Quick Reference Handbook of Formulae and Theorems for Pre-U Edexcel Chemistry | Pre-U Edexcel 化学公式定理速查手册

📚 Quick Reference Handbook of Formulae and Theorems for Pre-U Edexcel Chemistry | Pre-U Edexcel 化学公式定理速查手册

This handbook compiles the essential formulae, relationships and theorems examined in the Edexcel Pre-U Chemistry specification. Each section pairs a concise English statement with its Chinese equivalent, enabling rapid revision and cross‑referencing. Mastery of these expressions underpins success in calculations, data analysis and qualitative explanations throughout the course.

本手册汇编了 Edexcel Pre‑U 化学考试中不可或缺的公式、关系式与定理。每一个要点均以简明英文表述搭配对应的中文释义，方便快速复习与对照。掌握这些表达式是完成计算、数据分析以及课程中所有定性解释的基础。

1. The Mole and Stoichiometry | 摩尔与化学计量

The mole is the fundamental unit for amount of substance. One mole contains exactly 6.02214076 × 10²³ elementary entities (Avogadro’s constant, N_A). The number of moles n is given by n = m / M, where m is mass (g) and M is molar mass (g mol⁻¹).

摩尔是物质的量的基本单位。1 摩尔精确包含 6.02214076 × 10²³ 个基本单元（阿伏伽德罗常数 N_A）。物质的量 n 由 n = m / M 给出，其中 m 为质量（g），M 为摩尔质量（g mol⁻¹）。

n = m / M

For solutions, the amount of solute is related to concentration c (mol dm⁻³) and volume V (dm³): n = c V. When a volumetric solution of known concentration is used in a titration, the reacting ratio from the balanced equation determines the unknown concentration.

对于溶液，溶质的物质的量与浓度 c（mol dm⁻³）和体积 V（dm³）有关：n = c V。当已知浓度的标准溶液用于滴定时，由配平的化学方程式得出的计量比可确定未知浓度。

n = c V

Gas volumes at the same temperature and pressure compare directly with mole ratios (Avogadro’s law). At room temperature and pressure (RTP, 20 °C, 1 atm), 1 mol of any gas occupies 24.0 dm³ (molar volume).

相同温度和压力下，气体体积可直接与物质的量之比对应（阿伏伽德罗定律）。在常温常压下（RTP，20 °C，1 atm），1 mol 任何气体所占体积为 24.0 dm³（摩尔体积）。

V_gas = n × 24.0 dm³ mol⁻¹

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2. 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 obtained by dividing the mass or percentage composition of each element by its relative atomic mass A_r, then dividing by the smallest value to obtain integer subscripts.

实验式表示化合物中原子的最简整数比。通过将各元素的质量或百分含量除以相对原子质量 A_r，再除以最小比值即得整数下标。

Atom ratio = (mass % / A_r) → smallest whole‑number ratio

The molecular formula gives the actual number of atoms of each element in one molecule. It is a whole‑number multiple of the empirical formula. The multiplier is found from the relative molecular mass M_r:

分子式表示一个分子中各元素的实际原子个数。它是实验式的整数倍。倍数由相对分子质量 M_r 求出：

Multiplier = M_r / (empirical formula mass)

Thus the molecular formula = (empirical formula)_n, where n is the multiplier.

因此，分子式 = (实验式)_n，其中 n 为倍数。

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3. Ideal Gas Equation | 理想气体状态方程

The ideal gas equation links pressure p, volume V, amount n and absolute temperature T: pV = nRT, where R is the ideal gas constant (8.31 J K⁻¹ mol⁻¹). All quantities must be in SI units: p in Pa, V in m³, T in K.

理想气体状态方程将压强 p、体积 V、物质的量 n 和热力学温度 T 联系起来：pV = nRT，其中 R 为理想气体常数（8.31 J K⁻¹ mol⁻¹）。所有量必须采用国际单位制：p 以 Pa，V 以 m³，T 以 K 为单位。

pV = nRT

For a fixed mass of gas under two sets of conditions, the combined gas law is:

对于一定质量的气体在两种条件下的变化，可应用联合气体定律：

p₁V₁ / T₁ = p₂V₂ / T₂

Deviations from ideal behaviour occur at high pressure and low temperature because real gases have finite molecular volume and intermolecular attractions. The van der Waals equation corrects for these effects but is not required for direct calculation.

