IB Chemistry: Chemical Equilibrium and the Extent of Reaction | IB化学：化学平衡与反应限度

📚 IB Chemistry: Chemical Equilibrium and the Extent of Reaction | IB化学：化学平衡与反应限度

Chemical equilibrium is one of the central ideas in IB Chemistry. It explains why many reactions do not simply run to completion, but instead settle at a point where reactants and products coexist. This “point of balance” is called the equilibrium position, and it tells us the extent of reaction: how far the reaction has proceeded when the forward and reverse rates are equal.

化学平衡是 IB 化学的核心概念之一。它解释了为什么许多反应不会彻底进行到底，而是停留在反应物与产物共存的某个状态。这个“平衡点”称为平衡位置，它告诉我们反应限度：即当正逆反应速率相等时，反应已经进行的程度。

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1. Dynamic Equilibrium | 动态平衡

A reversible reaction in a closed system can reach a state called dynamic equilibrium. At this point the forward reaction and the reverse reaction are still taking place, but they occur at exactly the same rate. Because the two rates are equal, the concentrations of reactants and products stay constant over time.

封闭体系中的可逆反应可以到达一种称为“动态平衡”的状态。此时正反应和逆反应仍在进行，但速率完全相同。由于两个速率相等，反应物和产物的浓度随时间保持不变。

• A closed system is required: no matter may enter or leave, otherwise equilibrium cannot be established.

  需要封闭体系：物质不能进出，否则无法建立平衡。

• Macroscopic properties such as colour, pressure, pH and concentration remain constant.

  宏观性质，如颜色、压强、pH 和浓度，均保持不变。

• The rate of the forward reaction equals the rate of the reverse reaction: rate(forward) = rate(reverse).

  正反应速率等于逆反应速率：v(正) = v(逆)。

• Equilibrium is dynamic, not static: molecules continue to react in both directions.

  平衡是动态的而非静止的：分子仍在两个方向上持续反应。

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2. The Equilibrium Law and Kc | 平衡定律与 Kc

For a general reaction with stoichiometric coefficients, the equilibrium law gives an expression for the equilibrium constant Kc using concentrations.

对于具有化学计量系数的一般反应，平衡定律给出了用浓度表示的平衡常数 Kc 的表达式。

aA + bB ⇌ cC + dD

The equilibrium constant is written as:

平衡常数写作：

Kc = ([C]ᶜ[D]ᵈ) / ([A]ᵃ[B]ᵇ)

Square brackets represent concentration in mol dm⁻³. The value of Kc is constant at a given temperature.

方括号表示浓度，单位为 mol dm⁻³。在给定温度下，Kc 为常数。

Pure solids and pure liquids are not included in the expression because their “concentrations” are effectively constant. Only aqueous species and gases appear in Kc.

纯固体和纯液体不出现在平衡常数表达式中，因为它们的“浓度”实际上恒定不变。只有水溶液中的物种和气体才出现在 Kc 中。

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3. Kp and Gas-Phase Equilibria | Kp 与气相平衡

For reactions involving gases, partial pressures are used instead of concentrations. The equilibrium constant is then called Kp.

对于涉及气体的反应，用分压代替浓度。此时平衡常数称为 Kp。

Kp = p(C)ᶜ p(D)ᵈ / [p(A)ᵃ p(B)ᵇ]

Here p(A), p(B), p(C) and p(D) are the equilibrium partial pressures of the gases, usually measured in atm or kPa.

其中 p(A)、p(B)、p(C) 和 p(D) 是气体的平衡分压，通常以 atm 或 kPa 为单位。

For a mixture, the partial pressure of a gas A is its mole fraction multiplied by the total pressure:

对于混合气体，气体 A 的分压等于其摩尔分数乘以总压强：

p(A) = x(A) × P(total)

Since Kp is based on pressure, its units depend on the change in moles of gas. A catalyst never changes Kp, and neither does changing pressure.

由于 Kp 基于压强，其单位取决于气体物质的量变化。催化剂不会改变 Kp，改变压强也不会改变 Kp。

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4. Reaction Quotient Q vs K | 反应商 Q 与 K

The reaction quotient Q has exactly the same form as Kc or Kp, but it is calculated using concentrations or pressures at any moment during a reaction, not necessarily at equilibrium. Comparing Q with K tells us which direction the reaction will shift.

反应商 Q 的形式与 Kc 或 Kp 完全相同，但它使用反应过程中任意时刻的浓度或分压来计算，而不一定是在平衡时。将 Q 与 K 比较，可以判断反应将向哪个方向移动。

• If Q < K, the reaction proceeds in the forward direction to form more products.

  若 Q < K，反应正向进行，生成更多产物。

• If Q > K, the reaction proceeds in the reverse direction to form more reactants.

  若 Q > K，反应逆向进行，生成更多反应物。

• If Q = K, the system is at equilibrium.

  若 Q = K，体系处于平衡。

This idea is essential for predicting the behaviour of a disturbed equilibrium, especially in HL problems.

这一概念对于预测受扰平衡的行为至关重要，尤其是在 HL 题目中。

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5. Le Chatelier’s Principle | 勒夏特列原理

Le Chatelier’s principle states that if a dynamic equilibrium is disturbed by changing conditions, the position of equilibrium shifts in the direction that opposes the change.

