A-Level Chemistry: Equilibrium Expressions and the Equilibrium Constant Kc | A-Level 化学：平衡表达式与平衡常数Kc

📚 A-Level Chemistry: Equilibrium Expressions and the Equilibrium Constant Kc | A-Level 化学：平衡表达式与平衡常数Kc

Chemical equilibrium is one of the most important ideas in A-Level Chemistry. Many reactions do not simply go to completion; instead, they reach a state where the forward and reverse reactions occur at the same rate. This article explains how to write equilibrium expressions and how to use the equilibrium constant, Kc, in calculations.

化学平衡是A-Level化学中最重要的概念之一。许多反应并不会简单地完全进行到底，而是达到一种正向反应与逆向反应速率相等的状态。本文将讲解如何书写平衡表达式，以及如何运用平衡常数Kc进行计算。

1. Reversible Reactions and Dynamic Equilibrium | 可逆反应与动态平衡

In a closed system, a reversible reaction can proceed in both the forward and reverse directions. Initially, the forward reaction is faster because the concentrations of reactants are high. As reactants are used up and products accumulate, the forward rate decreases and the reverse rate increases. Eventually, the two rates become equal.

在封闭体系中，可逆反应可以同时向正向和逆向两个方向进行。初始时，由于反应物浓度较高，正反应速率较快。随着反应物的消耗和生成物的积累，正反应速率下降，逆反应速率上升。最终，两个方向的速率达到相等。

This state is called dynamic equilibrium. It is dynamic because the reaction has not stopped; it continues at the molecular level, but there is no observable change in the concentrations of reactants and products.

这种状态称为动态平衡。说它“动态”，是因为反应并未停止，在分子层面上仍然继续进行，只是反应物和生成物的浓度不再发生可观察的变化。

Dynamic equilibrium only occurs in a closed system, and the conditions such as temperature and pressure must remain constant.

动态平衡只发生在封闭体系中，且温度、压强等条件必须保持不变。

2. The Equilibrium Constant Kc: Definition | 平衡常数Kc的定义

For a reaction at equilibrium, there is a mathematical relationship between the concentrations of reactants and products. This relationship is known as the equilibrium expression, and its value at a fixed temperature is called the equilibrium constant, Kc. The subscript ‘c’ indicates that concentrations in mol dm⁻³ are used.

对于处于平衡状态的反应，反应物浓度与产物浓度之间存在一种数学关系。这种关系称为平衡表达式，其在一定温度下的数值称为平衡常数Kc。下标“c”表示使用以mol dm⁻³为单位的浓度。

For a general reaction:

对于一个一般反应：

aA + bB ⇌ cC + dD

The equilibrium expression is written as:

其平衡表达式写作：

Kc = [C]^c[D]^d / [A]^a[B]^b

Here, the square brackets mean concentration in mol dm⁻³. The coefficients a, b, c and d from the balanced equation become powers in the expression.

其中方括号表示以mol dm⁻³为单位的浓度。平衡方程式中的系数a、b、c和d在表达式中变为指数。

This expression is called the ‘mass action’ or equilibrium law. It is valid only at a specific temperature.

该表达式称为“质量作用定律”或平衡定律。它仅在特定温度下成立。

3. Writing Equilibrium Expressions | 书写平衡表达式

To write an equilibrium expression, you must first have a correctly balanced chemical equation. The products always appear in the numerator, and the reactants appear in the denominator. Each concentration is raised to the power of its stoichiometric coefficient.

要书写平衡表达式，首先必须有一个配平正确的化学方程式。生成物总是出现在分子中，反应物出现在分母中。每个浓度都要以其化学计量系数为指数。

Consider the Haber process:

以哈伯法为例：

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

The equilibrium expression is:

其平衡表达式为：

Kc = [NH₃]² / ([N₂][H₂]³)

Notice that the coefficient 2 for NH₃ becomes the power 2, and the coefficient 3 for H₂ becomes the power 3.

注意NH₃的系数2变成了指数2，H₂的系数3变成了指数3。

Another common example is the formation of sulfur trioxide:

另一个常见例子是三氧化硫的生成：

2SO₂(g) + O₂(g) ⇌ 2SO₃(g)

Its expression is:

其表达式为：

Kc = [SO₃]² / ([SO₂]²[O₂])

In this example, SO₂ and SO₃ both have coefficients of 2, so both are squared.

