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Deep Understanding of Gibbs Free Energy | 深入理解吉布斯自由能

2026-08-30 13:33 · 本文部分内容由AI辅助创作

📚 Deep Understanding of Gibbs Free Energy | 深入理解吉布斯自由能

Gibbs free energy is a thermodynamic quantity that predicts whether a reaction is spontaneous under constant temperature and pressure. It combines enthalpy, entropy and temperature into a single value, ΔG, and is one of the most important concepts in A-Level Chemistry.

吉布斯自由能是一种热力学量，用于预测在恒温恒压条件下反应是否自发。它将焓、熵和温度结合为一个值 ΔG，是A-Level化学中最重要的概念之一。

1. What Is Gibbs Free Energy? | 什么是吉布斯自由能？

S, where H is enthalpy, T is temperature and S is entropy. It represents the maximum useful work obtainable from a closed system at constant pressure and temperature.

吉布斯自由能定义为 G = H − TS，其中 H 是焓，T 是温度，S 是熵。它表示在恒压恒温下从封闭系统可获得的最大有用功。

; if ΔG > 0, the reverse reaction is spontaneous; if ΔG = 0, the system is at equilibrium.

对于化学反应，吉布斯自由能变化为 ΔG = G(生成物) − G(反应物)。如果 ΔG < 0，正反应自发；如果 ΔG > 0，逆反应自发；如果 ΔG = 0，系统处于平衡。

2. Enthalpy and Entropy: Two Competing Factors | 焓与熵：两种竞争因素

Enthalpy change ΔH measures heat released or absorbed at constant pressure. A negative ΔH (exothermic) favours spontaneity because systems naturally tend to minimise energy.

焓变 ΔH 衡量恒压条件下释放或吸收的热量。负 ΔH（放热）有利于自发反应，因为系统天然倾向于降低能量。

Entropy change ΔS measures the change in disorder or randomness. A positive ΔS (greater disorder) favours spontaneity because energy and matter tend to spread out. The balance between ΔH and TΔS determines whether a reaction is spontaneous.

熵变 ΔS 衡量混乱度或随机性的变化。正 ΔS（混乱度增加）有利于自发反应，因为能量和物质倾向于分散。ΔH 与 TΔS 之间的平衡决定了反应是否自发。

3. The Gibbs Equation | 吉布斯方程

The central equation for Gibbs free energy change is:

ΔG = ΔH − TΔS

Here, ΔH is in J mol⁻¹, T is in kelvin (K), and ΔS is in J K⁻¹ mol⁻¹. If ΔH is given in kJ mol⁻¹, you must convert it to J mol⁻¹ before substituting into the equation.

其中 ΔH 的单位是 J mol⁻¹，T 的单位是开尔文（K），ΔS 的单位是 J K⁻¹ mol⁻¹。如果 ΔH 以 kJ mol⁻¹ 给出，代入方程前必须转换为 J mol⁻¹。

Since TΔS has units of J mol⁻¹, the final value of ΔG will also be in J mol⁻¹. You may then convert it back to kJ mol⁻¹ if needed.

由于 TΔS 的单位是 J mol⁻¹，因此 ΔG 的最终单位也是 J mol⁻¹。如有需要，你可以再将其转换为 kJ mol⁻¹。

4. Spontaneity Rules Using Signs | 利用符号判断自发性的规则

The signs of ΔH and ΔS determine how temperature affects spontaneity. The table below summarises all four cases.

ΔH 和 ΔS 的符号决定了温度如何影响自发性。下表总结了所有四种情况。

ΔH ΔS Result 结果
Negative / 负 Positive / 正 ΔG always negative; spontaneous at all temperatures ΔG 总为负；所有温度下自发
Positive / 正 Negative / 负 ΔG always positive; non-spontaneous at all temperatures ΔG 总为正；所有温度下非自发
Negative / 负 Negative / 负 Spontaneous at low temperatures 低温下自发
Positive / 正 Positive / 正 Spontaneous at high temperatures 高温下自发

5. Temperature Dependence: The Threshold Temperature | 温度依赖：阈值温度

ontaneous only above a threshold temperature. This temperature is found by setting ΔG = 0:

对于 ΔH 为正、ΔS 为正的反应，反应只在高于阈值温度时才变成自发。该温度可通过令 ΔG = 0 求出：

T = ΔH / ΔS

At this temperature, the reaction is at equilibrium. Above it, ΔG < 0, so the reaction is spontaneous. Below it, ΔG > 0, so it is non-spontaneous.

