IB Chemistry: Predicting Spontaneity of Reactions | IB化学：反应自发性的判断

📚 IB Chemistry: Predicting Spontaneity of Reactions | IB化学：反应自发性的判断

A spontaneous reaction is one that can proceed without continuous external input once it has been started. In IB Chemistry, predicting whether a reaction is spontaneous is not based on how fast it happens, but on thermodynamic stability. The central tool used by the IB syllabus is the Gibbs free energy change, ΔG.

自发反应是指一旦引发后，无需持续外部输入就可以继续进行的过程。在IB化学中，判断反应是否自发并不取决于反应速率，而是取决于热力学稳定性。IB教学大纲使用的核心工具是吉布斯自由能变ΔG。

You cannot decide spontaneity from ΔH alone. Many exothermic reactions are spontaneous, but some endothermic reactions are also spontaneous. Entropy, the measure of disorder, plays an equally important role.

你不能仅凭ΔH判断自发性。虽然许多放热反应是自发的，但也有些吸热反应同样是自发的。熵——混乱度的量度——也起着同样重要的作用。

1. The Gibbs Free Energy Equation | 吉布斯自由能方程

The Gibbs free energy change combines enthalpy, temperature and entropy into one expression. For a process at constant pressure and temperature, the equation is:

吉布斯自由能变将焓、温度和熵合并到一个表达式中。对于恒压恒温过程，方程为：

ΔG = ΔH – TΔS

Here ΔH is the enthalpy change in kJ mol⁻¹, ΔS is the entropy change in J K⁻¹ mol⁻¹, and T is the temperature in kelvin. A negative ΔG indicates a spontaneous process, positive ΔG indicates a non-spontaneous process, and ΔG = 0 indicates equilibrium.

其中ΔH是焓变，单位kJ mol⁻¹；ΔS是熵变，单位J K⁻¹ mol⁻¹；T是温度，单位K。ΔG为负表示过程自发，ΔG为正表示过程非自发，ΔG=0表示过程处于平衡状态。

2. Enthalpy: The Energy Driver | 焓变：能量驱动力

Enthalpy change records heat absorbed or released when reactants become products at constant pressure. An exothermic reaction has ΔH < 0 and tends to lower the energy of the system, which generally favours spontaneity.

焓变记录的是恒压下反应物变为产物时所吸收或释放的热量。放热反应ΔH < 0，会降低体系能量，通常有利于自发进行。

However, exothermicity is not enough. Melting ice is endothermic yet spontaneous above 0 °C. Some endothermic dissolving processes are also spontaneous because the system gains disorder.

然而，仅放热并不够。冰融化是吸热的，但在0 °C以上却是自发的。一些吸热的溶解过程之所以自发，是因为体系混乱度增加了。

3. Entropy: The Disorder Driver | 熵变：混乱度驱动力

Entropy measures the number of ways energy can be distributed among particles. Gases have much higher entropy than liquids and solids. A reaction tends to be spontaneous if the total entropy of the universe increases.

熵衡量能量在粒子间分配的方式数。气体的熵远高于液体和固体。如果宇宙总熵增大，反应就趋向于自发。

For the system only, a positive ΔS is favourable. Entropy increases when gases are produced, when the number of particles increases, when solids dissolve, or when temperature rises. For example, thermal decomposition of many carbonates produces a gas and therefore has ΔS > 0.

仅对体系而言，正的ΔS是有利的。当气体产生、粒子数增多、固体溶解或温度升高时，熵会增加。例如，许多碳酸盐的热分解会产生气体，因此ΔS > 0。

4. Sign Combinations and Spontaneity | ΔH与ΔS符号组合与自发性的判断

Since ΔG = ΔH – TΔS, whether a reaction is spontaneous can be classified by the signs of ΔH and ΔS. The table below summarises the possibilities:

因为ΔG = ΔH – TΔS，所以反应是否自发可按ΔH和ΔS的符号进行分类。下表总结了各种可能情况：

ΔH	ΔS	Spontaneity \| 自发性
Negative (exothermic 放热)	Positive (increase in disorder 熵增)	Spontaneous at all temperatures 任何温度均自发
Positive (endothermic 吸热)	Negative (decrease in disorder 熵减)	Non-spontaneous at all temperatures 任何温度均非自发
Negative (exothermic 放热)	Negative (entropy decreases 熵减)	Spontaneous only at low temperatures 仅在低温下自发
Positive (endothermic 吸热)	Positive (entropy increases 熵增)	Spontaneous only at high temperatures 仅在高温下自发

When ΔH and ΔS have opposite signs, the TΔS term cannot change the sign of ΔG, so spontaneity does not depend on temperature. When they have the same sign, temperature matters critically.

