Gibbs Free Energy and Spontaneity Notes

Thermodynamics and Spontaneity

• Introduction
  • Focus on Gibbs Free Energy (G), its relation to entropy, and its predictive capabilities regarding spontaneity.

Second Law of Thermodynamics

• States that the entropy of the universe always increases for a spontaneous process:
  \Delta S_{universe} > 0

• Entropy change of the universe is given by:
  \Delta S{universe} = \Delta S{system} + \Delta S_{surroundings}

  • Note: \Delta S{surroundings} = - \Delta S{system}

• At constant temperature (T) and pressure (P):
  \Delta S{universe} = \Delta S{system} - \Delta S_{surroundings}

Gibbs Free Energy

• Deriving Gibbs Free Energy:

  • Multiply both sides by -T:
    -\Delta S{universe} = -\Delta S{system} + \Delta S_{surroundings}
  • Define Gibbs Free Energy change of the system: \Delta G_{system} = \Delta H - T \Delta S
    • Note: No subscript implies "system" (not universe).

• Importance of Gibbs Free Energy:

  • Calculated using properties of the system alone.

Relationship to Entropy Change

• At constant T and P, Gibbs free energy change is proportional to:
  \Delta G = -\Delta S_{universe}

• Predicting spontaneity:

  • \Delta G < 0 \Rightarrow spontaneous
  • \Delta G > 0 \Rightarrow nonspontaneous
  • \Delta G = 0 \Rightarrow at equilibrium

Chemical Potential

• Gibbs Free Energy is sometimes referred to as Chemical Potential (in kJ/mol).
• Just as physical objects move in a way that lowers potential energy, chemical reactions tend towards lower Gibbs Free Energy.

Factors Affecting Gibbs Free Energy

• Spontaneity example at different temperatures:
  • Spontaneous at 25°C and nonspontaneous at -4°C.
• Influencing factors:
  • Temperature (T)
  • Always positive when in Kelvin.
  • Enthalpy Change (ΔH) and Entropy Change (ΔS).

Analysis of Specific Reaction

Example:

• Reaction:
  4 C(s) + 6 H{2}(g) + 2 O{2}(g) \rightarrow 2 C{2}H{5}OH(l)
• Given:
  \Delta G = -469.6 \text{kJ}
• Spontaneity Determination:
  • Can use either \Delta S_{universe} or \Delta G ; \Delta G is easier!
  • Check change in number of gas moles:
  • \Delta S{gas} = gas{prod} - gas_{react} = 0 - 8 = -8
  • Decrease in gas moles => \Delta S is negative.

Temperature Influence on Spontaneity

• At high temperatures:
  • \Delta G may become positive (nonspontaneous).
• At low temperatures:
  • \Delta G may be negative (spontaneous).

Summary

• Gibbs Free Energy defined in context of the Second Law of Thermodynamics.
• Predictive capability of Gibbs free energy regarding spontaneity under different temperature conditions.