在这个温度下，反应处于平衡。高于它，ΔG < 0，反应自发；低于它，ΔG > 0，反应非自发。

O(l), ΔH is positive and ΔS is positive. Melting occurs above 273 K because at T > 273 K, TΔS exceeds ΔH, making ΔG negative.

例如：对于冰融化，H₂O(s) → H₂O(l)，ΔH 为正，ΔS 为正。融化在273 K以上发生，因为当 T > 273 K 时，TΔS 超过 ΔH，使得 ΔG 为负。

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6. Standard Gibbs Free Energy Change | 标准吉布斯自由能变化

The standard Gibbs free energy change, ΔG°, refers to reactants and products in their standard states, usually 1 bar pressure and a specified temperature, commonly 298 K. It can be calculated using:

标准吉布斯自由能变化 ΔG° 是指反应物和产物在标准状态下的自由能变化，通常为 1 bar 压力和指定温度，常见为 298 K。它可以通过以下方式计算：

ΔG° = ΔH° − TΔS°

Alternatively, it can be found from standard Gibbs free energies of formation, ΔGf°:

或者，可以通过标准生成吉布斯自由能 ΔGf° 来计算：

ΔG° = ΣΔGf°(products) − ΣΔGf°(reactants)

eir most stable form under standard conditions are assigned zero free energy of formation.

元素在其标准状态下的 ΔGf° = 0。在标准条件下最稳定形式的纯物质，其标准生成自由能为零。

7. Gibbs Free Energy and Equilibrium Constant K | 吉布斯自由能与平衡常数 K

ction quotient Q equals the equilibrium constant K. The relationship between ΔG° and K is:

在平衡时，ΔG = 0，反应商 Q 等于平衡常数 K。ΔG° 与 K 的关系为：

ΔG° = −RT ln K

Because ln K = 2.303 log₁₀ K, the equation can also be written as ΔG° = −2.303RT log₁₀ K.

其中 R 是气体常数（8.31 J K⁻¹ mol⁻¹），T 以开尔文为单位，ln 是自然对数。由于 ln K = 2.303 log₁₀ K，该方程也可以写成 ΔG° = −2.303RT log₁₀ K。

ilibrium. If K < 1, ΔG° is positive, meaning reactants are favoured. If K = 1, ΔG° = 0.

如果 K > 1，ΔG° 为负，说明平衡时有利于产物。如果 K < 1，ΔG° 为正，说明有利于反应物。如果 K = 1，则 ΔG° = 0。

8. Non-Standard Conditions: Reaction Quotient Q | 非标准条件：反应商 Q

For concentrations that are not at equilibrium, the actual free energy change is given by:

对于未达到平衡的浓度，实际自由能变化由下式给出：

ΔG = ΔG° + RT ln Q

If ΔG < 0, the forward reaction is spontaneous. If ΔG > 0, the reverse reaction is spontaneous. This equation is useful for predicting the direction of a reaction when the system is not at equilibrium.

如果 ΔG < 0，正反应自发；如果 ΔG > 0，逆反应自发。该方程在系统未达到平衡时用于预测反应方向非常有用。

9. Worked Example: Calculating ΔG° | 计算实例：计算 ΔG°

Consider the reaction: 2NO₂(g) ⇌ 6.6 J K⁻¹ mol⁻¹, calculate ΔG° at 298 K and determine whether the reaction is spontaneous.

考虑反应：2NO₂(g) ⇌ N₂O₄(g)。已知 ΔH° = −58.0 kJ mol⁻¹，ΔS° = −176.6 J K⁻¹ mol⁻¹，计算 298 K 下的 ΔG° 并判断反应是否自发。

Step 1: Convert ΔH° to J mol⁻¹.

步骤1：将 ΔH° 转换为 J mol⁻¹。

ΔH° = −58.0 × 1000 = −58000 J mol⁻¹

Step 2: Substitute into the Gibbs equation.

步骤2：代入吉布斯方程。

ΔG° = ΔH° − TΔS° = −58000 − (298 × (−176.6))

= −58000 + 52626.8 = −5373.2 J mol⁻¹

Step 3: Convert to kJ mol⁻¹ and state the conclusion.

步骤3：转换为 kJ mol⁻¹ 并得出结论。

ΔG° = −5.37 kJ mol⁻¹

Because ΔG° < 0, the forward reaction is spontaneous at 298 K.

因为 ΔG° < 0，正反应在 298 K 下自发。

10. Common Misconceptions | 常见误区

11. Exam Tips | 考试要点

To score well in CIE A-Level Chemistry questions on Gibbs free energy, keep the following tips in mind:

要在CIE A-Level化学关于吉布斯自由能的题目中获得高分，请记住以下要点：