当ΔH和ΔS符号相反时，TΔS项无法改变ΔG的正负号，因此自发性不随温度改变。当两者符号相同时，温度就成为关键因素。

5. Temperature Dependence and the Crossover Point | 温度依赖性与转变温度

For an endothermic reaction with ΔS > 0, the TΔS term grows as temperature increases. At some temperature the term TΔS overtakes ΔH, and ΔG changes from positive to negative. This is the temperature at which ΔG = 0:

对ΔS > 0的吸热反应，随着温度升高，TΔS项逐渐增大。在某个温度，TΔS项会超过ΔH，ΔG从正值变为负值。这就是ΔG = 0的温度：

T = ΔH / ΔS

Above this temperature the reaction becomes spontaneous. For an exothermic reaction with ΔS < 0, the opposite occurs: TΔS becomes increasingly negative, so above the crossover temperature the reaction becomes non-spontaneous.

在此温度以上，反应变为自发。对于ΔS < 0的放热反应，情况相反：TΔS变得越来越负，因此超过转变温度后反应变为非自发。

Always remember to convert ΔS into kJ K⁻¹ mol⁻¹ before using it in the Gibbs equation, because ΔH is normally expressed in kJ.

使用吉布斯方程前，务必把ΔS换算为kJ K⁻¹ mol⁻¹，因为ΔH通常以kJ为单位给出。

6. Standard Gibbs Free Energy and the IB Databook Context | 标准吉布斯自由能的判断

For standard conditions, the symbol ΔG° is used. Standard conditions in IB Chemistry are 100 kPa pressure, 1.0 mol dm⁻³ solutions, and usually 298 K.

在标准条件下，使用符号ΔG°。IB化学中的标准条件是100 kPa压强、1.0 mol dm⁻³溶液浓度，通常为298 K。

A practical method is to calculate ΔG°f from formation values using the same type of “products minus reactants” rule used for ΔH:

实际计算中，可以利用标准生成吉布斯自由能ΔG°f，按照与ΔH相同的“生成物减反应物”规则计算：

ΔG° = ΣΔG°f(products) – ΣΔG°f(reactants)

If ΔG° < 0, the reaction is spontaneous under standard conditions. However, a reaction that is non-spontaneous under standard conditions may still become spontaneous under non-standard conditions or at another temperature.

如果ΔG° < 0，则反应在标准条件下自发。然而，在标准条件下非自发的反应，在非标准条件或其他温度下仍然可能变为自发。

7. Linking ΔG to the Reaction Quotient and K | ΔG与反应商、平衡常数的联系

Gibbs free energy also depends on concentrations and gas pressures. The reaction quotient Q compares the current amounts of products and reactants. The relationship is:

吉布斯自由能还与浓度和气体分压有关。反应商Q比较产物与反应物当前的数量。关系式为：

ΔG = ΔG° + RT ln Q

When Q < K, the ratio of products to reactants is too small, lnQ is negative, and ΔG < 0 so the forward reaction is spontaneous. When Q > K, the reverse reaction is spontaneous. At equilibrium Q = K and ΔG = 0.

当Q < K时，产物相对于反应物的比例太低，lnQ为负，ΔG < 0，正向反应自发。当Q > K时，逆向反应自发。在平衡时，Q = K，ΔG = 0。

Setting Q = K at equilibrium gives the fundamental equation:

在平衡时令Q = K，可得到基本方程：

ΔG° = -RT ln K

This shows that a large negative ΔG° corresponds to K > 1, a large positive ΔG° corresponds to K < 1, and ΔG° near zero gives K near 1.

这说明：ΔG°很负时K > 1；ΔG°很正时K < 1；ΔG°接近零时K接近1。

8. The Electrochemical Connection | 电化学联系

Spontaneity can also be judged using cell potential. For a redox reaction, the relationship is:

自发性的判断也可以借助电池电动势来完成。对于氧化还原反应，关系为：

ΔG° = -nFE°

Here n is the number of moles of electrons transferred, F is the Faraday constant, 96 500 C mol⁻¹, and E° is the standard cell potential. A positive E° gives a negative ΔG°, so the reaction is spontaneous.

其中n是转移电子物质的量，F是法拉第常数96 500 C mol⁻¹，E°是标准电池电动势。正值E°给出负值ΔG°，因此反应自发。

This explains why a galvanic cell produces electricity only when E°cell > 0. If E°cell < 0, the reverse reaction would be spontaneous and no current would flow in the intended direction.

这解释了原电池只有在E°cell > 0时才能产生电流。如果E°cell < 0，则逆反应自发，预期的方向不会有电流通过。

9. Worked Example: Calcium Carbonate Decomposition | 例题1：碳酸钙分解

Consider the decomposition of calcium carbonate:

考虑碳酸钙的分解：

CaCO₃(s) → CaO(s) + CO₂(g)

For this reaction ΔH = +178 kJ mol⁻¹ and ΔS = +160 J K⁻¹ mol⁻¹. At 298 K, convert ΔS to kJ K⁻¹ mol⁻¹: ΔS = +0.160 kJ K⁻¹ mol⁻¹.

