH⁻]。298 K 时，K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴，且 pH + pOH = 14。

For a strong monoprotic acid, [H⁺] = c, so pH = –log c. For a strong base, [OH⁻] = c, pOH = –log c, then pH = 14 – pOH.

对于强一元酸，[H⁺] = c，因此 pH = –log c。对于强碱，[OH⁻] = c，pOH = –log c，然后 pH = 14 – pOH。

Weak acid dissociation constant: K_a = [H⁺][A⁻] / [HA]. If [H⁺] is small and dissociation negligible, [H⁺] ≈ √K_a c, where c is the nominal concentration.

弱酸解离常数：K_a = [H⁺][A⁻] / [HA]。若 [H⁺] 很小且解离可忽略，则 [H⁺] ≈ √K_a c，c 为标称浓度。

Henderson–Hasselbalch equation for a buffer: pH = pK_a + log ([A⁻] / [HA]). The buffer works best when pH ≈ pK_a.

缓冲溶液的 Henderson–Hasselbalch 方程：pH = pK_a + log ([A⁻] / [HA])。当 pH ≈ pK_a 时缓冲效果最好。

For a weak base, K_b = [BH⁺][OH⁻] / [B], and [OH⁻] ≈ √K_b c, then

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