在这个例子中，SO₂和SO₃的系数都为2，因此两者都要平方。

4. Conventions: Omitting Solids and Pure Liquids | 约定：忽略固体和纯液体

In a heterogeneous equilibrium, some substances are in different physical states. Only species whose concentration can change independently are included in the Kc expression. Solids and pure liquids are omitted because their concentrations are effectively constant.

在多相平衡中，有些物质处于不同的物理状态。只有浓度可以独立变化的物种才被包含在Kc表达式中。固体和纯液体的浓度实际上是常数，因此被省略。

For example, consider the thermal decomposition of calcium carbonate:

例如，考虑碳酸钙的热分解：

CaCO₃(s) ⇌ CaO(s) + CO₂(g)

The equilibrium expression is simply:

其平衡表达式简化为：

Kc = [CO₂]

The solids CaCO₃ and CaO do not appear in the expression. This is because their concentrations are fixed by the amount of solid present and do not affect the equilibrium position.

固体CaCO₃和CaO不出现在表达式中。这是因为它们的浓度由固体存在的量决定且保持不变，不会影响平衡位置。

Another example involving a pure liquid is:

另一个涉及纯液体的例子是：

C₂H₅OH(l) + CH₃COOH(l) ⇌ CH₃COOC₂H₅(l) + H₂O(l)

Here, all species are liquids and are miscible. Because water is formed in the reaction and is not the solvent in large excess, it might be included. However, if water is present in excess as a solvent, it would be omitted. Always pay attention to the physical states given in the question.

在这个例子中，所有物质都是液体且互溶。由于水是反应中生成的，且不是大量过量的溶剂，因此可能会被包含。然而，如果水作为溶剂大量过量存在，则会被省略。做题时一定要注意题目给出的物理状态。

5. Units of Kc | Kc的单位

The units of Kc depend on the form of the equilibrium expression. They are not always mol dm⁻³; they must be derived from the expression each time. To find the units, substitute the units of concentration into the expression and simplify.

Kc的单位取决于平衡表达式的具体形式。它并不总是mol dm⁻³，必须每次根据表达式推导。要找到单位，只需将浓度的单位代入表达式并化简即可。

For the reaction:

对于反应：

H₂(g) + I₂(g) ⇌ 2HI(g)

the expression is:

其表达式为：

Kc = [HI]² / ([H₂][I₂])

The units are:

其单位为：

(mol dm⁻³)² / (mol dm⁻³ × mol dm⁻³) = 1

So Kc has no units for this reaction.

因此该反应的Kc没有单位。

For the reaction:

对于反应：

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

the units are:

其单位为：

(mol dm⁻³)² / (mol dm⁻³ × (mol dm⁻³)³) = dm⁶ mol⁻²

So Kc has units of dm⁶ mol⁻². Different reactions give different units, so you must always calculate them.

因此Kc的单位为dm⁶ mol⁻²。不同反应会得到不同单位，因此必须每次计算。

6. What the Magnitude of Kc Tells Us | Kc的数值告诉我们什么

The size of Kc indicates how far a reaction proceeds at equilibrium. A large Kc value means that, at equilibrium, the concentration of products is much greater than that of reactants. The equilibrium lies to the right, or towards the products.

Kc数值的大小表明反应在平衡时进行的程度。Kc值很大意味着平衡时生成物浓度远大于反应物浓度。平衡位置靠右，即偏向生成物。

A small Kc value means that the reactants are favoured. The equilibrium lies to the left, and very little product is formed.

Kc值很小则意味着反应物占优势。平衡位置靠左，生成的产物很少。

If Kc > 10³, the equilibrium lies far to the right.

如果Kc > 10³，平衡位置远在右侧。
If Kc < 10⁻³, the equilibrium lies far to the left.

如果Kc < 10⁻³，平衡位置远在左侧。
If Kc is between roughly 10⁻³ and 10³, both reactants and products are present in significant amounts.

如果Kc约在10⁻³到10³之间，则反应物和生成物都以显著量存在。

It is important not to say that Kc ‘shows how fast’ a reaction is. A reaction with a large Kc could be very slow. Kc tells us about the position of equilibrium, not the rate.

