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).