在高压低温下，气体行为偏离理想状态，因为真实气体有有限的分子体积和分子间引力。范德华方程对此进行修正，但不要求直接计算。

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4. Enthalpy Changes | 焓变

Enthalpy change ΔH is the heat transferred in a reaction at constant pressure. A negative ΔH signifies an exothermic process; a positive ΔH signifies an endothermic one. Standard conditions are 100 kPa and a stated temperature, usually 298 K.

焓变 ΔH 是恒压下反应传递的热量。ΔH 为负表示放热过程；ΔH 为正表示吸热过程。标准条件是 100 kPa 和指定的温度，通常为 298 K。

The enthalpy change of a reaction can be measured by calorimetry: q = m c ΔT, where q is heat transferred (J), m is mass of solution (g), c is specific heat capacity (usually 4.18 J g⁻¹ K⁻¹ for aqueous solutions) and ΔT is the temperature change (K). Then ΔH = −q / n (for an exothermic reaction in solution).

反应的焓变可通过量热法测量：q = m c ΔT，其中 q 为传递的热量（J），m 为溶液质量（g），c 为比热容（水溶液通常为 4.18 J g⁻¹ K⁻¹），ΔT 为温度变化（K）。则 ΔH = −q / n（对于溶液中的放热反应）。

q = m c ΔT

ΔH = −q / n

Standard enthalpy changes include ΔH_f° (formation), ΔH_c° (combustion), ΔH_neut° (neutralisation) and ΔH_rxn° (reaction).

标准焓变包括 ΔH_f°（生成）、ΔH_c°（燃烧）、ΔH_neut°（中和）和 ΔH_rxn°（反应）。

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5. Hess’s Law | 盖斯定律

Hess’s law states that the total enthalpy change for a reaction is independent of the route taken, provided the initial and final conditions are the same. It allows the calculation of ΔH for a reaction that cannot be measured directly by combining known enthalpy changes.

盖斯定律指出，只要初态和终态相同，反应的总焓变与路径无关。这允许通过组合已知的焓变，计算无法直接测量的反应 ΔH。

For example, using formation enthalpies:

例如，用生成焓计算：

ΔH°_rxn = Σ ΔH_f° (products) − Σ ΔH_f° (reactants)

Or using combustion enthalpies:

或用燃烧焓计算：

ΔH°_rxn = Σ ΔH_c° (reactants) − Σ ΔH_c° (products)

Hess’s law is a consequence of the first law of thermodynamics; enthalpy is a state function. Enthalpy level diagrams and Born–Haber cycles are graphical applications of Hess’s law.

盖斯定律是热力学第一定律的推论；焓是状态函数。焓级图和玻恩‑哈伯循环是盖斯定律的图解应用。

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6. Rate Equations and Order of Reaction | 速率方程与反应级数

The rate equation for a reaction aA + bB → products often takes the form:

反应 aA + bB → 产物的速率方程常具有以下形式：

Rate = k [A]^m [B]ⁿ

where k is the rate constant, and m and n are the orders of reaction with respect to A and B. The overall order is m + n. Orders are determined experimentally, not from the stoichiometric coefficients.

其中 k 为速率常数，m 和 n 分别是对 A 和 B 的反应级数。总级数为 m + n。级数由实验确定，而非来自化学计量数。

The units of the rate constant depend on the overall order:

速率常数的单位取决于总级数：

• Zero order: Rate = k, units mol dm⁻³ s⁻¹

  零级：Rate = k，单位为 mol dm⁻³ s⁻¹

• First order: Rate = k[A], units s⁻¹

  一级：Rate = k[A]，单位为 s⁻¹

• Second order: Rate = k[A]² or k[A][B], units dm³ mol⁻¹ s⁻¹

  二级：Rate = k[A]² 或 k[A][B]，单位为 dm³ mol⁻¹ s⁻¹

The integrated first‑order rate law is ln[A] = ln[A]₀ − kt, giving a straight‑line plot of ln[A] vs time.

