TR

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.”