Entropy and Gibbs Free Energy

Entropy (S) Definition

_____ a measure of disorder or randomness in a system. Higher ____ means more disorder, while lower ____ means more order.

Phase Changes of Increasing ___:

• Solid < Liquid < Gas

Entropy and the Second Law of Thermodynamics

The entropy of the universe (Δ𝑆_universe) always increases in a spontaneous process:

• Δ𝑆_universe = Δ𝑆_system + Δ𝑆_surroundings > 0

Entropy Changes in a Reaction

Δ𝑆

• Δ𝑆 > 0: Disorder increases (more gas molecules, phase change to gas, mixing substances)

• Δ𝑆 < 0: Disorder decreases (fewer gas molecules, phase change to solid, more organization)

Gibbs Free Energy (G) Definition

The energy available to do work in a system at constant temperature and pressure.

• It determines whether a reaction is spontaneous.

Gibbs Free Energy Equation

ΔG = ΔH - TΔS

• ΔG = Gibbs Free Energy Change

• ΔH = Enthalpy Change (heat energy)

• T = Temperature

• ΔS = Entropy Change

Spontaneity and Gibbs Free Energy

• ΔG < 0 = Spontaneous Rxn

• ΔG > 0 = Non-spontaneous Rxn

• ΔG = 0 Rxn is at Equilibrium

Standard Gibbs Free Energy Change

ΔG∘_reaction = ΔG_Products - ΔG_Reactants

Entropy of the Surroundings

ΔS_surroundings = - ( ΔH / T)

• For a rxn at constant P

• Since heat transfer affects the surroundings, exothermic reactions (ΔH<0) increase Δ𝑆_surroundings,

• Endothermic reactions (ΔH>0) decrease Δ𝑆_surroundings

Always Spontaneous Rxn

ΔH<0 & ΔS>0

• ΔG < 0 for all Temps

Never Spontaneous Rxn

ΔH>0 & ΔS<0

• ΔG > 0 for all T

Spontaneous at Low Temp

ΔH<0 & ΔS<0

Spontaneous at High Temp

ΔH>0 & ΔS>0

Standard Entropy

S∘

• the entropy of a substance at standard conditions (298 K, 1 atm).

• Unlike enthalpy (H), entropy values are always positive because absolute zero (0 K) is the only state with S=0

ΔS∘​_reaction​ = S∘_Products - S∘_Reactants

Phase Changes and Entropy

ΔS is positive when going to a more disordered state:

• Solid → Liquid → Gas (more disorder)

ΔS is negative when going to a more ordered state:

• Gas → Liquid → Solid (less disorder)

The temperature at which phase changes occur is when ΔG=0, meaning

• T = ΔH / ΔS

Relationship Between Temperature and Spontaneity

• When ΔG changes sign, the reaction shifts from non-spontaneous to spontaneous.

• If ΔH and ΔS have opposite signs, spontaneity does not depend on temperature.

• If ΔH and ΔS have the same sign, temperature matters

  • Endothermic & Increasing Entropy (ΔH>0 & ΔS>) → Spontaneous at high T

  • Exothermic & Decreasing Entropy (ΔH<0 & ΔS<0) → Spontaneous at low T

First Law of Thermodynamics

Energy is Conserved

• q_system​ = −q_surroundings​

• The heat lost or gained by a system is equal in magnitude but opposite in sign to the heat gained or lost by the surroundings.

• If q_system >0 (positive), the system absorbs heat (endothermic), and the surroundings lose heat.

• If q_system < 0 (negative), the system releases heat (exothermic), and the surroundings gain heat.

Factors Depending on Entropy

• Entropy depends on temp

  • For any substance, S increases as temp increases

• Entropy depends on the physical state of a substance

  • S increases as solid changes to liquid to gas

• Entropy is related to atomic size and molecular complexity