📚 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？
Gibbs free energy is defined as G = H − TS, 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。
For a chemical reaction, the change in Gibbs free energy is ΔG = G(products) − G(reactants). If ΔG < 0, the forward reaction is spontaneous; 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
For a reaction where ΔH is positive and ΔS is positive, the reaction becomes spontaneous 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。
Example: For ice melting, H₂O(s) → H₂O(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。
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)
Elements in their standard states have ΔGf° = 0. Pure substances in their 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
At equilibrium, ΔG = 0 and the reaction 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
Here R is the gas constant (8.31 J K⁻¹ mol⁻¹), T is in kelvin, and ln is the natural logarithm. 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。
If K > 1, ΔG° is negative, meaning products are favoured at equilibrium. 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) ⇌ N₂O₄(g). Given ΔH° = −58.0 kJ mol⁻¹ and ΔS° = −176.6 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
- Confusing ΔH with ΔG: A negative ΔH does not guarantee spontaneity. The entropy term TΔS can overcome the enthalpy effect.
- 混淆 ΔH 与 ΔG：负 ΔH 并不保证自发。熵项 TΔS 可能超过焓效应。
- Forgetting to convert units: ΔH is often given in kJ mol⁻¹, while ΔS is given in J K⁻¹ mol⁻¹. Convert before using the formula.
- 忘记转换单位：ΔH 常以 kJ mol⁻¹ 给出，而 ΔS 以 J K⁻¹ mol⁻¹ 给出。使用公式前需要转换。
- Not using kelvin for temperature: Always add 273 to Celsius values. A common error is using Celsius directly in the equation.
- 温度未使用开尔文：始终将摄氏度加273。常见错误是直接将摄氏温度代入方程。
- Assuming ΔG° is the same as ΔG under all conditions: ΔG° refers to standard states; actual ΔG changes with concentration and pressure.
- 认为 ΔG° 在所有条件下都等于 ΔG：ΔG° 指标准状态；实际 ΔG 随浓度和压力变化。
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：
- Always write the Gibbs equation with correct signs: ΔG = ΔH − TΔS.
- 始终正确写出吉布斯方程符号：ΔG = ΔH − TΔS。
- Ensure temperature is in kelvin and ΔS is in J K⁻¹ mol⁻¹ before calculation.
- 计算前确保温度以开尔文为单位
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