Gibbs Free Energy and the Equilibrium Constant

`DeltaG`: Gibbs Free Energy

`DeltaG` is the change of Gibbs (free) energy for a system and `DeltaG°` is the Gibbs energy change for a system under standard conditions (1 atm, 298K). On an energy diagram, `DeltaG` can be represented as:

Where `DeltaG` is the difference in the energy between reactants and products. In addition `DeltaG` is unaffected by external factors that change the kinetics of the reaction. For example if E_a(activation energy) were to decrease in the presence of a catalyst or the kinetic energy of molecules increases due to a rise in temperature, the `DeltaG` value would remain the same.

K: The Equilibrium Constant

K is the equilibrium constant of a reaction and is given by the reaction quotient:

`aA + bB ⇌ cC + dD`

`K = ([A]^a [B]^b)/([C]^c [D]^d)`

The connection between Gibbs free energy and constant equilibrium are directly related in the following  equation:

ΔG = - R*T*ln(K_eq)

• `R = 8.314 J mol C^(-1)`
• `T = Temperature in K`
• `n = "moles of "e^(-)" in a balanced redox reaction."`
• `F = "Faraday's Constant" = 96,485 C"/mol"`

These relationships are summarized as follows:

`DeltaG_"rxn"^0	K	Product Formation
`DeltaG_"rxn"^0 < 0`	K > 1	Products favored over reactants at equilibrium.
`DeltaG_"rxn"^0= 0`	K = 1	At equilibrium when [C]c[D]d…= [A]a[B]b…(very rare)
`DeltaG_"rxn"^0 > 0`	K < 1	Reactants favored over products at equilibrium