Hess's Law and Reaction Enthalpy Calculations | 盖斯定律与反应热计算

📚 Hess’s Law and Reaction Enthalpy Calculations | 盖斯定律与反应热计算

In physical chemistry, determining the energy changes of reactions is essential. Some reactions are too slow, too fast, or have side reactions, making direct calorimetric measurement impossible. Hess’s law offers a logical and reliable way to calculate these enthalpy changes indirectly.

在物理化学中，确定反应的能量变化至关重要。有些反应过于缓慢、过于快速或伴随副反应，使得直接量热测量无法实现。盖斯定律提供了一种逻辑可靠的方法来间接计算这些焓变。

1. Enthalpy and Enthalpy Change | 焓与焓变

Enthalpy (H) is the total heat content of a system at constant pressure. The change in enthalpy, ΔH, represents the heat exchanged with the surroundings during a reaction at constant pressure.

焓（H）是恒压条件下系统的总热含量。焓变 ΔH 表示恒压反应过程中系统与外界交换的热量。

ΔH is negative for exothermic reactions, which release heat, and positive for endothermic reactions, which absorb heat. Its standard unit is kilojoules per mole (kJ mol⁻¹).

放热反应的 ΔH 为负值，表示释放热量；吸热反应的 ΔH 为正值，表示吸收热量。其常用单位是千焦每摩尔（kJ mol⁻¹）。

2. What Is Hess’s Law? | 什么是盖斯定律？

Hess’s law states that the enthalpy change for a chemical reaction is independent of the route by which the reaction occurs, as long as the initial and final states are the same.

盖斯定律指出：在始态和终态相同的条件下，化学反应的总焓变与反应路径无关。

In practical terms, if a reaction can be expressed as the sum of two or more elementary steps, the overall ΔH is simply the sum of the ΔH values of those steps.

在实际应用中，如果一个反应可以表示为两个或多个基本步骤之和，那么总 ΔH 就是这些步骤 ΔH 的加和。

3. Why Hess’s Law Works | 盖斯定律为何成立

Enthalpy is a state function, meaning its value depends only on the current state of the system, not on how that state was reached. Temperature, pressure, amount of substance and physical state determine the enthalpy of a system.

焓是一个状态函数，意味着它的取值只取决于系统当前的状态，而与达到该状态的过程无关。温度、压力、物质的量以及物理状态决定了系统的焓。

Because ΔH depends only on the initial and final states, any pathway connecting these states gives the same overall enthalpy change. One useful analogy is the vertical distance between two mountain points: no matter which trail you take, the altitude difference stays the same.

由于 ΔH 仅取决于始态和终态，因此连接这两个状态的任何路径都会得到相同的总焓变。一个有用的类比是两座山点之间的竖直距离：无论你走哪条山路，高度差始终保持不变。

4. Standard Enthalpy Changes | 标准焓变

Standard enthalpy changes are measured under standard conditions: 100 kPa (1 bar) pressure and usually 298.15 K (25 °C). They are denoted by a superscript degree symbol, for example ΔH°.

标准焓变是在标准条件下测定的：压力为 100 kPa（1 bar），温度通常为 298.15 K（25 °C）。标准焓变用上标“°”表示，例如 ΔH°。

The standard enthalpy of formation, ΔH°f, is the enthalpy change when one mole of a compound is formed from its elements in their standard states under standard conditions. The standard enthalpy of formation of an element in its most stable form is defined as zero.

标准摩尔生成焓 ΔH°f 是指在标准条件下，由稳定态的元素单质生成 1 mol 化合物时的焓变。最稳定形态的元素单质的标准摩尔生成焓被定义为零。

5. Manipulating Thermochemical Equations | 热化学方程式的变换

To apply Hess’s law, you often need to combine known equations. Three operations are permitted:

要应用盖斯定律，你通常需要组合已知方程式。允许三种操作：

Reverse the direction of a reaction: the sign of ΔH changes.

反转反应的方向：ΔH 的符号改变。
Multiply all coefficients by a factor: ΔH is multiplied by the same factor.

