The concept of entropy is linked to microstates. For an ideal gas at equilibrium, macroscopic properties like pressure, volume, and temperature remain constant. However, microscopically, particles are constantly changing positions and velocities. A microstate represents a specific arrangement of all positions and energies (kinetic energies for ideal gases) of gas particles at a given moment in time. Even when macroscopic properties appear stable, the system transitions between countless microstates.

Boltzmann's equation, S = k ln W, defines entropy (S) as Boltzmann's constant (k) multiplied by the natural logarithm of W, where W is the number of microstates. An increase in the number of microstates (W) leads to an increase in entropy, while a decrease in W results in a decrease in entropy. Entropy is also conceptually described as disorder or the dispersal of matter or energy, terms that correspond to an increase in the number of microstates.

Consider a mole of ideal gas expanding into a larger volume while temperature remains constant. Doubling the volume increases the number of possible positions for gas particles, thereby increasing the number of microstates. According to Boltzmann's equation, this increase in microstates leads to a positive change in entropy (ΔS > 0).

Increasing the temperature of an ideal gas while keeping volume and moles constant increases the average speed of the particles. Using a Maxwell-Boltzmann distribution, higher temperatures indicate a broader range of velocities and kinetic energies available to the particles. This greater range of energies translates to more possible microstates, resulting in a positive change in entropy (ΔS > 0).

Increasing the number of moles of an ideal gas, while keeping temperature and volume constant, means there are more particles. This leads to more possible arrangements of particles and more ways to distribute energy within the system. Consequently, the number of available microstates increases, causing a positive change in entropy (ΔS > 0).

Evaporation of liquid water to gaseous water demonstrates an increase in entropy. In the liquid state, water molecules are held by intermolecular forces, limiting their movement. In the gaseous state (approximated as an ideal gas), these forces are negligible, leading to increased freedom of movement and a higher number of possible positions. This expansion of accessible states results in an increase in microstates and thus a positive change in entropy (ΔS > 0). This is also why gases are considered more 'disordered' than liquids.

For reactions involving gases, the change in the number of moles of gas significantly impacts entropy. If a reaction reduces the total number of moles of gas (e.g., 2SO₂ + O₂ → 2SO₃, going from 3 moles of gas to 2 moles), it decreases the number of available microstates. A decrease in microstates leads to a negative change in entropy (ΔS < 0) for the system.