Free Energy

Table of Contents
Thermodynamics Gateway Page
In this module:
DG and Reactions
DG and Temperature
Coupling Reactions
Free Energy in Industry
Free Energy in Living Things
Free Energy and Equilibrium

Standard Free Energy of Formation (DGfº)

Gibbs Free Energy is a state function, just as enthalpy and entropy are. This means that the DG of the sum of a series of reactions is equal to the sum of the DG's of the individual reactions:

C(s) + 1/2 O2 CO(g) DGº = -137.168 kJ
CO(g) + 1/2 O2 CO2 DGº = -257.191 kJ
C(s) + O2 CO2 DGº = -394.359 kJ

Similar to enthalpy, thermodynamics tables contain an entry for the standard free energy of formation (DGfº). These are the free energy changes for a very specific kind of thermochemical equation:

  • one mole of a compound is formed
  • the reactants are elements in their standard states
  • the standard free energy of formation of an element in its standard state is zero

The standard free energies of formation can be used to calculate the free energy change of any reaction under standard conditions.

Calculate the free energy change for the formation of methanol from carbon monoxide and hydrogen gas:

CO(g) + 2H2(g) CH3OH(l)
Remember to include units with your answer.
That is incorrect. Try again.
The solution is shown below.

DGº = 1 mol•DGfº(CH3OH(l)) - 1 mol•DGfº(CO(g)) - 2 mol•DGfº(H2(g))
DGº = 1 mol•(-166.27 kJ/mol) - 1 mol•(-137.186 kJ/mol) - 2 mol•(0)
DGº = -29.10 kJ