Module 5.4: Gibbs Free Energy

5.4.1 Definition

I In order to avoid determining spontaneity by calculating both the change in entropy of the surroundings and the system, the state function Gibbs energy (G) was introduced

1. The Gibbs Free Energy is defined as G = H − TS, but the change in free energy is more commonly used: $\Delta \textrm{G} = \Delta \textrm{H} - \textrm{T} \Delta \textrm{S}$ (Eq. 98)

2. provided that the temperature and pressure of the system is constant,

   1. if $\Delta \textrm{G}$ is greater than zero, the reverse process is spontaneous

   2. if $\Delta \textrm{G}$ is equal to zero, the process is at equilibrium

   3. if $\Delta \textrm{G}$ is less than zero, the forward process is spontaneous

3. the direction of spontaneous change is always in the direction of decreasing free energy.

5.4.2 Usage of Free Energy

II Gibbs free energy of reaction ($\Delta \textrm{G}$): the difference in molar Gibbs free energies of the products and reactants

1. like the change in enthalpy and entropy for a reaction, it can be calculated by: $\Delta \textrm{G} = \sum_{\textrm{products}} \textrm{n} \textrm{G}_{m} - \sum_{\textrm{reactants}} \textrm{n} \textrm{G}_{m}$ (Eq. 99)

2. there is a crucial difference between this and the standard Gibbs free energy of reaction; the Gibbs free energy of reaction in terms of the standard molar Gibbs energies

   1. there is only one possible value for $\Delta \textrm{G}^{\Theta}$ in a particular reaction and temperature

   2. the value of $\Delta \textrm{G}$ changes as the composition of the reaction mixture changes, and therefore its value and sign may change as the reaction proceeds.

III Eq. 99 is rarely used as their absolute values are rarely known; the changes of Gibbs free energy is what is extremely useful.

1. standard Gibbs free energy of formation ($\Delta \textrm{G}_{f}^{\Theta}$): the change in standard free energy (per mole) from its elements in their most stable form (known as reference state) to its final product

   1. the values of $\Delta \textrm{G}_{f}^{\Theta}$ can be calculated through the definition of free energy.

   2. $\Delta \textrm{G}_{f}^{\Theta} = 0$ for elements in their most stable form.

2. this value also is an indication of stability of a certain molecule:

   1. if $\Delta \textrm{G}_{f}^{\Theta}$ is positive, the molecule is a thermodynamically unstable compound that is less stable than its elements in their most stable form (reference states)

   2. if $\Delta \textrm{G}_{f}^{\Theta}$ is negative, the molecule is a thermodynamically stable compound that is more stable than its elements in their most stable form (reference states)

   3. although molecules with positive $\Delta \textrm{G}_{f}^{\Theta}$ maybe thermodynamically unstable, they can last forever if its decomposition is very slow (remember, thermodynamics is independent of kinetics!)

      1. benzene is thermodynamically unstable, but can last a lifetime.

3. Like Eq. 82, the Gibbs free energies of reaction can be calculated by $\Delta \textrm{G}_{f}^{\Theta}$ of its reactants and products: $\Delta \textrm{G}_{r}^{\Theta} = \sum_{\textrm{products}} \textrm{n} \Delta \textrm{G}_{f}^{\Theta} - \sum_{\textrm{reactants}} \textrm{n} \Delta \textrm{G}_{f}^{\Theta}$ (Eq. 100)