Entropy & Free Energy

Entropy Definition

• Entropy (S): Measure of disorder in a system.
• States of Matter Order:
  • Aqueous > Gases > Liquids > Solids
• Key Relationships:
  • Compounds become more disordered when they dissolve.
  • Heavier compounds have higher entropy than lighter ones.
  • More moles of gas increase entropy.
  • Higher temperatures result in higher entropy.

Spontaneity of Reactions

• Always Spontaneous:
  • Exothermic reactions (releasing heat)
  • Reactions with increasing entropy
• Never Spontaneous:
  • Endothermic reactions (absorbing heat)
  • Reactions with decreasing entropy
• Sometimes Spontaneous:
  1. Exothermic & Decreasing Entropy: Only spontaneous at low temperatures.
  2. Endothermic & Increasing Entropy: Only spontaneous at high temperatures.

Favorability of Reactions

• Non-Spontaneous Reaction:
  • Spontaneous in the reverse direction
  • Reactant-favored
• Spontaneous Reaction:
  • Non-spontaneous in the reverse direction
  • Product-favored
  • Thermodynamically-favored

Signs and Their Meanings

• Entropy Change (ΔS):
  • +ΔS = Increasing disorder
  • -ΔS = Decreasing disorder
• Gibbs Free Energy Change (ΔG):
  • +ΔG = Non-spontaneous
  • -ΔG = Spontaneous
• Enthalpy Change (ΔH):
  • +ΔH = Endothermic
  • -ΔH = Exothermic

Reaction Favorability Based on ΔS and ΔH

1. ΔS+ and ΔH+:
   • NOT thermodynamically-favored
   • Driven by entropy
2. ΔS- and ΔH-:
   • Thermodynamically-favored
   • Driven by enthalpy
3. ΔS+ and ΔH-:
   • Thermodynamically-favored
   • Driven by both entropy and enthalpy
4. ΔS- and ΔH+:
   • NOT thermodynamically-favored
   • Driven by neither

Keq in Free Energy Calculations

• Use the constant: R = 8.314 J/(mol·K).
• Convert ΔG from kJ to J for calculations.
• Remember to account for the negative sign in calculations.
• Use ln K not log K for calculations.
• A spontaneous reaction generally has a large K value, which results in a negative ΔG value.

Additional Notes

• Convert entropy (S) from J to kJ by dividing by 1,000.
• Use temperature in Kelvin (K).
• At equilibrium, ΔG = 0. This equation is commonly used to solve for temperature (T).