9.2 Absolute Entropy and Entropy Change in Chemistry

In our journey through thermodynamics, we now turn to entropy—a measure of the disorder or randomness in a system. Unlike enthalpy, which you encountered in Unit 5 and can only be expressed as a change (ΔH°), entropy can be represented in absolute terms (S°) or as a change (ΔS°). This post will explore both concepts and their significance in understanding chemical reactions.

Comparing S° (Absolute Entropy) and ΔS° (Change in Entropy)

Absolute Entropy (S°)

Absolute entropy quantifies the total disorder in a system at a given state under standard conditions (1 atm and 273 K). It reflects the possible arrangements or “chaos” present in a molecule. While calculating S° can be complex, you’ll typically be given these values for reactions on the AP Chemistry exam or find them listed in tables at the back of textbooks.

Key takeaway: S° values help compare different substances and are fundamental in understanding how much disorder a particular compound has inherently.

Change in Entropy (ΔS°)

ΔS° describes how entropy changes during a chemical reaction. Just as you applied Hess’s Law for enthalpy changes (ΔH°), you can use a similar method for entropy:

• ΔS° = Σ S° (products) – Σ S° (reactants)

Entropy is a state function, meaning its value is independent of the pathway taken to reach a final state. It only depends on the initial and final states. This concept ensures that ΔS° remains consistent, regardless of how a reaction occurs.

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Understanding State Functions

A state function depends only on the initial and final states, not the path taken. Think of climbing a mountain: your altitude change remains constant whether you take a straight path or zigzag. In contrast, the distance traveled varies, making it a non-state function. Entropy, like altitude change, is a state function.

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Applying the Entropy Change Formula

When calculating entropy changes, remember to consider stoichiometric coefficients! These values often appear as multipliers in the entropy calculation formula:

Interpreting ΔS°: Positive vs. Negative Values

The sign of ΔS° reveals whether a reaction becomes more or less ordered:

• Positive ΔS°: Indicates increased disorder (more randomness).
• Negative ΔS°: Indicates increased order (less randomness).

Example Problem 1: Calculating ΔS°

Given the following reaction and entropies of substances at 298 K:

• Reaction: 2KI (s) + Cl2 (g) → 2KCl (s) + I2 (s)
• S° values (J/mol•K): KI = 125, KCl = 150, Cl2 = 175, I2 = 250

Calculate ΔS°:

1. Apply the formula:
   ΔS° = Σ S° (products) – Σ S° (reactants)
   ΔS° = [(2 * 150) + 250] – [(2 * 125) + 175]
   ΔS° = (300 + 250) – (250 + 175)
   ΔS° = 550 – 425 = -25 J/mol•K

Interpretation: The negative ΔS° indicates the system became more ordered during the reaction.

Example Problem 2: Predicting the Sign of ΔS°

Consider: 2Na (s) + Cl2 (g) → 2NaCl (s)

• Reactants: 3 total moles, including a gas (more disorder).
• Products: 2 moles of a solid (more order).

Since the reaction transitions from a more disordered state (with a gas) to a more ordered state (solid NaCl), ΔS° is negative, indicating a decrease in entropy.

Practical Implications of Entropy Changes

Understanding entropy changes helps chemists predict:

• Reaction spontaneity (combined with enthalpy and Gibbs Free Energy).
• Stability and feasibility of reactions.
• Energy dispersal in reactions, contributing to insights on reaction mechanisms.