对于该反应，ΔH = +178 kJ mol⁻¹，ΔS = +160 J K⁻¹ mol⁻¹。在298 K下，先把ΔS换算为kJ K⁻¹ mol⁻¹：ΔS = +0.160 kJ K⁻¹ mol⁻¹。

ΔG = 178 – (298 × 0.160) = 178 – 47.7 = +130.3 kJ mol⁻¹

The positive ΔG shows that decomposition is not spontaneous at room temperature. This is why limestone does not decompose on its own in a classroom.

ΔG为正表明分解在室温下不自发。这就是为什么石灰石不会在教室里自行分解。

The crossover temperature is T = ΔH/ΔS = 178/0.160 = 1112.5 K. Above about 1113 K, ΔG becomes negative, which is why heating limestone in a lime kiln works.

转变温度为T = ΔH/ΔS = 178/0.160 = 1112.5 K。当温度高于约1113 K时，ΔG变为负值，这就是石灰窑中加热石灰石能够分解的原因。

10. Worked Example: Haber Process Reaction | 例题2：哈伯法反应

For the synthesis of ammonia:

对于氨的合成反应：

N₂(g) + 3H₂(g) → 2NH₃(g)

Assume ΔH = -92.2 kJ mol⁻¹ and ΔS = -199 J K⁻¹ mol⁻¹ = -0.199 kJ K⁻¹ mol⁻¹. At 298 K:

假设ΔH = -92.2 kJ mol⁻¹，ΔS = -199 J K⁻¹ mol⁻¹ = -0.199 kJ K⁻¹ mol⁻¹。在298 K下：

ΔG = -92.2 – (298 × (-0.199)) = -92.2 + 59.3 = -32.9 kJ mol⁻¹

Because ΔH is negative and very large, the reaction is spontaneous at low temperature. However, ΔS is negative because four gas molecules become two gas molecules.

因为ΔH为负且数值很大，该反应在低温下自发。然而，ΔS为负，因为四个气体分子变成了两个气体分子。

At high temperature the TΔS term becomes more negative than ΔH, so ΔG becomes positive. The crossover temperature is 92.2/0.199 = 463 K, meaning the reaction becomes non-spontaneous at higher temperatures under standard conditions.

在高温下，TΔS项会变得比ΔH更负，因此ΔG变为正值。转变温度为92.2/0.199 = 463 K，意味着在标准条件下，温度更高时反应将变为非自发。

11. Common Pitfalls in Predicting Spontaneity | 判断自发性时的常见误区

Using ΔS in J with ΔH in kJ without conversion. Always convert ΔS to kJ K⁻¹ mol⁻¹ or ΔH to J mol⁻¹ before calculation.
用J为单位的ΔS与kJ为单位的ΔH直接计算而不换算。计算前务必把ΔS换算为kJ K⁻¹ mol⁻¹，或把ΔH换算为J mol⁻¹。
Assuming that spontaneous means fast. Gibbs free energy says nothing about activation energy or rate.
误以为自发等于快速。吉布斯自由能完全不涉及活化能或反应速率。
Confusing ΔG with ΔG°. ΔG° refers to standard conditions, while ΔG is the actual free energy change at the current concentrations and partial pressures.
混淆ΔG与ΔG°。ΔG°指标准条件，ΔG是当前浓度和分压下的实际自由能变。
Thinking that a positive entropy change alone makes a reaction spontaneous. All exothermic reactions are not spontaneous either; both ΔH and TΔS must be balanced.
只看到熵增就认为一定自发，或只看到放热就认为一定自发。必须综合考虑ΔH与TΔS的平衡。
Ignoring the sign of ΔS when predicting how temperature affects spontaneity. If ΔS and ΔH have opposite signs, changing temperature will not flip ΔG.
预测温度影响时忽略ΔS的符号。如果ΔS和ΔH异号，改变温度不会使ΔG改变正负。

12. Final Summary | 最终总结

To predict whether a reaction is spontaneous, calculate or estimate ΔG using the equation ΔG = ΔH – TΔS. A negative ΔG means the forward process is thermodynamically favoured; a positive ΔG means the reverse process is favoured.

要判断反应是否自发，请用方程ΔG = ΔH – TΔS计算或估算ΔG。ΔG为负意味着正向过程在热力学上有利；ΔG为正则意味着逆向过程有利。

Reaction type \| 反应类型	ΔH	ΔS	Spontaneity rule \| 自发性规则
Exothermic / entropy increase 放热且熵增	Negative	Positive	Always spontaneous 总是自发
Endothermic / entropy decrease 吸热且熵减	Positive	Negative	Never spontaneous 永不自发
Exothermic / entropy decrease 放热且熵减	Negative	Negative	Spontaneous at low T 低温自发
Endothermic / entropy increase 吸热且熵增	Positive	Positive	Spontaneous at high T 高温自发

In IB exam problems, always state your assumptions, check units, and use ΔG = 0 to find the temperature at which equilibrium exists. With practice, predicting spontaneity becomes a clear and systematic process.

在IB考试题中，应说明你的假设，检查单位，并用ΔG = 0求平衡存在的温度。多加练习后，判断自发性就会成为一个清晰且系统的过程。

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IB Chemistry: Predicting Spontaneity of Reactions | IB化学：反应自发性的判断