📚 Understanding Equilibrium Constants: Concepts and Applications | 平衡常数的概念与应用
In chemical equilibria, the equilibrium constant is a central quantity that expresses the relationship between the concentrations (or pressures) of reactants and products when a reversible reaction has reached dynamic equilibrium. It is one of the most examined concepts in A-level Chemistry because it connects kinetics, energetics, and industrial yield.
在化学平衡中，平衡常数是核心量，它表达了可逆反应达到动态平衡时反应物与产物浓度（或分压）之间的关系。它是 A-Level 化学中最常考的考点之一，因为它将反应速率、能量变化和工业生产产率联系在一起。
1. What Is Dynamic Equilibrium? | 什么是动态平衡
Dynamic equilibrium occurs in a closed system when the forward and reverse reactions take place at the same rate. The macroscopic concentrations of reactants and products remain constant, but individual molecules continue to react at the microscopic level.
动态平衡发生在封闭体系中，此时正反应与逆反应速率相等。反应物和产物的宏观浓度保持不变，但单个分子在微观层面上仍在持续反应。
Both forward and reverse reactions are still occurring, so the equilibrium is dynamic rather than static.
正逆反应仍在进行，因此该平衡是动态的，而不是静态的。
Equilibrium can only be reached in a closed system at constant temperature.
只有在恒温的封闭体系中才能达到平衡。
A common example is N₂O₄(g) ⇌ 2NO₂(g); the brown color remains constant at equilibrium.
一个常见的例子是 N₂O₄(g) ⇌ 2NO₂(g)，平衡时棕色的深浅保持不变。
2. The Law of Mass Action and the Definition of Kc | 质量作用定律与 Kc 的定义
For a general reversible reaction aA + bB ⇌ cC + dD, where all substances are gases or aqueous solutions, the equilibrium constant Kc is given by the law of mass action.
对于一般可逆反应 aA + bB ⇌ cC + dD，若所有物质均为气体或溶液，则平衡常数 Kc 可由质量作用定律给出。
Kc = [C]c[D]d / [A]a[B]b
Square brackets [ ] represent equilibrium concentrations in mol dm⁻³.
方括号 [ ] 表示平衡浓度，单位为 mol dm⁻³。
The exponents are the stoichiometric coefficients from the balanced chemical equation.
指数来自配平化学方程式中的化学计量系数。
For the Haber process N₂(g) + 3H₂(g) ⇌ 2NH₃(g), the expression is Kc = [NH₃]² / ([N₂][H₂]³).
对于哈伯法 N₂(g) + 3H₂(g) ⇌ 2NH₃(g)，其表达式为 Kc = [NH₃]² / ([N₂][H₂]³)。
3. Kp: Equilibrium Constant in Terms of Pressure | Kp：用分压表示的平衡常数
For reactions involving gases, the equilibrium constant can also be written using partial pressures. The relationship is the same as Kc, but pressure terms replace concentration terms.
对于涉及气体的反应，平衡常数也可以用分压来表示。其形式与 Kc 相同，只是用分压代替浓度。
Kp = (PCc × PDd) / (PAa × PBb)
The relationship between Kp and Kc for the same reaction is:
对同一反应，Kp 与 Kc 的关系为：
Kp = Kc × (RT)Δn
Δn = (moles of gaseous products) − (moles of gaseous reactants).
Δn =（气态产物总物质的量）−（气态反应物总物质的量）。
R must be chosen to match the units of pressure and concentration. For example, if Kc uses mol dm⁻³ and Kp uses kPa, R = 8.31 kPa dm³ mol⁻¹ K⁻¹.
选择 R 时必须与浓度和压力的单位相匹配。例如，Kc 用 mol dm⁻³、Kp 用 kPa 时，R = 8.31 kPa dm³ mol⁻¹ K⁻¹。
For N₂O₄(g) ⇌ 2NO₂(g), Δn = +1, so Kp = Kc(RT).
对于 N₂O₄(g) ⇌ 2NO₂(g)，Δn = +1，因此 Kp = Kc(RT)。
4. The Units of Kc and Kp | Kc 与 Kp 的单位
The units of an equilibrium constant depend on the change in the number of moles of gas, Δn. If Δn = 0, the constant is dimensionless.
