Gibbs Free Energy | 吉布斯自由能考点精讲

📚 Gibbs Free Energy | 吉布斯自由能考点精讲

Gibbs free energy is the single most powerful concept for predicting the feasibility of a chemical reaction. It unites enthalpy and entropy into one criterion that tells us whether a process will occur spontaneously under constant temperature and pressure. In IB and Edexcel Chemistry, you will be expected to calculate ΔG, interpret its sign, relate it to equilibrium constants, and explain how temperature can turn a non‑spontaneous reaction into a spontaneous one.

吉布斯自由能是预测化学反应能否自发进行最强大的概念。它将焓和熵统一为一个判据，告诉我们恒温恒压下过程是否会自发发生。在 IB 和 Edexcel 化学中，你需要会计算 ΔG，解读它的正负，将其与平衡常数关联，并解释温度如何使原本非自发的反应变得自发。

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

Gibbs free energy (G) is a thermodynamic potential that measures the maximum amount of reversible work a system can perform at constant temperature and pressure. It is defined by the equation G = H − TS, where H is enthalpy, T is the absolute temperature in kelvin, and S is entropy. In chemistry, we almost always work with changes in Gibbs free energy, ΔG.

吉布斯自由能 (G) 是衡量系统在恒温恒压下所能做的最大可逆功的热力学势。它的定义方程为 G = H − TS，其中 H 是焓，T 是开尔文温度，S 是熵。在化学中，我们几乎总是使用吉布斯自由能的变化量 ΔG。

For a chemical reaction at constant T and P, the change in Gibbs free energy is given by:

对于恒温恒压下的化学反应，吉布斯自由能变化由下式给出：

ΔG = ΔH − TΔS

This equation combines the two driving forces of a reaction: the tendency to minimise enthalpy (exothermic, ΔH < 0) and the tendency to maximise entropy (ΔS > 0).

该方程结合了反应的两个驱动力：焓降低的趋势（放热，ΔH < 0）和熵增大的趋势（ΔS > 0）。

2. Spontaneity and the Sign of ΔG | 自发性与 ΔG 的符号

A reaction is considered spontaneous (thermodynamically feasible) if it can proceed without external energy input once initiated. The sign of ΔG directly determines spontaneity:

如果一个反应在引发后无需外界能量输入即可进行，则认为它是自发的（热力学上可行）。ΔG 的符号直接决定了自发性：

ΔG < 0: the forward reaction is spontaneous (exergonic).
ΔG > 0: the forward reaction is non‑spontaneous; the reverse reaction is spontaneous.
ΔG = 0: the system is at equilibrium; no net change occurs.

ΔG < 0：正反应自发（放能过程）。
ΔG > 0：正反应非自发，逆反应自发。
ΔG = 0：体系处于平衡态，无净变化。

It is crucial to remember that thermodynamic spontaneity says nothing about the rate of reaction; a spontaneous reaction may be kinetically very slow (e.g., the conversion of diamond to graphite).

必须牢记，热力学自发性与反应速率无关；一个自发的反应在动力学上可能极慢（例如金刚石转变为石墨）。

3. ΔG = ΔH − TΔS: The Master Equation | ΔG = ΔH − TΔS：核心方程

The term TΔS represents the energy tied up in the disorder of the system at temperature T. The larger the positive ΔS, the more negative TΔS becomes, making ΔG more negative and therefore favouring spontaneity. Conversely, a decrease in entropy (ΔS < 0) makes −TΔS positive, opposing spontaneity.

TΔS 这一项代表温度 T 下因系统混乱度而被束缚的能量。ΔS 正值越大，−TΔS 就越负，使 ΔG 更负，从而有利于自发。相反，熵的减小 (ΔS < 0) 使 −TΔS 为正，不利于自发。

When using this equation, pay close attention to unit consistency. ΔH is often given in kJ mol⁻¹, while S and ΔS are typically given in J K⁻¹ mol⁻¹. You must convert ΔH to J mol⁻¹ or convert TΔS to kJ mol⁻¹ before combining them.

使用此方程时，要特别注意单位一致。ΔH 常使用 kJ mol⁻¹，而 S 和 ΔS 多以 J K⁻¹ mol⁻¹ 给出。你必须先将 ΔH 转换为 J mol⁻¹ 或将 TΔS 转换为 kJ mol⁻¹，再相加。

ΔG = [ΔH (kJ mol⁻¹) × 1000] − T [ΔS (J K⁻¹ mol⁻¹)]

4. Standard Gibbs Free Energy Change, ΔG° | 标准吉布斯自由能变

The standard Gibbs free energy change, ΔG°, refers to the change when all reactants and products are in their standard states (298 K, 100 kPa, 1 mol dm⁻³ for solutions). It can be calculated in two ways:

标准吉布斯自由能变 ΔG° 是指所有反应物和产物都处于标准状态时的变化（298 K，100 kPa，溶液 1 mol dm⁻³）。有两种计算方法：

Method 1: Using standard free energies of formation:

方法一： 利用标准生成吉布斯自由能：

ΔG° = Σ n ΔG°_f(products) − Σ m ΔG°_f(reactants)

Method 2: Using ΔH° and ΔS° via ΔG° = ΔH° − TΔS° (recall that T = 298 K for standard conditions).

