Gas Reaction Equilibrium Constant Kp | 气体反应平衡常数Kp

📚 Gas Reaction Equilibrium Constant Kp | 气体反应平衡常数Kp

In gaseous equilibria, the extent of reaction can be quantified using an equilibrium constant based on partial pressures, known as Kp. This constant is especially useful for reactions involving gases, where measuring pressures is often more convenient than measuring concentrations.

在气体平衡中，反应进行的程度可以通过基于分压的平衡常数 Kp 来量化。该常数对于涉及气体的反应特别有用，因为测量压力通常比测量浓度更方便。

1. Partial Pressures and Mole Fractions | 分压与摩尔分数

For a gas mixture, the partial pressure of a component is the pressure it would exert if it occupied the container alone. According to Dalton’s law, the total pressure is the sum of all partial pressures. The mole fraction of a component i is xᵢ = nᵢ / n_total, and its partial pressure is Pᵢ = xᵢ × P_total.

对于气体混合物，某组分的分压是指它单独占据容器时所施加的压力。根据道尔顿定律，总压等于所有分压之和。组分 i 的摩尔分数为 xᵢ = nᵢ / n_total，其分压为 Pᵢ = xᵢ × P_total。

2. Writing Kp Expressions | 写出 Kp 表达式

Consider a general homogeneous gas-phase reaction:

aA(g) + bB(g) ⇌ cC(g) + dD(g)

Kp is defined as the ratio of the partial pressures of the products to those of the reactants, each raised to the power of its stoichiometric coefficient:

Kp = (P_C^c × P_D^d) / (P_A^a × P_B^b)

Note that only gases appear in the expression; pure solids and liquids are omitted because their activities are constant.

对于一般的均相气相反应：aA(g) + bB(g) ⇌ cC(g) + dD(g)，Kp 定义为产物的分压乘积与反应物的分压乘积之比，各分压以其化学计量系数为指数。注意，只有气体出现在表达式中；纯固体和纯液体被省略，因为它们的活度为常数。

3. Relationship Between Kp and Kc | Kp 与 Kc 的关系

Using the ideal gas law, the partial pressure of a gas is related to its molar concentration c by P = cRT. Substituting this into the Kp expression gives a direct link between Kp and Kc:

Kp = Kc(RT)^Δn

where Δn = (c + d) − (a + b) is the change in the number of moles of gas from reactants to products. The value of R must be consistent with the pressure units used.

利用理想气体定律，气体的分压与摩尔浓度 c 的关系为 P = cRT。将其代入 Kp 表达式，可得 Kp 与 Kc 的直接联系：Kp = Kc(RT)^Δn。其中 Δn = (c + d) − (a + b) 是从反应物到产物气体摩尔数的变化量。R 的取值必须与所用的压力单位一致。

4. Units of Kp | Kp 的单位

The units of Kp depend on Δn. If pressure is measured in atm, kPa or Pa, the units are (atm)^Δn, (kPa)^Δn or (Pa)^Δn, respectively. When Δn = 0, Kp is dimensionless. In CIE exams, you must state the units unless Δn = 0.

Kp 的单位取决于 Δn。若压力以 atm、kPa 或 Pa 为单位，则 Kp 的单位分别为 (atm)^Δn、(kPa)^Δn 或 (Pa)^Δn。当 Δn = 0 时，Kp 无单位。在 CIE 考试中，除非 Δn = 0，否则必须写出单位。

5. Calculating Kp from Equilibrium Data | 从平衡数据计算 Kp

Consider the decomposition of dinitrogen tetroxide: N₂O₄(g) ⇌ 2NO₂(g). At a certain temperature, a mixture at equilibrium contains 0.20 mol N₂O₄ and 0.40 mol NO₂, and the total pressure is 2.00 atm. Using Dalton’s law:

P(N₂O₄) = (0.20 / 0.60) × 2.00 = 0.667 atm

P(NO₂) = (0.40 / 0.60) × 2.00 = 1.333 atm

The equilibrium constant is:

Kp = (P_NO₂)² / P_N₂O₄ = (1.333)² / 0.667 = 2.67 atm

So Kp = 2.67 atm (or 2.67 × 10⁵ Pa if converted).