一级反应的积分速率方程为 ln[A] = ln[A]₀ − kt，ln[A] 对时间作图得一直线。

The half‑life t_½ of a first‑order reaction is constant:

一级反应的半衰期 t_½ 为常数：

t_½ = ln 2 / k ≈ 0.693 / k

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7. Equilibrium Constant Kc and Kp | 平衡常数 Kc 与 Kp

For a reversible reaction aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration is:

对于可逆反应 aA + bB ⇌ cC + dD，以浓度表示的平衡常数为：

K_c = [C]^c[D]^d / [A]^a[B]^b

Square brackets denote equilibrium concentrations in mol dm⁻³. K_c is temperature dependent; its value is constant at a given temperature.

方括号表示平衡浓度，单位为 mol dm⁻³。K_c 与温度有关；在给定温度下其值为常数。

For gas‑phase equilibria, the equilibrium constant in terms of partial pressure is:

对于气相平衡，以分压表示的平衡常数为：

K_p = (p_C^c p_D^d) / (p_A^a p_B^b)

where p_i is the partial pressure of component i. Partial pressure = mole fraction × total pressure.

其中 p_i 为组分 i 的分压。分压 = 摩尔分数 × 总压。

p_i = x_i P_total

The relationship between K_p and K_c is K_p = K_c (RT)^Δn, where Δn = (c+d) − (a+b).

K_p 与 K_c 的关系为 K_p = K_c (RT)^Δn，其中 Δn = (c+d) − (a+b)。

K_p = K_c (RT)^Δn

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8. pH and Acid–Base Equilibria | pH 与酸碱平衡

The pH of an aqueous solution is defined as:

水溶液的 pH 定义为：

pH = − log₁₀ [H⁺]

where [H⁺] is in mol dm⁻³. Similarly, pOH = − log[OH⁻], and at 298 K, pH + pOH = 14.00 (from K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶).

其中 [H⁺] 单位为 mol dm⁻³。类似地，pOH = − log[OH⁻]，且在 298 K 时 pH + pOH = 14.00（由 K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ 得出）。

For a weak acid HA with acid dissociation constant K_a:

对于弱酸 HA，其酸解离常数 K_a 为：

K_a = [H⁺][A⁻] / [HA]

The Henderson–Hasselbalch equation is useful for buffer solutions:

汉德森‑哈塞尔巴尔赫方程对缓冲溶液很有用：

pH = pK_a + log ([A⁻] / [HA])

where pK_a = − log K_a. A buffer is most effective when the ratio [A⁻]/[HA] is close to 1, i.e., pH ≈ pK_a.

其中 pK_a = − log K_a。当 [A⁻]/[HA] 接近 1，即 pH ≈ pK_a 时，缓冲能力最强。

For a dibasic acid or a diprotic acid, two dissociation constants K_a1 and K_a2 apply in successive steps.

对于二元酸或 diprotic acid，存在分步解离常数 K_a1 和 K_a2。

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9. Electrode Potentials and Nernst Equation | 电极电势与能斯特方程

The standard electrode potential E° is measured under standard conditions (298 K, 100 kPa, 1.0 mol dm⁻³ solutions). The cell potential E°_cell is calculated as:

标准电极电势 E° 在标准条件（298 K，100 kPa，1.0 mol dm⁻³ 溶液）下测量。电池电动势 E°_cell 计算如下：

E°_cell = E°_right − E°_left

A positive E°_cell indicates a thermodynamically feasible reaction; ΔG° = −nFE°_cell, where n is the number of moles of electrons transferred and F is the Faraday constant (96 500 C mol⁻¹).

E°_cell 为正表示反应热力学可行；ΔG° = −nFE°_cell，其中 n 为转移电子的物质的量，F 为法拉第常数（96 500 C mol⁻¹）。

The Nernst equation allows calculation of the electrode potential under non‑standard conditions:

能斯特方程可用于计算非标准条件下的电极电势：

E = E° − (RT / nF) ln Q

where Q is the reaction quotient with the same form as K_c. At 298 K, the equation simplifies to:

其中 Q 为反应商，形式与 K_c 相同。298 K 时，可简化为：

E = E° − (0.0592 / n) log Q (in volts)

For a metal/metal‑ion half‑cell, E = E° − (0.0592 / n) log (1 / [Mⁿ⁺]) at 298 K.