方法二： 通过 ΔG° = ΔH° − TΔS° 使用 ΔH° 和 ΔS° 计算（注意标准状态下 T = 298 K）。

Values of ΔG°_f for elements in their reference states are zero, just as for ΔH°_f. This provides a direct route to calculate ΔG° for any reaction from tabulated data.

与 ΔH°_f 一样，处于标准参考态的单质的 ΔG°_f 为零。这为通过数据表计算任何反应的 ΔG° 提供了直接途径。

5. Temperature Dependence of Spontaneity | 温度对自发性的影响

Since ΔG = ΔH − TΔS, the temperature can change the sign of ΔG and therefore the spontaneity of a reaction. The outcome depends on the signs of ΔH and ΔS, as summarised in the table below.

由于 ΔG = ΔH − TΔS，温度可以改变 ΔG 的符号，从而改变反应的自发性。结果取决于 ΔH 和 ΔS 的符号，如下表所示。

ΔH	ΔS	ΔG = ΔH − TΔS	Spontaneity \| 自发性
Negative (−)	Positive (+)	Always negative	Spontaneous at all T
Positive (+)	Negative (−)	Always positive	Never spontaneous (reverse is always spontaneous)
Negative (−)	Negative (−)	Negative at low T, positive at high T	Spontaneous only below a certain temperature
Positive (+)	Positive (+)	Positive at low T, negative at high T	Spontaneous only above a certain temperature

The temperature at which the reaction just becomes spontaneous (ΔG = 0) is given by:

反应恰好变为自发（ΔG = 0）时的温度由下式求得：

T = ΔH / ΔS (with ΔH and ΔS in consistent units)

T = ΔH / ΔS（ΔH 和 ΔS 单位一致）

This is an especially common examination question: calculate the temperature above or below which a reaction becomes feasible.

这是考试中极常见的题目：计算反应在高于或低于多少温度时变得可行。

6. Relationship between ΔG° and the Equilibrium Constant | ΔG° 与平衡常数的关系

One of the most important equations linking thermodynamics and equilibrium is:

联系热力学与平衡的最重要方程之一是：

ΔG° = −R T ln K

where R is the gas constant (8.31 J K⁻¹ mol⁻¹), T the temperature in kelvin, and K the equilibrium constant. This equation tells us:

其中 R 是气体常数（8.31 J K⁻¹ mol⁻¹），T 是开尔文温度，K 是平衡常数。该方程表明：

If ΔG° is negative, ln K > 0, so K > 1: products are favoured at equilibrium.
If ΔG° is positive, ln K < 0, so K < 1: reactants are favoured at equilibrium.
If ΔG° = 0, then K = 1: reactants and products are equally favoured.

若 ΔG° 为负，ln K > 0，故 K > 1：平衡时产物占优。
若 ΔG° 为正，ln K < 0，故 K < 1：平衡时反应物占优。
若 ΔG° = 0，则 K = 1：反应物与产物优势相同。

Note that the units of ΔG° must be in J mol⁻¹ (not kJ mol⁻¹) when using R = 8.31 J K⁻¹ mol⁻¹. This is a frequent source of error in calculations.

请注意，当 R = 8.31 J K⁻¹ mol⁻¹ 时，ΔG° 的单位必须是 J mol⁻¹ 而不是 kJ mol⁻¹，这是计算中常见的错误来源。

7. Non‑Standard Conditions: ΔG and the Reaction Quotient Q | 非标准条件下 ΔG 与反应商 Q

When reactants and products are not in their standard states, ΔG differs from ΔG°. The relationship is given by the reaction quotient Q:

当反应物和产物不处于标准状态时，ΔG 不同于 ΔG°。其关系通过反应商 Q 给出：

ΔG = ΔG° + R T ln Q

Here Q has the same form as the equilibrium constant expression, but uses the actual non‑equilibrium concentrations or pressures.

这里 Q 的形式与平衡常数表达式相同，但使用的是实际非平衡时的浓度或分压。

If Q < K, then ln Q < ln K, ΔG < 0: the forward reaction is spontaneous until equilibrium is reached.
If Q > K, ΔG > 0: the reverse reaction is spontaneous.
If Q = K, ΔG = 0: the system is at equilibrium.

若 Q < K，则 ln Q < ln K，ΔG < 0：正反应自发进行直至平衡。
若 Q > K，ΔG > 0：逆反应自发进行。
若 Q = K，ΔG = 0：体系处于平衡。

This equation is conceptually powerful because it shows that even a reaction with a positive ΔG° can be made spontaneous by manipulating the concentrations to make Q very small.