考虑四氧化二氮的分解：N₂O₄(g) ⇌ 2NO₂(g)。在某温度下，平衡混合物中含有 0.20 mol N₂O₄ 和 0.40 mol NO₂，总压为 2.00 atm。根据道尔顿定律：P(N₂O₄) = (0.20 / 0.60) × 2.00 = 0.667 atm；P(NO₂) = (0.40 / 0.60) × 2.00 = 1.333 atm。平衡常数为：Kp = (P_{NO₂})² / P_{N₂O₄} = (1.333)² / 0.667 = 2.67 atm。因此 Kp = 2.67 atm（若换算则为 2.67 × 10⁵ Pa）。

6. Using Kp to Predict the Position of Equilibrium | 用 Kp 判断平衡位置

We can compare the reaction quotient Qp (calculated from current partial pressures) with Kp. If Qp < Kp, the reaction proceeds forward to produce more products. If Qp > Kp, it proceeds in the reverse direction. When Qp = Kp, the system is at equilibrium.

我们可将反应商 Qp（由当前分压计算得到）与 Kp 比较。若 Qp < Kp，反应正向进行以生成更多产物；若 Qp > Kp，反应逆向进行。当 Qp = Kp 时，体系处于平衡状态。

7. Effect of Pressure on an Equilibrium Mixture | 压力对平衡混合物的影响

According to Le Chatelier’s principle, increasing the total pressure shifts the equilibrium to the side with fewer moles of gas. However, Kp itself is unaffected by pressure changes at constant temperature. Only the individual partial pressures redistribute to keep Kp constant.

根据勒夏特列原理，增大总压会使平衡向气体摩尔数较少的一侧移动。然而，在恒温条件下，Kp 本身不受压力变化的影响。只是各分压会重新分布，以维持 Kp 不变。

8. Effect of Temperature on Kp | 温度对 Kp 的影响

Kp changes with temperature because the equilibrium position shifts. For an exothermic forward reaction, raising the temperature decreases Kp and favours the reverse reaction. For an endothermic forward reaction, raising the temperature increases Kp. The van’t Hoff equation describes this quantitatively:

d(ln Kp) / dT = ΔH° / (RT²)

where ΔH° is the standard enthalpy change. This explains why Kp is a function of temperature only, not of pressure or concentration.

Kp 随温度变化，因为平衡位置会移动。对于正向放热反应，升高温度会降低 Kp 并有利于逆向反应；对于正向吸热反应，升高温度会使 Kp 增大。范特霍夫方程定量描述了这一关系：d(ln Kp) / dT = ΔH° / (RT²)，其中 ΔH° 为标准焓变。这解释了为什么 Kp 仅仅是温度的函数，而不是压力或浓度的函数。

9. Catalysts and Kp | 催化剂与 Kp

Catalysts increase the rate at which equilibrium is reached but do not alter the equilibrium position or the value of Kp. They lower the activation energy for both forward and reverse reactions equally. Hence, Kp is independent of the presence of a catalyst.

催化剂能加快到达平衡的速率，但不会改变平衡位置或 Kp 的数值。它们同等地降低正逆反应的活化能。因此，Kp 与催化剂的存在与否无关。

10. Exam Tips and Common Pitfalls | 考试要点与常见误区

Here are important reminders for CIE exams:

Ensure the reaction is homogeneous and all species are gases before writing Kp.

在写出 Kp 之前，确保反应是均相且所有物种都是气体。
Exclude solids and liquids from the Kp expression.

在 Kp 表达式中省略固体和液体。
Use consistent pressure units throughout the calculation.

在整个计算过程中使用一致的压力单位。
Raise each partial pressure to the power equal to its stoichiometric coefficient.

每个分压的指数等于其化学计量系数。
Determine Δn correctly to state the units of Kp.

正确计算 Δn 以给出 Kp 的单位。
Remember that Kp only changes with temperature, not pressure or catalyst.

记住 Kp 只随温度变化，不随压力或催化剂变化。

11. Summary | 总结

Kp is a powerful tool for describing gaseous equilibria. It is expressed in terms of partial pressures, relates to Kc through Kp = Kc(RT)^Δn, has units depending on Δn, and is only affected by temperature. Mastering the calculation of partial pressures and the correct manipulation of Kp expressions is essential for A-Level Chemistry.

Kp 是描述气体平衡的有力工具。它以分压表示，通过 Kp = Kc(RT)^Δn 与 Kc 联系，其单位取决于 Δn，并且仅受温度影响。掌握分压的计算以及 Kp 表达式的正确运用是 A-Level 化学的重要内容。

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Gas Reaction Equilibrium Constant Kp | 气体反应平衡常数Kp