对于金属/金属离子半电池，298 K 下 E = E° − (0.0592 / n) log (1 / [Mⁿ⁺])。

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10. Born–Haber Cycle and Lattice Energy | 玻恩‑哈伯循环与晶格能

The Born–Haber cycle is an application of Hess’s law to ionic compounds. It relates lattice energy (ΔH_LE) to other measurable enthalpy changes: atomisation enthalpy, ionisation energy, electron affinity and the enthalpy of formation.

玻恩‑哈伯循环是将盖斯定律应用于离子化合物。它把晶格能 (ΔH_LE) 与其他可测焓变联系起来：原子化焓、电离能、电子亲和能和生成焓。

The general cycle for NaCl (s) is:

对于 NaCl(s) 的一般循环为：

ΔH_f° = ΔH_at°(Na) + IE(Na) + ½ D(Cl−Cl) + EA(Cl) + ΔH_LE

Making ΔH_LE the subject:

移项得：

ΔH_LE = ΔH_f° − [ΔH_at°(Na) + IE(Na) + ½ D(Cl−Cl) + EA(Cl)]

Lattice energy is always negative (exothermic) for a stable ionic solid. Its magnitude increases with smaller ionic radii and larger ionic charges (charge density).

晶格能对稳定离子固体来说总是负值（放热）。其绝对值随离子半径减小和电荷增大（电荷密度增大）而增大。

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11. Entropy and Gibbs Free Energy | 熵与吉布斯自由能

Entropy S is a measure of the disorder of a system. The second law of thermodynamics states that the total entropy of an isolated system always increases for a spontaneous process.

熵 S 是系统无序度的量度。热力学第二定律表明，孤立系统的总熵在自发过程中总是增加的。

The standard entropy change for a reaction is calculated from standard molar entropies S°:

反应的标准熵变可由标准摩尔熵 S° 计算：

ΔS°_rxn = Σ S°(products) − Σ S°(reactants)

Gibbs free energy change ΔG determines the spontaneity of a reaction at constant temperature and pressure:

吉布斯自由能变 ΔG 决定恒温恒压下反应的自发性：

ΔG = ΔH − TΔS

ΔG must be negative for a spontaneous process. At equilibrium ΔG = 0. The standard Gibbs free energy change is related to the equilibrium constant:

自发过程要求 ΔG 为负。平衡时 ΔG = 0。标准吉布斯自由能变与平衡常数的关系为：

ΔG° = −RT ln K

where K is K_c or K_p. The temperature at which a reaction just becomes feasible (ΔG° = 0) can be estimated by T = ΔH° / ΔS°.

其中 K 为 K_c 或 K_p。反应刚变为可行（ΔG° = 0）时的温度可由 T = ΔH° / ΔS° 估计。

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12. Arrhenius Equation | 阿伦尼乌斯方程

The Arrhenius equation describes the temperature dependence of the rate constant k:

阿伦尼乌斯方程描述了速率常数 k 与温度的关系：

k = A e^{−E_a / (RT)}

or in logarithmic form:

或其对数形式：

ln k = ln A − E_a / (RT)

where A is the pre‑exponential factor (frequency factor), E_a is the activation energy (J mol⁻¹), R = 8.31 J K⁻¹ mol⁻¹, and T is the absolute temperature (K). A plot of ln k against 1/T yields a straight line with gradient −E_a/R.

其中 A 为指前因子（频率因子），E_a 为活化能（J mol⁻¹），R = 8.31 J K⁻¹ mol⁻¹，T 为热力学温度（K）。以 ln k 对 1/T 作图得一直线，斜率为 −E_a/R。

For two different temperatures T₁ and T₂, the activation energy can be calculated using:

对于两个不同温度 T₁ 和 T₂，可用下式计算活化能：

ln (k₂ / k₁) = − (E_a / R) (1/T₂ − 1/T₁)

A larger activation energy gives a steeper temperature dependence; the rate increases more rapidly when the temperature rises.

活化能越大，温度依赖性越陡；温度升高时反应速率增加得越快。

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