将所有系数乘以一个因数：ΔH 也乘以相同的因数。
Add two or more equations: their ΔH values are added together.

将两个或多个方程式相加：它们的 ΔH 值也相加。

Always check that the balanced equation and its physical states are correct before combining. Phase symbols are essential because ΔH depends on whether substances are solid, liquid or gas.

在组合之前，务必检查配平的方程式及其物理状态是否正确。相态符号至关重要，因为 ΔH 取决于物质是固态、液态还是气态。

6. Hess’s Law Using Enthalpies of Formation | 用生成焓计算盖斯定律

Any reaction can be imagined to proceed by first decomposing reactants into their elements, then combining those elements to form products. This provides a convenient formula using standard enthalpies of formation.

任何反应都可以想象为先分解反应物为元素单质，再由这些单质合成产物。这为我们提供了一个利用标准生成焓计算的便捷公式。

ΔH°rxn = Σ ΔH°f(products) − Σ ΔH°f(reactants)

In this formula, each ΔH°f value must be multiplied by the stoichiometric coefficient of the corresponding substance in the balanced equation.

在此公式中，每个 ΔH°f 值都必须乘以对应物质在配平方程式中的化学计量系数。

7. Hess’s Law Using Bond Enthalpies | 用键焓计算盖斯定律

Bond enthalpy is the energy required to break one mole of a particular bond in a gaseous substance. Breaking bonds requires energy (positive), while forming bonds releases energy (negative).

键焓是指在气态物质中断裂 1 mol 某种化学键所需要的能量。断裂化学键需要吸收能量（正值），而形成化学键会释放能量（负值）。

For a reaction involving only gaseous molecules, the approximate enthalpy change can be estimated from average bond enthalpies (BE):

对于只涉及气态分子的反应，可以用平均键焓（BE）估算反应的焓变：

ΔH ≈ Σ BE(bonds broken) − Σ BE(bonds formed)

Bond enthalpy calculations are approximate because tabulated values are averages across different compounds. They are most accurate for simple gaseous reactions.

键焓计算是近似值，因为表中给出的数值是不同化合物中的平均值。对于简单气态反应，其准确度最高。

8. Worked Example 1: Combining Reactions | 实例1：组合反应方程式

Given the following reactions:

已知以下反应：

C(s) + O₂(g) → CO₂(g)　ΔH₁ = −393.5 kJ mol⁻¹

CO(g) + ½O₂(g) → CO₂(g)　ΔH₂ = −283.0 kJ mol⁻¹

Calculate the enthalpy change for the target reaction C(s) + ½O₂(g) → CO(g).

计算目标反应 C(s) + ½O₂(g) → CO(g) 的焓变。

The target equation can be obtained by subtracting the second equation from the first:

目标方程式可以通过用第一个方程式减去第二个方程式得到：

ΔH = ΔH₁ − ΔH₂ = (−393.5) − (−283.0) = −110.5 kJ mol⁻¹

Thus the enthalpy change for the formation of one mole of CO from carbon and oxygen is −110.5 kJ mol⁻¹.

因此，由碳和氧生成 1 mol CO 的焓变为 −110.5 kJ mol⁻¹。

9. Worked Example 2: Formation Data | 实例2：使用生成焓数据

Calculate the standard enthalpy change for the thermal decomposition of calcium carbonate:

计算碳酸钙热分解的标准焓变：

CaCO₃(s) → CaO(s) + CO₂(g)

The standard enthalpies of formation are listed below.

标准生成焓数据如下表所示。

Substance	ΔH°f / kJ mol⁻¹
CaCO₃(s)	−1207
CaO(s)	−635
CO₂(g)	−393.5

Using the formation enthalpy formula:

使用生成焓公式：

ΔH°rxn = [ΔH°f(CaO) + ΔH°f(CO₂)] − ΔH°f(CaCO₃)

= [(−635) + (−393.5)] − (−1207)

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Hess’s Law and Reaction Enthalpy Calculations | 盖斯定律与反应热计算