必须注意，不能说Kc“表示反应有多快”。Kc很大的反应可能非常慢。Kc告诉我们的是平衡位置，而不是反应速率。

7. Calculating Equilibrium Concentrations Using Kc | 用Kc计算平衡浓度

To calculate Kc, you need the equilibrium concentrations of all species in the expression. These are often found by constructing an ICE table: Initial, Change, Equilibrium.

要计算Kc，需要表达式中所有物种的平衡浓度。通常通过建立ICE表格来找到这些浓度：I代表初始浓度，C代表浓度变化，E代表平衡浓度。

Worked example:

计算示例：

PCl₅(g) ⇌ PCl₃(g) + Cl₂(g)

2.00 mol of PCl₅ is placed in a 5.00 dm³ container. At equilibrium, 0.50 mol of PCl₅ remains. Calculate Kc.

将2.00 mol的PCl₅置于一个5.00 dm³的容器中。平衡时，剩余0.50 mol的PCl₅。计算Kc。

Step 1: Calculate the initial concentration of PCl₅.

第一步：计算PCl₅的初始浓度。

[PCl₅]₀ = 2.00 / 5.00 = 0.400 mol dm⁻³

Step 2: Calculate the equilibrium concentration of PCl₅.

第二步：计算PCl₅的平衡浓度。

[PCl₅] = 0.50 / 5.00 = 0.100 mol dm⁻³

Step 3: Determine the change in concentration of PCl₅.

第三步：确定PCl₅的浓度变化。

Change = 0.400 − 0.100 = 0.300 mol dm⁻³

Since the stoichiometry is 1:1:1, the concentrations of PCl₃ and Cl₂ that form are both 0.300 mol dm⁻³.

由于化学计量比为1:1:1，生成的PCl₃和Cl₂的浓度均为0.300 mol dm⁻³。

Step 4: Write the equilibrium expression and substitute the equilibrium concentrations.

第四步：写出平衡表达式并代入平衡浓度。

Kc = [PCl₃][Cl₂] / [PCl₅] = (0.300 × 0.300) / 0.100 = 0.900

Step 5: Determine the units.

第五步：确定单位。

(mol dm⁻³)(mol dm⁻³) / (mol dm⁻³) = mol dm⁻³

So Kc = 0.900 mol dm⁻³.

因此Kc = 0.900 mol dm⁻³。

This example shows how important it is to convert moles to concentrations when using Kc. Never use moles directly in the Kc expression.

这个例子说明了使用Kc时把物质的量转化为浓度是多么重要。绝不能在Kc表达式中直接使用物质的量。

8. The Reaction Quotient Qc and Predicting Direction | 反应商Qc与方向预测

The reaction quotient Qc has exactly the same form as Kc, but it is calculated using concentrations that are not necessarily at equilibrium. Comparing Qc with Kc tells you which direction the reaction will shift to reach equilibrium.

反应商Qc的形式与Kc完全相同，但它使用的浓度不一定是平衡浓度。比较Qc与Kc可以判断反应将朝哪个方向移动以达到平衡。

For the general reaction:

对于一般反应：

aA + bB ⇌ cC + dD

the reaction quotient is:

其反应商为：

Qc = [C]^c[D]^d / [A]^a[B]^b

If Qc < Kc, there are more reactants relative to products than at equilibrium. The forward reaction is favoured, and more products will form.

如果Qc < Kc，意味着相对于平衡状态，反应物偏多。正反应占优势，会生成更多产物。
If Qc > Kc, there are more products relative to reactants than at equilibrium. The reverse reaction is favoured, and products will be converted back into reactants.

如果Qc > Kc，意味着相对于平衡状态，产物偏多。逆反应占优势，产物会转化回反应物。
If Qc = Kc, the system is already at equilibrium; no net change will occur.

如果Qc = Kc，体系已经处于平衡；不会发生净变化。

The reaction quotient is especially useful when you mix reactants and products in arbitrary amounts and need to predict whether the reaction will go forwards or backwards before reaching equilibrium.

反应商在我们将反应物和产物以任意量混合后、需要判断反应在达到平衡前会正向还是反向进行时尤其有用。

9. Effect of Changing Conditions on Kc | 条件改变对Kc的影响

Kc only depends on the temperature. It does not change when you alter concentration, pressure or add a catalyst. These changes may shift the position of equilibrium, but they do not change the value of Kc.

