A Molecular Interpretation of Entropy

Many processes can lead to an increase in a system's entropy

• Increasing the volume that a gas can occupy will increase the disorder of a gas
• Dissolving a solute into a solution will increase the entropy of the solute - typically resulting in an increase in the entropy of the system. (Note: the solvation of a solute can sometimes result in a significant decrease in the solvent entropy - leading to a net decrease in entropy of the system)
• Phase changes from solid to liquid, or liquid to gas, lead to an increase in the entropy of the system

Some processes can lead to a decrease in the entropy of a system

• A gas molecule dissolved in a liquid is much more confined by neighboring molecules than when its in the gaseous state. Thus, the entropy of the gas molecule will decrease when it is dissolved in a liquid
• A phase change from a liquid to a solid (i.e. freezing), or from a gas to a liquid (i.e. condensation) results in an decrease in the disorder of the substance, and a decrease in the entropy
• A chemical reaction between gas molecules that results in a net decrease in the overall number of gas molecules will decrease the disorder of the system, and result in a decrease in the entropy

2NO(g) + O₂(g) ® 2NO₂(g) DS < 0

Let's first consider the last example, the decrease in entropy associated with a decrease in the number of gas molecules for a chemical reaction

2NO(g) + O₂(g) ® 2NO₂(g)

• The product (NO₂) involves the formation of a new N-O bond. The O atoms, originally in a separate O₂ molecule, are now connected to the NO molecule via a new N-O bond
• Since they are now physically bonded to the other molecule (forming a new, larger, single molecule) the O atoms have less freedom to move around
• The reaction has resulted in a loss of the degrees of freedom of the atoms (O atoms)
• There is a reduction in the disorder of the system (i.e. due to the reduction in the degrees of freedom, the system is more ordered after the reaction). DS < 0.

Individual molecules have degrees of freedom related to their motions within a substance

• Translational motion. The entire molecule can move in some direction in three dimensions

• Rotational motion. The entire molecule can rotate around any axis, (even though it may not actually change its position translationally)

• Vibrational motion. The atoms within a molecule have certain freedom of movement relative to each other; this displacement can be periodic motion like the vibration of a tuning fork

• The greater the energy that is stored in these motions, the greater the degrees of freedom, and the greater the entropy

If we lower the temperature of the system, the thermal energy decreases

• the energy stored in translational, rotational and vibrational motions decreases
• the entropy of the system decreases

• S = 0 corresponds to perfect order. The position of the atoms or molecules in the crystal would be perfectly defined
• As the temperature increases, the entropy of the atoms in the lattice increase
• Vibrational motions cause the atoms and molecules in the lattice to be less well ordered

Continued heating of a solid lattice

• In a solid lattice, neighboring molecules are constrained to a certain position in the lattice (that's what makes a solid a solid)
• In the liquid state, a molecule is free to move about the entire volume of the liquid
• Molecules in a liquid have a higher degree of freedom than in a solid
• The liquid has a higher entropy than a solid
• As we heat a solid, there is a gradual increase in the entropy of the system
• At the melting point there is a dramatic increase in the entropy of the system as neighboring molecules are free to move past each other
• After all the solid has melted, the system is in the liquid state
• As we heat the liquid, there is a graduate increase in the entropy
• In the vapor state, a molecule is free to move about the entire container (potentially the entire universe)
• Molecules in the vapor state have a higher degree of freedom than in the liquid state
• The vapor has a higher entropy than the liquid
• At the boiling point there is a dramatic increase in the entropy of the system
• After all the liquid has vaporized, the system is in a gaseous state
• As we heat the gas, there is a gradual increase in the entropy of the system

In general, the entropy is expected to increase for the following types of processes:

1. The melting of a solid to form a liquid
2. The vaporization of a liquid (or solid) to produce a gas
3. Chemical reactions that involve phase changes of solid ® liquid/gas, or liquid ® gas
4. Chemical reactions that result in an increase in the number of gaseous molecules
5. Any time the temperature of a susbstance is increased