勒夏特列原理指出：如果动态平衡因条件改变而受到扰动，平衡位置会朝着抵抗这种改变的方向移动。

This principle is a powerful qualitative tool. It allows chemists to predict how concentration, pressure and temperature changes affect the yield of a reaction, without performing any calculations.

该原理是一个强大的定性工具。它使化学家无需计算即可预测浓度、压强和温度变化如何影响反应的产率。

For example, if a product is removed continuously from a reactor, the equilibrium shifts to the right to replace it. This is why many industrial processes remove ammonia or sulfur trioxide as soon as it is formed.

例如，如果连续从反应器中移走产物，平衡会向右移动以补充产物。这就是许多工业生产过程一旦生成氨或三氧化硫便将其移走的原因。

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6. Concentration and Pressure Effects | 浓度与压强的影响

Changing the concentration of a reactant or product does not change the value of Kc; it only changes the position of equilibrium until Q again equals K.

改变反应物或产物的浓度不会改变 Kc 的数值；它只会改变平衡位置，直到 Q 重新等于 K。

• Increasing the concentration of a reactant shifts the equilibrium to the right.

  增加反应物浓度，平衡向右移动。

• Decreasing the concentration of a product shifts the equilibrium to the right.

  减少产物浓度，平衡向右移动。

• Increasing the concentration of a product shifts the equilibrium to the left.

  增加产物浓度，平衡向左移动。

For gaseous equilibria, changing pressure affects the position only when the number of moles of gas is different on each side of the equation.

对于气相平衡，改变压强只有在方程式两边气体物质的量不同时才影响平衡位置。

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

Here 4 moles of gas become 2 moles of gas. Increasing pressure shifts the equilibrium to the right because the right side has fewer gas molecules.

这里 4 mol 气体变为 2 mol 气体。增大压强使平衡向右移动，因为右边气体分子数更少。

Adding an inert gas at constant volume does not change the partial pressures of the reacting gases, so it causes no shift. At constant pressure, however, the total volume increases and partial pressures change, so the equilibrium may shift.

在恒容条件下加入惰性气体，不会改变反应气体的分压，因此平衡不移动。但在恒压条件下，总体积增大，分压改变，平衡可能移动。

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7. Temperature and Catalyst Effects | 温度与催化剂的影响

Temperature is special because it changes the value of K itself. The direction of the shift depends on whether the forward reaction is exothermic or endothermic.

温度非常特殊，因为它会改变 K 本身的值。移动方向取决于正反应是放热还是吸热。

• For an exothermic forward reaction, increasing temperature shifts the equilibrium to the left and decreases K.

  对于正反应放热的反应，升高温度使平衡向左移动，并降低 K。

• For an endothermic forward reaction, increasing temperature shifts the equilibrium to the right and increases K.

  对于正反应吸热的反应，升高温度使平衡向右移动，并增大 K。

A catalyst lowers the activation energy for both the forward and reverse reactions equally. It speeds up the rate at which equilibrium is reached, but it does not change the position of equilibrium and does not change the value of K.

催化剂对正、逆反应等程度地降低活化能。它加快达到平衡的速度，但不会改变平衡位置，也不会改变 K 的数值。

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8. ICE Tables and Calculations | ICE 表格与计算

ICE stands for Initial, Change and Equilibrium. This method is used to solve equilibrium problems systematically.

ICE 分别代表 Initial（初始）、Change（变化）和 Equilibrium（平衡）。这种方法用于系统地解决平衡计算问题。

Consider the Haber process equation:

考虑哈伯法反应方程式：

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

Suppose a mixture starts with 1.00 mol dm⁻³ N₂, 3.00 mol dm⁻³ H₂ and no NH₃. The ICE table is:

假设初始时 N₂ 浓度为 1.00 mol dm⁻³，H₂ 浓度为 3.00 mol dm⁻³，NH₃ 为 0。ICE 表格如下：

Species	N₂	H₂	NH₃
Initial / 初始 (mol dm⁻³)	1.00	3.00	0
Change / 变化 (mol dm⁻³)	−x	−3x	+2x
Equilibrium / 平衡 (mol dm⁻³)	1.00 − x	3.00 − 3x	2x

If the equilibrium concentration of NH₃ is 0.500 mol dm⁻³, then 2x = 0.500, so x = 0.250. The equilibrium concentrations are:

如果 NH₃ 的平衡浓度为 0.500 mol dm⁻³，则 2x = 0.500，因此 x = 0.250。平衡浓度为：

[N₂] = 0.750 mol dm⁻³, [H₂] = 2.25 mol dm⁻³, [NH₃] = 0.500 mol dm⁻³

Then Kc is calculated as:

然后计算 Kc：

Kc = (0.500)² / [(0.750)(2.25)³] = 0.0293 dm⁶ mol⁻²

Always check the units of Kc by adding the exponents of the concentration terms.

始终通过将浓度项的指数相加来检查 Kc 的单位。

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9. Equilibrium and Thermodynamics | 平衡与热力学

The equilibrium constant is related to the standard Gibbs free energy change of the reaction by the equation:

平衡常数与反应的标准吉布斯自由能变通过以下方程关联：

ΔG° = −RT ln K

Here R is the gas constant, T is the temperature in kelvin, and K is the equilibrium constant.

其中 R 是气体常数，T 是开尔文温度，K 是平衡常数。

If ΔG° is

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