📚 Pre-U WJEC Chemistry: Formulas & Theorems Quick Reference Handbook | Pre-U WJEC 化学：公式定理速查手册
This bilingual quick-reference handbook brings together the key formulas, equations, and quantitative relationships required for the WJEC Pre-U Chemistry course. It spans stoichiometry, energetics, kinetics, equilibria, electrochemistry, and spectroscopy, offering a concise revision aid for mastering calculations and conceptual problems.
本双语速查手册汇集了 WJEC Pre-U 化学课程所需的全部核心公式、方程式和定量关系，涵盖化学计量、能量学、动力学、平衡、电化学和光谱学，为掌握计算与概念题提供简洁的复习工具。
1. Fundamental Quantities and Units | 基本量与单位
The amount of substance, n, is measured in moles (mol). Molar mass M (g mol⁻¹) links mass m (g) to n: n = m/M.
n = m / M
物质的量 n 以摩尔(mol)为单位。摩尔质量 M (g·mol⁻¹) 将质量 m (g) 与 n 联系起来：n = m/M。
Concentration c (mol dm⁻³) relates the amount of solute to the volume V (dm³) of solution.
c = n / V
浓度 c (mol·dm⁻³) 将溶质的量与溶液体积 V (dm³) 关联。
Molar gas volume Vₘ at room temperature and pressure (298 K, 100 kPa) is taken as 24.0 dm³ mol⁻¹.
Vₘ = V / n ≈ 24.0 dm³ mol⁻¹
在常温常压(298 K, 100 kPa)下，气体摩尔体积 Vₘ 取 24.0 dm³·mol⁻¹。
The Avogadro constant N_A = 6.02 × 10²³ mol⁻¹ gives the number of entities per mole. Number of particles N = n × N_A.
N = n × N_A
阿伏伽德罗常数 N_A = 6.02 × 10²³ mol⁻¹ 给出每摩尔的微粒数。粒子数 N = n × N_A。
2. Mole and Stoichiometry | 摩尔与化学计量
In a reaction aA + bB → cC + dD, the mole ratio is read directly from the balanced equation. The limiting reagent determines the theoretical yield.
Mole ratio A : B : C : D = a : b : c : d
在反应 aA + bB → cC + dD 中，摩尔比直接从配平方程读取。限制试剂决定理论产量。
Percentage yield compares the actual mass of product obtained to the theoretical mass.
% yield = (actual yield / theoretical yield) × 100%
产率百分数将实际所得产品质量与理论质量进行比较。
Atom economy evaluates how efficiently reactant atoms are incorporated into the desired product.
% atom economy = (molar mass of desired product / sum of molar masses of all products) × 100%
原子经济性评估反应物原子被结合到目标产物中的效率。
In volumetric analysis, the titre volume is used with the known concentration to find the unknown via n₁ = n₂ (at equivalence) or the ratio c₁V₁/n₁ = c₂V₂/n₂.
c₁V₁ / n₁ = c₂V₂ / n₂
在滴定分析中，利用滴定体积和已知浓度，通过等当量时 n₁ = n₂ 或关系式 c₁V₁/n₁ = c₂V₂/n₂ 求取未知浓度。
3. Gas Laws and Kinetic Theory | 气体定律与动力学理论
The ideal gas equation links pressure p (Pa), volume V (m³), amount n (mol) and temperature T (K). R = 8.31 J K⁻¹ mol⁻¹.
pV = nRT
理想气体方程联系压力 p (Pa)、体积 V (m³)、物质的量 n (mol) 与温度 T (K)。R = 8.31 J·K⁻¹·mol⁻¹。
For a fixed mass of gas, the combined gas law holds: p₁V₁/T₁ = p₂V₂/T₂.
p₁V₁ / T₁ = p₂V₂ / T₂
对于一定质量的气体，适用联合气体定律。
Dalton’s law states that the total pressure is the sum of partial pressures; the partial pressure of component i is pᵢ = χᵢ × P_total, where χᵢ = nᵢ / n_total.
P_total = Σ pᵢ pᵢ = χᵢ P_total
道尔顿定律指出总压等于分压之和；组分 i 的分压 pᵢ = χᵢ × P_total，其中 χᵢ = nᵢ / n_total 为摩尔分数。
Kinetic theory relates pressure to the mean square speed c² of particles: pV = ⅓ n M c². The average kinetic energy per mole is (3/2)RT.
pV = ⅓ n M c² KE_avg = (3/2) RT
动力学理论将压力与粒子均方速率 c² 关联。每摩尔平均动能 = (3/2)RT。
4. Energetics and Calorimetry | 能量学与量热法
Heat absorbed or released by a substance is calculated from its mass, specific heat capacity c (J g⁻¹ K⁻¹) and temperature change ΔT.
Q = m c ΔT
物质吸收或放出的热量由质量、比热容 c (J·g⁻¹·K⁻¹) 和温度变化 ΔT 计算。
The enthalpy change of a reaction is obtained from calorimetry: ΔH = –Q / n (measured under constant pressure).
ΔH = –Q / n
反应焓变通过量热法获得：ΔH = –Q / n (在恒压下测量)。
Hess’s Law: the total enthalpy change for a reaction is independent of the route taken. It allows ΔH to be found from formation or combustion data.
