The calculated value of Gibbs free energy is useful for prediction of reaction spontaneity. There are few complications in the actual calculation procedure once you have the units correctly matched.
Gibbs free energy calculations
Gibbs free energy is calculated using the relationship:
|ΔG = ΔH - TΔS|
Note that the units of enthalpy change are usually quoted in kiloJoules, whereas the units for entropy are given in Joules per Kelvin. This means that you must convert the entropy values to kiloJoules per Kelvin before using the Gibbs free energy relationship.
Example: Methanol can be made from synthesis gas, produced by the reaction:
For this reaction ΔH = +210 kJ and ΔS= 216 JK-1. What is the value of ΔG for this process at 298K?
ΔS = 216 JK-1, therefore: ΔS = 0.216 kJ K-1
ΔG = ΔH - TΔS
∴ ΔG = 210 - (298 x 0.216) = 210 - 64 = 146 kJ
Temperature and equilibrium
The condition for equilibrium in a process is that Gibbs free energy is zero.
|ΔH - TΔS = 0|
The temperature at which equilibrium is established may be calculated if the enthalpy and entropy changes for the system are known. This is the case for changes of state. If the enthalpy value for the change is known as are the absolute entropies of the starting and finishing materials, then the equilibrium temperature can be calculated.
Example: Use the following data to find the temperature at which water boils.
ΔS = 189 - 71 JK-1 = 118 JK-1 = 0.118 kJ K-1
T = ΔH/ΔS = 44/0.118 = 373 (3 sig figs)
Therefore the boiling point of water = 373K
As noted in the previous section, a system at equilibrium has a Gibbs free energy change of zero.
A reaction which reaches equilibrium does so from a situation in which ΔG is firstly negative and then moves towards zero as the reaction proceeds.
The equilibrium constant gives the relationship between the product and reactant concentrations at equilibrium and as the Gibbs free energy change is zero under these conditions it is reasonable to assume that there is a relationship between Gibbs free energy and the equilibrium constant.
ΔG = -RTlnk
Where R is the Universal gas constant, T is the absolute temperature and k is the equilibrium constant.