Equilibrium Expressions and the Equilibrium Constant, Kc | 平衡表达式与平衡常数 Kc

📚 Equilibrium Expressions and the Equilibrium Constant, K_c | 平衡表达式与平衡常数 K_c

Chemical equilibrium is a core concept in A-Level Chemistry. When a reversible reaction reaches equilibrium, the rates of the forward and reverse reactions become equal, and the concentrations of reactants and products remain constant. The equilibrium constant, K_c, provides a quantitative measure of the position of equilibrium, allowing chemists to predict the extent of a reaction under given conditions. This article explores how to write equilibrium expressions, calculate K_c, and interpret its significance.

化学平衡是 A-Level 化学的核心概念。当可逆反应达到平衡时，正反应和逆反应的速率相等，反应物和产物的浓度保持恒定。平衡常数 K_c 为平衡位置提供了定量的度量，使化学家能够预测在给定条件下反应进行的程度。本文将探讨如何书写平衡表达式、计算 K_c 并解释其意义。

1. Introduction to Reversible Reactions and Equilibrium | 可逆反应与化学平衡简介

Many chemical reactions are reversible, meaning they can proceed in both the forward and reverse directions. In such reactions, the conversion of reactants to products and products back to reactants occurs simultaneously. The reversible nature is often indicated by the symbol ⇌. At the start, only reactants are present; as the forward reaction proceeds, products form. Once products accumulate, the reverse reaction begins to regenerate reactants. Eventually, the rates of the forward and reverse reactions become equal. This state is called dynamic equilibrium. At equilibrium, the concentrations of all species remain constant over time, but they are not necessarily equal. The reaction is still occurring in both directions, but there is no net change in concentrations.

许多化学反应是可逆的，这意味着它们既可以正向进行，也可以逆向进行。在这类反应中，反应物转化为产物和产物重新生成反应物同时发生。可逆性通常用符号 ⇌ 表示。开始时仅存在反应物；随着正反应的进行，产物生成。一旦产物积累，逆反应开始重新生成反应物。最终，正反应和逆反应的速率相等，这种状态称为动态平衡。在平衡状态下，所有物种的浓度随时间保持恒定，但它们不一定相等。反应仍双向进行，但浓度没有净变化。

2. Defining the Equilibrium Constant, K_c | 平衡常数 K_c 的定义

For a general reversible reaction written as:

对于一般的可逆反应：

aA + bB ⇌ cC + dD

the equilibrium constant expressed in terms of concentration, K_c, is defined by the following equilibrium expression:

以浓度表示的平衡常数 K_c 由以下平衡表达式定义：

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

Here, square brackets denote the equilibrium concentration of a species in mol dm⁻³. The exponents a, b, c and d are the stoichiometric coefficients taken directly from the balanced chemical equation. This form follows from the law of mass action, which states that at a given temperature, the ratio of the product of the concentrations of the products raised to their stoichiometric coefficients to that of the reactants remains constant. K_c is therefore a constant for a particular reaction at a fixed temperature.

此处，方括号表示物种的平衡浓度，单位为 mol dm⁻³。指数 a、b、c 和 d 是配平化学方程式中的化学计量数。这一形式源自质量作用定律，该定律指出：在给定温度下，产物浓度以其化学计量数为指数的乘积与反应物浓度以其化学计量数为指数的乘积之比为一常数。因此，对于特定反应，在固定温度下，K_c 是一个常数。

3. Rules for Writing Equilibrium Expressions | 书写平衡表达式的规则

When constructing an equilibrium expression, several important rules must be followed. First, the expression must be based on a correctly balanced chemical equation. The stoichiometric coefficients become the exponents for the concentrations. Second, only species that are present in the reaction mixture and whose concentrations can change are included. The concentration of a pure solid is constant and is therefore omitted from the expression; the same applies to a pure liquid in a heterogeneous equilibrium. In dilute aqueous solutions, the concentration of water is effectively constant, so water is often omitted unless it is a reactant or product whose change is significant (e.g., in esterification where water is a product, not a solvent). Third, concentrations are always expressed in mol dm⁻³. Finally, the expression is written with products in the numerator and reactants in the denominator.

书写平衡表达式时，必须遵循几条重要规则。首先，表达式必须基于正确配平的化学方程式。化学计量数成为浓度的指数。其次，只包括存在于反应混合物中且其浓度可以变化的物种。纯固体的浓度是常数，因此不出现在表达式中；在多相平衡中，纯液体也是如此。在稀水溶液中，水的浓度实际上是常数，因此水通常被省略，除非它是反应物或产物且变化显著（例如在酯化反应中，水是产物而不是溶剂）。第三，浓度始终以 mol dm⁻³ 表示。最后，表达式写作产物在分子、反应物在分母的形式。

4. Homogeneous versus Heterogeneous Equilibria | 均相平衡与多相平衡

Equilibria are classified as homogeneous if all reactants and products are in the same phase (all gases or all aqueous ions). For a homogeneous gaseous reaction such as N₂(g) + 3H₂(g) ⇌ 2NH₃(g), all species are gases, and the equilibrium expression is K_c = [NH₃]² / ([N₂][H₂]³). In a heterogeneous equilibrium, the species exist in different phases. A classic example is the thermal decomposition of calcium carbonate: CaCO₃(s) ⇌ CaO(s) + CO₂(g). Here, CaCO₃ and CaO are pure solids, so their concentrations are constant and do not appear in the expression; thus K_c = [CO₂]. Another important case is the esterification reaction: CH₃COOH(l) + C₂H₅OH(l) ⇌ CH₃COOC₂H₅(l) + H₂O(l). Although all species are liquids, water is not the solvent, so it must be included: K_c = [CH₃COOC₂H₅][H₂O] / ([CH₃COOH][C₂H₅OH]).

如果所有反应物和产物处于同一相（均为气体或均为水溶液中的离子），平衡被归类为均相平衡。对于均相气相反应，如 N₂(g) + 3H₂(g) ⇌ 2NH₃(g)，所有物种都是气体，平衡表达式为 K_c = [NH₃]² / ([N₂][H₂]³)。在多相平衡中，物种存在于不同的相。一个经典例子是碳酸钙的热分解：CaCO₃(s) ⇌ CaO(s) + CO₂(g)。此处 CaCO₃ 和 CaO 是纯固体，其浓度恒定，不出现在表达式中；因此 K_c = [CO₂]。另一个重要情况是酯化反应：CH₃COOH(l) + C₂H₅OH(l) ⇌ CH₃COOC₂H₅(l) + H₂O(l)。尽管所有物种都是液体，水并非溶剂，因此必须包含在内：K_c = [CH₃COOC₂H₅][H₂O] / ([CH₃COOH][C₂H₅OH])。

5. Units of K_c | K_c 的单位

The units of K_c depend on the stoichiometry of the reaction. Since each concentration term has units of mol dm⁻³, the overall unit is (mol dm⁻³)^Δn, where Δn = (sum of stoichiometric coefficients of products appearing in the expression) – (sum of stoichiometric coefficients of reactants appearing in the expression). Solids and pure liquids are not counted because they are omitted from the expression. For example, for 2NH₃(g) ⇌ N₂(g) + 3H₂(g), Δn = (1+3) – 2 = 2, so the units would be (mol dm⁻³)² = mol² dm⁻⁶, but if we write the expression for the forward reaction N₂ +

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