Entropy

Introduction

• Entropy: a measure of the randomness of a system.
• It is related to the various modes of motion in molecules.
• Spontaneity is favored by an increase in entropy (S).
• One equation for entropy is S = k ln W
  • k = the Boltzmann constant (1.38 × 10–23 J/K).
  • W = the number of microstates possible
  • We will not do problems using this equation.

Microstates

• Microstate: a specific configuration of the locations and energies of the particles in a system.
• The most probable distribution has the largest number of microstates.
• The most probable distribution, therefore, is the one of greatest entropy.
• S = k ln W
• States of high entropy are favored because they are the most probable.
• This same principle applies to all systems, including those with larger numbers of particles.
• The most probable state will be the one in which the particles are divided evenly throughout the container.

Factors That Influence Entropy

• The phase of the substance
  • Gases have higher entropy than liquids, and liquids higher than solids (neglecting other variables).
• The temperature of the substance.
  • Temperature is proportional to the average kinetic energy of the particles.
  • With higher temperature, the particles have greater freedom to move around.
  • Entropy increases with increases in temperature.
• The type and number of particles that make up the substance.
  • Substances containing a larger number of atoms generally have greater entropy than those with fewer atoms..
• Mixtures tend to have greater entropy than pure compounds.
  • Dissolving a solid in a liquid almost always leads to an increase in entropy.