R1.4.1 Entropy (S) (Higher Level Only)

Entropy: A Measure of Disorder and Energy Dispersal

1. Imagine you’re at a party.
2. At first, everyone is neatly lined up, waiting for food. Gradually, people start moving around, chatting, and dancing.
3. The room becomes more chaotic, with energy and people spreading out.
4. This dynamic shift is a great analogy for entropy.

In chemistry, entropy describes how energy and matter are distributed in a system. The more "spread out" or disorganized they are, the higher the entropy.

What Is Entropy?

• When energy or matter becomes more spread out, the system's entropy increases.
• Conversely, when energy or matter becomes more concentrated, entropy decreases.

Entropy as Disorder

Entropy is often referred to as a measure of "disorder" or "randomness."

Entropy Comparisons: Solids, Liquids, and Gases

The state of matter significantly influences entropy. Under identical conditions:

• Gases exhibit the highest entropy because their particles can move freely in all directions, resulting in a vast number of possible arrangements.
• Liquids have lower entropy than gases, as their particles are more constrained in motion.
• Solids have the lowest entropy due to their structured, fixed arrangement.

This trend can be summarized as:
$$S_{\text{gas}}>S_{\text{liquid}}>S_{\text{solid}}$$

Entropy Changes During Phase Transitions

Entropy changes during phase transitions because the arrangement and motion of particles evolve:

• Melting (solid → liquid): Entropy increases ($\mathrm{\Delta }S>0$) as particles gain more freedom to move.
• Vaporization (liquid → gas): Entropy increases significantly ($\mathrm{\Delta }S>0$) because particles become highly dispersed.
• Condensation (gas → liquid): Entropy decreases ($\mathrm{\Delta }S<0$) as particles become more ordered.

Calculating Standard Entropy Change ($\mathrm{\Delta }{S}^{\circ }$)

1. Entropy is a state function, meaning its value depends only on the initial and final states of the system, not on the path taken.
2. The standard entropy change for a reaction, $\mathrm{\Delta }{S}^{\circ }$, can be calculated using the standard entropy values ($S^{\circ }$) of the reactants and products, which are provided in the IB Chemistry data booklet.

$$\mathrm{\Delta }{S}^{\circ }=\sum S^{\circ }(\text{products})-\sum S^{\circ }(\text{reactants})$$

• $S^{\circ }$ values are expressed in ${\text{J K}}^{-1}{\text{mol}}^{-1}$.
• Multiply each $S^{\circ }$ value by its stoichiometric coefficient from the balanced chemical equation.

Predicting Entropy Changes

You can often predict whether a reaction increases or decreases entropy by considering:

• States of Matter:
  • Reactions producing gases generally increase entropy.
  • Reactions consuming gases generally decrease entropy.
• Number of Particles:
  • If the total number of product molecules exceeds the total number of reactant molecules, entropy likely increases.
  • If the number decreases, entropy likely decreases.

Why Is the Entropy of a Perfect Crystal at 0 K Zero?

• At absolute zero (0 K), a perfect crystal has no thermal motion, and its particles are perfectly ordered.
• According to the Third Law of Thermodynamics, the entropy of a perfect crystal at 0 K is zero.

This is because there is only one possible arrangement (microstate) for the particles, meaning no randomness or dispersal of energy.

Reflection Questions