Year 13 CAIE Chemistry: Formula & Theorem Quick-Reference Handbook | Year 13 CAIE 化学公式定理速查手册

📚 Year 13 CAIE Chemistry: Formula & Theorem Quick-Reference Handbook | Year 13 CAIE 化学公式定理速查手册

Welcome to this quick-reference handbook designed for Year 13 CAIE Chemistry students. This article brings together the essential formulas, equations and theorems from the A2 syllabus. Use it to revise thermodynamics, equilibria, kinetics, electrochemistry and other key topics, ensuring you are well prepared for your examinations.

欢迎使用这份为 Year 13 CAIE 化学学生设计的速查手册。本文汇集了 A2 课程中必备的公式、方程和定理。你可以用它来复习热力学、平衡、动力学、电化学等核心主题，为考试做好充分准备。

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1. Thermodynamic Essentials | 热力学必备

ΔG = ΔH – TΔS

The Gibbs free energy change ΔG determines whether a reaction is thermodynamically feasible. ΔH is the enthalpy change, ΔS the entropy change, and T the absolute temperature in kelvin. A reaction is spontaneous when ΔG < 0.

吉布斯自由能变 ΔG 决定反应在热力学上是否可行。ΔH 为焓变，ΔS 为熵变，T 为开尔文温度。当 ΔG < 0 时，反应自发进行。

ΔG° = –RT ln K

The standard Gibbs free energy change ΔG° is related to the equilibrium constant K. R is the gas constant (8.31 J mol¹ K¹) and T is the temperature. This equation connects thermodynamic data with the position of equilibrium.

标准吉布斯自由能变 ΔG° 与平衡常数 K 相关。R 为气体常数 (8.31 J mol¹ K¹)，T 为温度。该方程将热力学数据与平衡位置联系起来。

ΔS° = ΣS°(products) – ΣS°(reactants)

The standard entropy change of a reaction is calculated from the absolute standard molar entropies of products and reactants. Positive ΔS suggests increased disorder.

反应的标准熵变由产物与反应物的标准摩尔熵计算得到。正值 ΔS 表示无序度增加。

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2. Equilibrium Constants | 平衡常数

Kc = [C]&supc;[D]&supd; / [A]&supa;[B]&supb;

For a general reaction aA + bB ⇒ cC + dD, the equilibrium constant Kc is expressed in terms of equilibrium concentrations. The indices a, b, c, d are the stoichiometric coefficients. Kc changes only with temperature.

对于一般反应 aA + bB ⇒ cC + dD，平衡常数 Kc 用平衡浓度表示。指数 a、b、c、d 为化学计量系数。Kc 只随温度变化而变化。

Kp = (pC)&supc;(pD)&supd; / (pA)&supa;(pB)&supb;

For gaseous equilibria, Kp uses partial pressures. The expression follows the same form as Kc. Total pressure does not affect the value of Kp, but can shift the position of equilibrium.

对于气相平衡，Kp 使用分压。表达式形式与 Kc 相同。总压力不改变 Kp 的值，但会使平衡位置发生移动。

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3. Acids, Bases and pH | 酸、碱与 pH

pH = –log₁₀[H¹]     pOH = –log₁₀[OH¹]

The pH is the negative logarithm (base 10) of the hydrogen ion concentration. In aqueous solution at 298 K, pH + pOH = 14. For strong acids and bases, full dissociation is assumed.

pH 是氢离子浓度的负对数（底数为 10）。在 298 K 的水溶液中，pH + pOH = 14。对于强酸和强碱，假定完全电离。

Kw = [H¹][OH¹] = 1.0 × 10¹⁰ (298 K)

The ionic product of water Kw relates the concentrations of H¹ and OH¹ ions in pure water and aqueous solutions. It is temperature dependent and used to link pH and pOH.

水的离子积 Kw 关联了纯水和水溶液中 H¹ 与 OH¹ 的浓度。它和温度有关，用于联系 pH 与 pOH。

pKa = –log₁₀Ka     pKb = –log₁₀Kb

Ka and Kb are the acid and base dissociation constants. The smaller the pKa, the stronger the acid. These values are essential for buffer calculations and weak acid/base equilibria.

Ka 和 Kb 分别是酸和碱的电离常数。pKa 越小，酸越强。这些数值是缓冲溶液计算和弱酸/弱碱平衡中的关键。

pH = pKa + log₁₀([A¹]/[HA])

The Henderson–Hasselbalch equation is used to calculate the pH of a buffer solution containing a weak acid HA and its conjugate base A¹.

亨德森–哈塞尔巴尔赫方程用于计算含有弱酸 HA 及其共轭碱 A¹ 的缓冲溶液的 pH。

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4. Solubility Product Ksp | 溶度积 Ksp

Kₛₘ = [M&supx;¹]&supa;[X&supy;¹]&supb; for MₚXₙ

The solubility product is the equilibrium constant for a sparingly soluble salt. For a salt with formula AₚBₙ, Ksp = [A&supy;¹]&supx;[B&supx;¹]&supy;. A larger Ksp indicates higher solubility. The common ion effect reduces solubility by shifting the equilibrium.

溶度积是难溶盐的平衡常数。对于盐 AₚBₙ，Ksp = [A&supy;¹]&supx;[B&supx;¹]&supy;。Ksp 越大，溶解度越高。同离子效应通过移动平衡降低溶解度。

When comparing solubilities, you must consider the stoichiometry of the salt. For a 1:1 salt like AgCl, solubility s = √Ksp. For a 1:2 salt like PbCl₂, s = (Ksp/4)¹⁰³.

比较溶解度时需考虑盐的化学计量比。对于 AgCl 这类 1:1 盐，溶解度 s = √Ksp。对于 PbCl₂ 这类 1:2 盐，s = (Ksp/4)¹⁰³。

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5. Electrochemistry & Nernst Equation | 电化学与能斯特方程

Eᵒcell = Eᵒcathode – Eᵒanode

The standard cell potential Eᵒcell is calculated from the standard reduction potentials of the two half-cells. A positive Eᵒcell indicates a spontaneous reaction under standard conditions.

标准电池电动势 Eᵒcell 由两个半电池的标准还原电势计算得出。正的 Eᵒcell 表明反应在标准条件下可自发进行。

ΔG° = –nFEᵒcell

This fundamental equation links thermodynamics and electrochemistry. n is the number of electrons transferred, and F is the Faraday constant (96 500 C mol¹). It allows the calculation of ΔG from cell potential.

这个基本方程连接热力学与电化学。n 是转移的电子数，F 为法拉第常数 (96 500 C mol¹)。可由电池电动势计算 ΔG。

E = E° – (RT/nF) ln Q

The Nernst equation calculates the cell potential under non-standard conditions. Q is the reaction quotient. At 298 K, it simplifies to E = E° – (0.0592 V / n) log₁₀ Q.

能斯特方程用于计算非标准条件下的电池电动势。Q 为反应商。在 298 K 时可简化为 E = E° – (0.0592 V / n) log₁₀ Q。

For a half-cell such as Cu²¹ / Cu, the electrode potential is: E = E° + (0.0592/2) log[Cu²¹] at 298 K. This explains why concentration changes affect cell voltage.

Published by TutorHao | Year 13 Chemistry Revision Series | aleveler.com

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