Question

Why is the standard entropy of a substance in the gas state greater than its standard entropy in the liquid state?

Short answer

The standard entropy of a substance in the gas state is greater than in the liquid state because gases have more disorder and more accessible microstates.

Step-by-step solution

Understanding Entropy

Entropy is a measure of the amount of disorder or randomness in a system. The greater the number of possible microstates for a given state, the higher the entropy.

Comparing Entropy Between States of Matter

The gas state of a substance has more disorder than the liquid state because gas particles are more spread out and move more freely, resulting in a larger number of accessible microstates.

Standard Entropy and States of Matter

The standard entropy (denoted as S°) is the entropy value for a standard state of a substance. Because gases are more disordered than liquids, the standard entropy of a substance in the gas state is greater than that in the liquid state.

Key concepts

Entropy

Entropy is a fundamental concept in thermodynamics that quantifies the level of disorder or randomness within a physical system. It is represented as a statistical measure of the number of different ways a system can be arranged, known as microstates. When we discuss entropy in relation to substances, we are referring to the unpredictability of particle positions and energy states.

As a core component of the second law of thermodynamics, entropy establishes that for any spontaneous process, the total entropy of a system and its surroundings will not decrease. In simpler terms, systems naturally progress towards a state of higher entropy; that is, they become more disordered over time unless energy is applied to maintain or increase order.

Regarding substances, when they transition from a solid to a liquid and finally to a gas, the entropy increases. Why is this the case? Well, as a substance heats up and moves through these phases, its particles gain more energy, move more freely, and have a greater number of positions and energy levels available to them. This results in an increased number of possible microstates and, therefore, a higher entropy.

States of Matter

The physical forms that different phases of matter take on—solid, liquid, and gas—are known as states of matter. Each state holds distinct characteristics that affect the behavior and arrangement of particles within a substance.

In solid form, particles are tightly packed in a fixed arrangement and can only vibrate in place, leading to low entropy. As a substance transitions to a liquid, the particles still touch but can move around each other, increasing the entropy due to more ways the particles can be arranged. Finally, in the gas state, particles are spread out and move independently and rapidly. This highly disordered state results in significantly more arrangement possibilities, or microstates, leading to the highest entropy among the states of matter.

Understanding the states of matter helps us predict the physical properties of substances at different temperatures and pressures. It's also crucial for grasping why changes in state—such as melting, freezing, boiling, and condensing—are accompanied by changes in entropy, as the particle arrangements become less or more orderly.

Microstates

The concept of microstates underpins the statistical nature of entropy. A microstate refers to a specific configuration of particles, including their locations and energies, within a system at a given instant. Imagine a simple dice game: each roll represents a different microstate. Now, think of these rolls on an enormous scale, where every particle within a substance can have multiple positions and energy levels—that's the realm of microstates in thermodynamics.

For any state of matter, the total number of microstates depends on the freedom the particles have to move. In gases, particles have the liberty to travel throughout the volume they occupy, leading to a vast number of microstates. This is why gases have a higher entropy than liquids or solids—there are simply more ways the system can be arranged.

To help students understand, imagine a room full of scattered toys versus a neatly organized shelf of toys. The scattered room represents a gas with countless arrangements (microstates) and high entropy, while the organized shelf resembles a solid with limited arrangements and lower entropy. The key takeaway is that the number of microstates is crucial for determining the entropy of a substance in its various states.