此方程在概念上很有说服力，因为它表明，通过控制浓度使 Q 很小，即使 ΔG° 为正的反应也可以变得自发。

8. Gibbs Free Energy in Electrochemistry | 吉布斯自由能与电化学

There is a direct connection between Gibbs free energy and the electromotive force (EMF) of an electrochemical cell:

吉布斯自由能与电化学电池的电动势 (EMF) 存在直接联系：

ΔG° = −n F E°_cell

where n is the number of moles of electrons transferred, F is the Faraday constant (96 500 C mol⁻¹), and E°_cell is the standard cell potential. A positive E°_cell yields a negative ΔG°, meaning the cell reaction is spontaneous as written.

其中 n 为转移电子的摩尔数，F 为法拉第常数 (96 500 C mol⁻¹)，E°_cell 为标准电池电势。正的 E°_cell 会得到负的 ΔG°，表明所写的电池反应是自发的。

This equation allows you to calculate ΔG° from electrochemical data, or to determine E°_cell from thermodynamic data. You can also relate the equilibrium constant to cell potential:

这个方程使你能够从电化学数据计算 ΔG°，或从热力学数据确定 E°_cell。你也可以将平衡常数与电池电势关联：

E°_cell = (R T / n F) ln K

These interconversions are highly examinable in both IB and Edexcel specifications.

这些相互转换在 IB 和 Edexcel 大纲中都是高频考点。

9. The van’t Hoff Equation | 范特霍夫方程

The van’t Hoff equation describes how the equilibrium constant K varies with temperature, assuming ΔH° is constant over the temperature range:

范特霍夫方程描述了平衡常数 K 如何随温度变化，假定 ΔH° 在该温度范围内恒定：

ln (K₂ / K₁) = − (ΔH° / R) (1/T₂ − 1/T₁)

A plot of ln K against 1/T yields a straight line with slope = −ΔH° / R, providing an experimental method to determine ΔH°. For an exothermic reaction (ΔH° < 0), K decreases with increasing temperature; for an endothermic reaction (ΔH° > 0), K increases with temperature.

以 ln K 对 1/T 作图得到一条直线，斜率 = −ΔH° / R，这为测定 ΔH° 提供了一种实验方法。对于放热反应 (ΔH° < 0)，K 随温度升高而减小；对于吸热反应 (ΔH° > 0)，K 随温度升高而增大。

This equation is particularly useful when calculating K at a new temperature from a known value at another temperature, a common IB/Edexcel data‑analysis question.

该方程在由已知温度下的 K 值计算新温度下的 K 值时尤为有用，这是 IB 和 Edexcel 常见的数据分析题。

10. Common Pitfalls and Exam Strategies | 常见陷阱与考试策略

Mistake 1: Unit confusion. Always convert enthalpy to joules when using ΔG = ΔH − TΔS with ΔS in J K⁻¹ mol⁻¹, or convert entropy to kJ K⁻¹ mol⁻¹. Similarly, in ΔG° = −RT ln K, ΔG° must be in J mol⁻¹ if R = 8.31.

错误 1：单位混淆。 当使用 ΔG = ΔH − TΔS 而 ΔS 单位为 J K⁻¹ mol⁻¹ 时，务必将焓转换为 J，或将熵转换为 kJ K⁻¹ mol⁻¹。同样，在 ΔG° = −RT ln K 中，若 R = 8.31，ΔG° 必须用 J mol⁻¹。

Mistake 2: Forgetting that T must be in kelvin. If a temperature is given in °C, add 273 (or 273.15 as required) before using it in any Gibbs free energy calculation.

错误 2：忘记温度必须用开尔文。 若题目给出的温度是 °C，在任何吉布斯自由能计算前要加上 273（或按要求加 273.15）。

Mistake 3: Misusing standard conditions. ΔG° applies at standard concentrations and 100 kPa. When conditions are non‑standard, you must use ΔG = ΔG° + RT ln Q. Many students incorrectly use ΔG° to predict spontaneity under non‑standard conditions.

错误 3：误用标准条件。 ΔG° 适用于标准浓度和 100 kPa 下的情况。当条件非标准时，必须使用 ΔG = ΔG° + RT ln Q。许多学生错误地用 ΔG° 来预测非标准条件下的自发性。

Exam strategy: When asked to explain how temperature affects feasibility, draw a quick sign‑analysis table for ΔH and ΔS. Then use T = ΔH/ΔS to find the transition temperature. Always state your assumption that ΔH and ΔS do not change with temperature (an approximation).

考试策略： 当被要求解释温度如何影响可行性时，快速画出 ΔH 和 ΔS 的符号分析表，然后使用 T = ΔH/ΔS 求出转折温度。务必说明你假定 ΔH 和 ΔS 不随温度变化（近似处理）。

Remember that a negative ΔG is necessary but not sufficient for a reaction to occur — kinetics may impose a high activation energy barrier. This distinction is a favourite in IB extended response and Edexcel 6‑mark questions.

记住，负的 ΔG 是反应发生的必要条件而非充分条件——动力学可能设置一个高的活化能垒。这层区别是 IB 扩展题和 Edexcel 6 分题中最爱考的内容。

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Gibbs Free Energy | 吉布斯自由能考点精讲