Calculating Entropy Changes | 熵变的计算

📚 Calculating Entropy Changes | 熵变的计算

Entropy changes are a central part of Cambridge A-Level Chemistry. This article explains how to calculate standard entropy changes of reactions, how to interpret their signs, and how to link them to reaction feasibility using total entropy changes.

熵变是剑桥 A-Level 化学的核心内容之一。本文将解释如何计算反应的标准熵变、如何解释其正负号，以及如何通过总熵变将熵变与反应可行性联系起来。

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1. Entropy: A Measure of Disorder | 熵：无序程度的量度

Entropy, given the symbol S, describes how energy is spread out between the particles in a system. The greater the number of ways particles can be arranged and energy quanta can be distributed, the higher the entropy.

熵用符号 S 表示，描述能量在体系粒子之间的分散程度。粒子的排列方式和能量量子分布方式越多，熵值越高。

Gases generally have higher entropy than liquids, and liquids have higher entropy than solids, because particles in a gas are far more randomly arranged and can move more freely.

气体的熵通常高于液体，液体的熵通常高于固体，因为气体粒子的排列更加随机，运动也更加自由。

For a chemical reaction, we usually calculate the entropy change of the system, ΔS, rather than absolute entropy values on their own.

对于化学反应，我们通常计算体系的熵变 ΔS，而不是单独的绝对熵值。

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2. Standard Entropy, S°, and Its Units | 标准熵 S° 及其单位

Standard entropy, S°, is the entropy of one mole of a substance under standard conditions: 298 K, 1 atm pressure, and solutions at 1 mol dm⁻³.

标准熵 S° 是一摩尔物质在标准条件下的熵：298 K、1 atm 压力，溶液浓度为 1 mol dm⁻³。

Standard entropies are always positive, unlike standard enthalpies of formation, because there is always some disorder in any substance. The units are joules per kelvin per mole, J K⁻¹ mol⁻¹.

标准熵始终为正值，这与标准生成焓不同，因为任何物质中总存在一定的无序度。其单位为焦耳每开尔文每摩尔，即 J K⁻¹ mol⁻¹。

Notice that entropy uses joules, while many enthalpy values are quoted in kilojoules. You must convert kJ to J before combining them in ΔG or total entropy calculations.

请注意，熵使用焦耳，而许多焓值以千焦表示。在将焓与熵结合进行 ΔG 或总熵计算之前，必须先将 kJ 转换为 J。

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3. The Core Equation for ΔS° | 计算 ΔS° 的核心公式

To calculate the standard entropy change of a reaction, subtract the total entropy of the reactants from the total entropy of the products:

要计算反应的标准熵变，用生成物的总熵减去反应物的总熵：

ΔS° = Σ S°(products) − Σ S°(reactants)

The symbol Σ means ‘sum of’, and each S° value is multiplied by the stoichiometric coefficient in the balanced equation.

符号 Σ 表示“求和”，每个 S° 值都要乘以配平化学方程式中的化学计量数。

• Always use the balanced equation to obtain the correct coefficients.
• 始终使用配平后的方程式来确定正确的化学计量数。
• If a product or reactant has a coefficient of 2 or 3, multiply its S° accordingly.
• 如果生成物或反应物的系数为 2 或 3，应相应乘以其 S° 值。

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4. Worked Example 1: CaCO₃ Decomposition | 例题 1：碳酸钙分解

Calcium carbonate decomposes on heating according to the equation:

碳酸钙受热分解的方程式为：

CaCO₃(s) → CaO(s) + CO₂(g)

Given the following standard entropy values, calculate ΔS° for the reaction.

根据下列标准熵值，计算该反应的 ΔS°。

Substance	S° / J K⁻¹ mol⁻¹
CaCO₃(s)	92.9
CaO(s)	39.7
CO₂(g)	213.6

Step 1: Write the expression. ΔS° = Σ S°(products) − Σ S°(reactants).

步骤 1：写出表达式。ΔS° = Σ S°(生成物) − Σ S°(反应物)。

Step 2: Substitute values. Products: (1 × 39.7) + (1 × 213.6) = 253.3 J K⁻¹ mol⁻¹. Reactants: 1 × 92.9 = 92.9 J K⁻¹ mol⁻¹.

步骤 2：代入数值。生成物：(1 × 39.7) + (1 × 213.6) = 253.3 J K⁻¹ mol⁻¹。反应物：1 × 92.9 = 92.9 J K⁻¹ mol⁻¹。

Step 3: ΔS° = 253.3 − 92.9 = +160.4 J K⁻

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