📚 Enthalpy Change of Formation from Enthalpy Changes of Combustion | 由燃烧焓变求生成焓变
In A-Level Chemistry, you often know combustion enthalpy data but need to find a standard enthalpy change of formation. This article shows how Hess’s law links the two through a common combustion-products cycle, with worked examples and exam tips.
在 A-Level 化学中，题目常常给出燃烧焓数据，却要求你求算标准生成焓变。本文将展示如何利用赫斯定律，通过共同的燃烧产物循环把两者联系起来，并给出例题与考试技巧。
1. The Core Problem | 核心问题
A formation enthalpy cannot always be measured directly, especially for compounds that do not form easily from their elements. Combustion enthalpies are much easier to measure by burning a substance in excess oxygen.
生成焓并不总能直接测量，尤其是那些不容易由元素单质直接生成的化合物。燃烧焓则容易通过物质在过量氧气中燃烧来测量。
Therefore, exam questions often give standard enthalpy changes of combustion and ask you to calculate a standard enthalpy change of formation.
因此，考试题目常常给出标准燃烧焓变，要求你计算标准生成焓变。
2. Key Definitions | 关键定义
The standard enthalpy change of formation, ΔfH°, is the enthalpy change when one mole of a compound is formed from its elements in their standard states under standard conditions, usually 298 K and 100 kPa.
标准生成焓变，ΔfH°，是指在标准条件下，通常为 298 K 和 100 kPa，由处于标准状态的元素单质生成 1 摩尔化合物时的焓变。
The standard enthalpy change of combustion, ΔcH°, is the enthalpy change when one mole of a substance is completely burned in excess oxygen under standard conditions, with all substances in their standard states.
标准燃烧焓变，ΔcH°，是指在标准条件下，1 摩尔物质在过量氧气中完全燃烧时的焓变，所有物质均处于标准状态。
By definition, the standard enthalpy of formation of any element in its standard state is zero.
根据定义，任何处于标准状态的元素单质，其标准生成焓为零。
3. Hess’s Law as the Link | 赫斯定律作为桥梁
Hess’s law states that the total enthalpy change for a chemical reaction is independent of the route taken, provided the initial and final conditions are the same.
赫斯定律指出，只要始态和终态相同，化学反应的总焓变与反应途径无关。
This allows us to use an indirect route: burn the elements to combustion products, and burn the compound to the same combustion products. The unknown formation enthalpy can then be found by difference.
这使我们能够使用间接途径：先将元素燃烧成燃烧产物，再将化合物燃烧成相同的燃烧产物。未知的生成焓便可通过差值求得。
4. The Combustion Cycle for Formation | 用于生成反应的燃烧循环
Consider a general formation reaction:
考虑一个通用的生成反应：
elements in standard states → compound
Now burn both the elements and the compound in excess oxygen. Both routes finish at the same combustion products, usually CO₂(g) and H₂O(l).
现在将元素和化合物分别与过量氧气燃烧。两条路线最终到达相同的燃烧产物，通常是 CO₂(g) 和 H₂O(l)。
elements + O₂ → combustion products
compound + O₂ → combustion products
The first route has an enthalpy change equal to the sum of the combustion enthalpies of the elements. The second route has an enthalpy change equal to the combustion enthalpy of the compound.
第一条路线的焓变等于各元素燃烧焓之和。第二条路线的焓变等于该化合物的燃烧焓。
By Hess’s law, the direct formation route plus the compound combustion route must equal the element combustion route:
根据赫斯定律，直接生成路线加上化合物燃烧路线，必须等于元素燃烧路线：
ΔfH°(compound) + ΔcH°(compound) = Σ ΔcH°(elements)
Rearranging gives the key formula:
重新整理得到关键公式：
ΔfH°(compound) = Σ ΔcH°(elements) − ΔcH°(compound)
5. General Sign Convention and Stoichiometry | 通用符号规则与化学计量数
For any reaction using combustion data, the general relationship is:
对于任何使用燃烧数据的反应，通用关系为：
ΔrH° = Σ ΔcH°(reactants) − Σ ΔcH°(products)
This is the reverse order compared with formation data, where the calculation is products minus reactants.
这与使用生成焓数据时的计算顺序相反；使用生成焓数据时是“生成物之和减去反应物之和”。
For a formation reaction, the reactants are elements and the product is one compound, so the formula becomes:
对于生成反应，反应物是元素单质，生成物是一种化合物，因此公式变为：
ΔfH°(compound) = Σ ΔcH°(elements) − ΔcH°(compound)
You must multiply each combustion enthalpy by the stoichiometric coefficient from the balanced formation equation.
