Free Energy

Introduction

• The second law of thermodynamics can be used to predict spontaneity.  
• But measurements on the surroundings are seldom made.
• This limits the use of the second law of thermodynamics.
• It is convenient to have a thermodynamic function that focuses on just the system and predicts spontaneity.
• The changes in Gibbs free energy (ΔG) or simply change in free energy allow us to predict spontaneity by focusing on the system only. 
• ΔG = ΔH – TΔS 

ΔG and Spontaneity

• The sign of ΔG indicates if a reaction will be spontaneous or not. 
  • If ΔG < 0, the reaction is spontaneous in the forward direction.
  • If ΔG > 0, the reaction is nonspontaneous in the forward direction
  • If ΔG = 0, the system is at equilibrium
• Spontaneous reactions, those with –ΔG, generally have:
  • ΔH < 0  
  • Exothermic reaction.
  • A negative ΔH will contribute to a negative ΔG. 
  • ΔS > 0
  • A positive ΔS will contribute to a negative ΔG.
  • Note that a reaction can still be spontaneous (have a –ΔG) when ΔH is positive or ΔS is negative, but not both.
  • Also note that there is a temperature dependence.

Direction of Spontaneity Change

• To calculate the temperature at which the spontaneity of a reaction changes from …
  • Spontaneous to nonspontaneous
  • Or nonspontaneous to spontaneous
• Find the temperature at which ΔG = 0
  • ΔG = 0 = ΔH – TΔS
  • T = ΔH / ΔS
  • This is the temperature at which ΔG = 0 and, by definition, the system is at equilibrium.

The Standard Free Energy Change

• Although the Change in Gibbs Free Energy equation is valid under all conditions, we will most often apply it at standard conditions. 
• Standard conditions:
  • Under standard conditions,  ΔG° = ΔH° – TΔS°
  • Pay attention to J vs. kJ in calculations!

Standard Free Energy of Formation

• Standard free energy of formation (∆G°f): the free energy change for the formation of one mole of a substance from its elements in their standard state at 1 bar and 25 °C.

• ΔG°  = ΣnΔG° f (products) – ΣnΔG° f (reactants)

  • This equation only works for calculating ∆G° of a reaction at the temperature for which the values of ∆G°f are tabulated, which is 298 K.

  ΔG°f  for any element in its most stable form at standard conditions is defined as zero.    ( Just as is the case for ΔHf )

  • But S° for an element is NOT zero!!

Equilibrium Constant and Coupled Reactions

• For a reaction to be spontaneous, K must be greater than 1.
  • But “spontaneous” here means that the products are favored when ALL components are  1 M  or 1 atm.  
• It should be clear that if K>1, (favored) then  ΔG° must be -
• As with enthalpy, free energy changes for reactions are additive
  • If Reaction 3 = Reaction 1 + Reaction 2 then, ΔG3 = ΔG1 + ΔG2
  • Also keep in mind that if a reaction is reversed, then the sign on ΔG is also reversed.
  • If a reaction is multiplied by a factor of “n,” then ΔG is also multiplied by a factor of “n.”

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