Kc只取决于温度。改变浓度、压强或加入催化剂不会改变Kc。这些条件可能会移动平衡位置，但不会改变Kc的值。

For an exothermic forward reaction, increasing the temperature decreases Kc. This is because heat is treated as a product, and the equilibrium shifts to the left, favouring reactants. For an endothermic forward reaction, increasing the temperature increases Kc.

对于正向放热的反应，升高温度会使Kc减小。这是因为热量被视为产物，平衡会向左移动，有利于反应物。对于正向吸热的反应，升高温度会使Kc增大。

Adding a catalyst lowers the activation energy for both the forward and reverse reactions equally. It speeds up the attainment of equilibrium but does not change the position of equilibrium or the value of Kc.

加入催化剂会同等程度地降低正反应和逆反应的活化能。它会加速平衡的到达，但不会改变平衡位置或Kc的值。

Changing pressure or concentration affects the equilibrium position according to Le Chatelier’s principle, but at a constant temperature Kc remains the same. When conditions change, the system adjusts until Qc once again equals Kc.

根据勒夏特列原理，改变压强或浓度会影响平衡位置，但在恒温下Kc保持不变。当条件改变时，系统会进行调整，直到Qc再次等于Kc。

10. Common Mistakes and Exam Tips | 常见错误与考试技巧

Many students lose marks on equilibrium questions because of careless errors. Here are some important mistakes to avoid.

许多学生在平衡题上失分是因为粗心错误。以下是一些需要避免的重要错误。

Using moles instead of concentrations. Always divide the number of moles by the total volume to get mol dm⁻³.

使用物质的量而不是浓度。务必用物质的量除以总体积，得到mol dm⁻³。
Including solids or pure liquids in the equilibrium expression. Remember to omit them.

在平衡表达式中包含固体或纯液体。记住要省略它们。
Using the wrong coefficients as powers. The powers in the Kc expression come directly from the balanced equation.

将错误的系数作为指数。Kc表达式中的指数直接来自配平的化学方程式。
Forgetting to include units. Always work out the units from the expression.

忘记写单位。务必根据表达式推导出单位。
Saying that Kc changes when concentration changes. Kc only changes with temperature.

错误地认为浓度改变会影响Kc。Kc只随温度改变。

In exam questions, always check the physical state symbols. If a substance is shown as (s) or (l) and is not in a mixture, it should be excluded from the Kc expression. Also check whether the question asks for the value only, or for both the value and units.

在考试题目中，务必检查物理状态符号。如果某物质以(s)或(l)表示，并且不处于混合物中，则它应被排除在Kc表达式之外。还要检查题目只要求数值，还是要求数值和单位都写出。

When asked to predict the effect of a change on Kc, think about temperature only. Changes in concentration or pressure alter the position of equilibrium but not Kc.

当被问到某个变化对Kc的影响时，只需要考虑温度。浓度或压强的改变会改变平衡位置，但不会改变Kc。

11. Summary | 总结

The equilibrium constant Kc is a fundamental quantity in chemical equilibria. It is defined by the equilibrium law and its value is constant at a fixed temperature.

平衡常数Kc是化学平衡中的基本量。它由平衡定律定义，且在固定温度下为常数。

To write the equilibrium expression, place the product concentrations in the numerator and the reactant concentrations in the denominator, each raised to the power of its stoichiometric coefficient. Omit solids and pure liquids. Be careful with units, as they differ from reaction to reaction.

书写平衡表达式时，将生成物浓度放在分子中，反应物浓度放在分母中，每一项的指数为其化学计量系数。省略固体和纯液体。注意单位，因为不同反应的单位不同。

The magnitude of Kc tells you whether products or reactants are favoured. The reaction quotient Qc can be used to predict the direction in which a reaction will move. Kc changes only with temperature, so any other changes to the system will not affect Kc, only the equilibrium position.

Kc的数值告诉你生成物还是反应物占优势。反应商Qc可用于预测反应移动的方向。Kc只随温度变化，因此对系统的任何其他改变都不会影响Kc，只会影响平衡位置。

By mastering equilibrium expressions and Kc calculations, you will be well prepared for CIE A-Level Chemistry exam questions on this topic.

掌握了平衡表达式和Kc计算，你就能从容应对CIE A-Level化学考试中与这一主题相关的题目。

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A-Level Chemistry: Equilibrium Expressions and the Equilibrium Constant Kc | A-Level 化学：平衡表达式与平衡常数Kc