必须根据配平后的生成方程式，将每一种燃烧焓乘以相应的化学计量数。
6. Worked Example 1: Methane | 例题 1：甲烷
Calculate the standard enthalpy of formation of methane, CH₄(g), using the following combustion data:
利用下列燃烧数据计算甲烷 CH₄(g) 的标准生成焓：
| ΔcH°(C(s)) | = −394 kJ mol⁻¹ |
| ΔcH°(H₂(g)) | = −286 kJ mol⁻¹ |
| ΔcH°(CH₄(g)) | = −890 kJ mol⁻¹ |
The formation equation is:
生成方程式为：
C(s) + 2H₂(g) → CH₄(g)
Sum of combustion enthalpies of elements:
元素燃烧焓之和：
Σ ΔcH°(elements) = (−394) + 2(−286) = −966 kJ mol⁻¹
Subtract the combustion enthalpy of methane:
减去甲烷的燃烧焓：
ΔfH°(CH₄(g)) = −966 − (−890) = −76 kJ mol⁻¹
This is close to the accepted value and shows that methane formation is exothermic.
该结果接近公认值，说明甲烷的生成是放热过程。
7. Worked Example 2: Ethanol | 例题 2：乙醇
Calculate the standard enthalpy of formation of ethanol, C₂H₅OH(l), using the following data:
利用下列数据计算乙醇 C₂H₅OH(l) 的标准生成焓：
| ΔcH°(C(s)) | = −394 kJ mol⁻¹ |
| ΔcH°(H₂(g)) | = −286 kJ mol⁻¹ |
| ΔcH°(C₂H₅OH(l)) | = −1367 kJ mol⁻¹ |
The balanced formation equation is:
配平后的生成方程式为：
2C(s) + 3H₂(g) + ½O₂(g) → C₂H₅OH(l)
Oxygen is an element in its standard state. Its combustion enthalpy is not needed because oxygen is the oxidiser and does not burn; it cancels in the cycle.
氧气是标准状态下的元素单质。由于氧气是氧化剂，本身不会燃烧，因此不需要其燃烧焓；它在循环中相互抵消。
Sum of combustion enthalpies of the reacting elements:
反应元素的燃烧焓之和：
Σ ΔcH°(elements) = 2(−394) + 3(−286) + 0 = −1646 kJ mol⁻¹
Now apply the formation formula:
现在应用生成焓公式：
ΔfH°(C₂H₅OH(l)) = −1646 − (−1367) = −279 kJ mol⁻¹
The negative value indicates that liquid ethanol is thermodynamically more stable than its elements in their standard states.
负值表明液态乙醇在热力学上比其标准状态下的元素单质更稳定。
8. The Role of Oxygen in the Cycle | 氧气在循环中的作用
In combustion cycles, oxygen gas is usually present on both sides of the cycle as the oxidiser. It is not assigned a combustion enthalpy because it does not undergo combustion itself.
在燃烧循环中，氧气作为氧化剂通常出现在循环两侧。由于氧气本身不发生燃烧，因此不给它分配燃烧焓。
If you are using a general cycle with O₂ as a reactant, you can set its combustion enthalpy to zero or simply leave it out of the sum for the elements.
如果在通用循环中将 O₂ 视为反应物，可以将其燃烧焓设为零，或直接在元素求和中省略它。
However, you must be careful with other elements such as carbon and hydrogen: these do have non-zero combustion enthalpies because they can be burned in oxygen.
但对碳和氢等其他元素则必须小心：它们可以在氧气中燃烧，因此具有非零的燃烧焓。
9. Common Mistakes | 常见错误
-
Using the wrong sign convention: with combustion data, use reactants minus products, not products minus reactants.
符号规则用错：使用燃烧数据时，应当是反应物之和减去生成物之和，而不是生成物减反应物。
-
Forgetting to multiply by stoichiometric coefficients in the balanced formation equation.
忘记乘以配平生成方程式中的化学计量数。
-
Giving elements such as O₂ a non-zero combustion enthalpy.
给 O₂ 等元素单质赋予了非零的燃烧焓。
-
Using inconsistent states for water: liquid water and gaseous water have different combustion enthalpies for hydrogen.
水的状态不一致：液态水和气态水对应的氢气燃烧焓不同。
-
Confusing formation data formula with combustion data formula.
将生成焓数据公式与燃烧焓数据公式相混淆。
10. Exam Technique | 考试技巧
Always start by writing the balanced formation equation for one mole of the compound from its elements in their standard states.
始终先写出由标准状态元素单质生成 1 摩尔化合物的配平生成方程式。
Then list the given combustion enthalpies next to the correct substances and multiply by any coefficients before summing.
然后将给出的燃烧焓写在对应物质旁边，先乘以相应系数再求和。
Finally, subtract the combustion enthalpy of the compound itself from the sum for the elements.
最后，从元素燃烧焓之和中减去该化合物本身的燃烧焓。
Check your final sign: most stable compounds have negative formation enthalpies, but some compounds, such as many nitrogen oxides, have positive values.
检查最终符号：大多数稳定化合物的生成焓为负值，但有些化合物，如一氧化氮等，可能为正值。
11. Practice Question | 练习题
Calculate the standard enthalpy of formation of propane, C₃H₈(g), given
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