ΔH_reaction = Σ ΔH_f⁰(products) – Σ ΔH_f⁰(reactants)
盖斯定律：反应的总焓变与途径无关。可利用生成焓或燃烧焓数据求出 ΔH。
Bond enthalpy calculations provide an estimate: ΔH ≈ Σ (bond energies broken) – Σ (bond energies formed). The Born–Haber cycle relates lattice enthalpy U to atomisation, ionisation, electron affinity and formation enthalpies.
ΔH_f⁰(MX) = ΔH_atom⁰(M) + IE(M) + ½ ΔH_diss⁰(X₂) + EA(X) + U(MX)
键焓计算提供估算值：ΔH ≈ Σ(断裂键能) – Σ(生成键能)。玻恩-哈伯循环将晶格焓 U 与原子化、电离、电子亲和和生成焓联系起来。
5. Chemical Kinetics | 化学动力学
The rate equation for a reaction aA + bB → products is determined experimentally; the orders m and n are not generally equal to a and b.
rate = k [A]ᵐ [B]ⁿ
反应 aA + bB → 产物 的速率方程由实验确定；级数 m 和 n 通常不等于 a 和 b。
The units of the rate constant k depend on the overall order. For a first-order reaction, k has units of s⁻¹; for second order, dm³ mol⁻¹ s⁻¹.
k = rate / ([A]ᵐ[B]ⁿ) → units: (mol dm⁻³)^{1 – overall order} s⁻¹
速率常数 k 的单位取决于总级数。一级反应 k 的单位为 s⁻¹；二级反应为 dm³·mol⁻¹·s⁻¹。
The half-life of a first-order reaction is constant and independent of initial concentration.
t½ = ln 2 / k
一级反应的半衰期恒定，与初始浓度无关。
The Arrhenius equation describes the temperature dependence of the rate constant. The two-point form helps calculate activation energy Eₐ.
k = A e^{–Eₐ/(RT)} ln k = ln A – Eₐ/(RT)
ln(k₂/k₁) = –(Eₐ/R) (1/T₂ – 1/T₁)
阿伦尼乌斯方程描述了速率常数与温度的关系。两点式可用于计算活化能 Eₐ。
6. Chemical Equilibrium | 化学平衡
The equilibrium constant Kc for aA + bB ⇌ cC + dD is expressed in terms of concentrations at equilibrium. Solids and pure liquids are omitted.
Kc = [C]ᶜ [D]ᵈ / ([A]ᵃ [B]ᵇ)
反应 aA + bB ⇌ cC + dD 的平衡常数 Kc 以平衡浓度表示。固体和纯液体不写入表达式。
For gaseous reactions, Kp uses partial pressures. Kp and Kc are related by Kp = Kc (RT)^{Δn}, where Δn = (c+d) – (a+b).
Kp = (p_C^c p_D^d) / (p_A^a p_B^b) Kp = Kc (RT)^{Δn}
对于气相反应，Kp 使用分压。Kp 与 Kc 的关系为 Kp = Kc (RT)^{Δn}，其中 Δn = (c+d) – (a+b)。
The reaction quotient Q has the same form as K but uses non-equilibrium concentrations. If Q < K, the forward reaction is favoured.
Q = [C]ᶜ[D]ᵈ / ([A]ᵃ[B]ᵇ) (non-equilibrium)
反应商 Q 的表达式与 K 相同，但使用非平衡浓度。若 Q < K，则正向反应有利。
Le Chatelier’s principle predicts the direction of shift for changes in concentration, pressure or temperature. A catalyst does not affect the equilibrium position or K.
Shift minimises imposed change; K varies only with temperature.
勒沙特列原理预测浓度、压力或温度改变时平衡移动的方向。催化剂不影响平衡位置或 K 值。
7. Acid–Base Equilibria | 酸碱平衡
The ionic product of water at 298 K is K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶. pH and pOH are defined as negative logarithms.
K_w = [H⁺][OH⁻] pH = –log₁₀[H⁺] pOH = –log₁₀[OH⁻]
pH + pOH = 14 (at 298 K)
水的离子积在 298 K 时为 K_w = 1.0 × 10⁻¹⁴ mol²·dm⁻⁶。pH 和 pOH 定义为负对数。
For a weak acid HA, the acid dissociation constant Kₐ is used. pKₐ = –log₁₀Kₐ.
Kₐ = [H⁺][A⁻] / [HA] pKₐ = –log₁₀Kₐ
对于弱酸 HA，使用酸解离常数 Kₐ。pKₐ = –log₁₀Kₐ。
The Henderson–Hasselbalch equation relates the pH of a buffer to the ratio of conjugate base and acid concentrations.
pH = pKₐ + log₁₀([A⁻] / [HA])
亨德森-哈塞尔巴尔赫方程将缓冲溶液的 pH 与共轭碱和酸的浓度比关联起来。
For a weak base B, the base dissociation constant K_b is used; pK_b = –log₁₀K_b, and pKₐ + pK_b = 14 for a conjugate pair.
K_b = [BH
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