Explain how the change in free energy determines the direction of a chemical reaction and how chemical reactions eventually reach a state of equilibrium.

Free energy refers to exactly that "energy that is free to perform and/or have a reaction." Also known as Gibbs (G) It is energy that is associated with a chemical reaction and is used for work. You also need 3 other variables: heat, temperature, and entropy. The formula for the above would be: G = H - T (E)