平衡常数的单位取决于气体总物质的量的变化 Δn。如果 Δn = 0，则常数没有单位。
| Reaction | Δn | Unit of Kc | Unit of Kp |
|---|---|---|---|
| N₂(g) + 3H₂(g) ⇌ 2NH₃(g) | 2 − 4 = −2 | mol⁻² dm⁶ | atm⁻² |
| H₂(g) + I₂(g) ⇌ 2HI(g) | 2 − 2 = 0 | no units | no units |
| N₂O₄(g) ⇌ 2NO₂(g) | 2 − 1 = +1 | mol dm⁻³ | atm |
Always write the units for K unless Δn = 0, because examiners frequently award a mark for correct units.
除非 Δn = 0，否则务必写出 K 的单位，因为考官经常为正确的单位给分。
5. What Does the Size of K Tell Us? | K 的数值大小说明了什么
The magnitude of the equilibrium constant indicates the extent of a reaction, not how fast it reaches equilibrium.
平衡常数的大小表示反应进行的程度，而不是反应到达平衡的快慢。
K >> 1: the equilibrium mixture contains mostly products; the reaction favours the forward direction.
K >> 1：平衡混合物中产物占主导；反应正向有利。
K << 1: the equilibrium mixture contains mostly reactants; the reaction favours the reverse direction.
K << 1：平衡混合物中反应物占主导；反应逆向有利。
K ≈ 1: significant amounts of both reactants and products are present at equilibrium.
K ≈ 1：平衡时反应物和产物均有显著的量。
6. Reaction Quotient Q: Predicting the Direction of Change | 反应商 Q：预测反应方向
The reaction quotient Q has exactly the same mathematical form as K, but it is calculated using non-equilibrium concentrations or pressures.
反应商 Q 的数学形式与 K 完全相同，但它是用非平衡时的浓度或分压来计算的。
Q = [C]c[D]d / [A]a[B]b at any instant
If Q < K, the reaction will proceed in the forward direction to increase products.
若 Q < K，反应将正向进行以增加产物。
If Q > K, the reaction will proceed in the reverse direction to increase reactants.
若 Q > K，反应将逆向进行以增加反应物。
If Q = K, the system is already at equilibrium.
若 Q = K，体系已经处于平衡状态。
Example: for N₂O₄(g) ⇌ 2NO₂(g), Kc = 0.36. If [NO₂] = 0.20 mol dm⁻³ and [N₂O₄] = 0.10 mol dm⁻³, then Q = (0.20)² / (0.10) = 0.40. Since Q > K, the reverse reaction is favoured.
例如：对于 N₂O₄(g) ⇌ 2NO₂(g)，Kc = 0.36。若 [NO₂] = 0.20 mol dm⁻³、[N₂O₄] = 0.10 mol dm⁻³，则 Q = (0.20)² / (0.10) = 0.40。因为 Q > K，所以逆向反应有利。
7. Calculating Kc from Equilibrium Concentrations | 由平衡浓度计算 Kc
Worked example: 0.100 mol of N₂O₄ is placed in a 1.00 dm³ closed vessel at constant temperature. At equilibrium, the concentration of NO₂ is 0.120 mol dm⁻³. Calculate Kc for N₂O₄(g) ⇌ 2NO₂(g).
例题：在恒温下将 0.100 mol N₂O₄ 放入 1.00 dm³ 的密闭容器中。平衡时 NO₂ 的浓度为 0.120 mol dm⁻³。计算 N₂O₄(g) ⇌ 2NO₂(g) 的 Kc。
Let x be the amount of N₂O₄ that reacts: [NO₂] = 2x = 0.120 mol dm⁻³, so x = 0.060 mol dm⁻³.
设 x 为发生反应的 N₂O₄ 的浓度：[NO₂] = 2x = 0.120 mol dm⁻³，因此 x = 0.060 mol dm⁻³。
[N₂O₄] at equilibrium = 0.100 − 0.060 = 0.040 mol dm⁻³.
平衡时 [N₂O₄] = 0.100 − 0.060 = 0.040 mol dm⁻³。
Kc = (0.120)² / (0.040) = 0.36 mol dm⁻³.
Kc = (0.120)² / (0.040) = 0.36 mol dm⁻³。
8. Using ICE Tables in Equilibrium Calculations | 用 ICE 表格进行平衡计算
ICE stands for Initial, Change, and Equilibrium. It is a systematic method for solving equilibrium problems with unknown quantities.
ICE 表示 Initial（初始）、Change（变化）和 Equilibrium（平衡）。这是解决含未知量平衡问题的系统方法。
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