Relationship between Free Energy and Equilibrium Constant

The equilibrium constant is a method that shows the reaction sign (whether the process is spontaneous or not). We have to express the status of the reaction when it changes by the concentration of products to the reactant (nonstandard state).

What is Gibbs Free Energy?

Gibbs free energy can be defined as the thermodynamic potential, the reversible or maximum work done by a thermodynamic system at constant pressure and temperature. The work done by electrical energy in one second is described as the product of the total Gibbs energy charge transferred and the electromotive force of the potential cell.

Gibbs free energy equation-

ΔG = ΔH – TΔS

Here,

ΔG stands for Gibbs free energy.

ΔH is the enthalpy change.

T is the temperature, and

ΔS is the change in entropy.

When ΔG < 0, the energy response is spontaneous.

When ΔG > 0, energetic responses are usually non-spontaneous.

The reaction reaches equilibrium when ΔG = 0.

Free Energy and Equilibrium Constant formula

There is a single value for a ΔG0 reaction at a specific temperature. But in the case of ΔG, there could be different values. Both values are important for a reaction to occur.

When the ratio of the products to reactants is in equilibrium, the reaction (Q) will exhibit the equilibrium constant (Q = K). For spontaneous processes where the free energy (ΔG = 0) decreases, the reaction of the process will proceed towards equilibrium.

At equilibrium, the forward and reverse processes occur at the same rate.

The following equation shows the relationship between the standard states of free energy at any point during the reaction.

ΔG = ΔG0 + RT ln Q (Q = K)

ΔG = ΔG0 + RT ln K=0 

Where ΔG = 0

0=ΔG0 + RT ln K

ΔG0 = – RT ln K

At temperature T, ΔG0 calculated as

ln K= – ΔG0/RT

The equilibrium constant, K= eRT/ΔG0

Where, 

 G – Free energy at any moment

ΔG0 – Standard state free energy in KJ/mol

R is the ideal gas constant and it is equal to 8.314 J/mol-k

T is the absolute temperature at Kelvin

K is equilibrium constant

• ΔG0 < 0, K>1 = Reaction Favours product formation
• ΔG0 > 0, K<1 = Reaction Favours reactant formation
• ΔG0 = 0, K=1 = Reaction Favours neither reactant nor product formation

If the enthalpy and entropy changes are known, this equation allows us to calculate various chemical reactions. This means that enthalpy and entropy can be measured according to the variation of the equilibrium constant with temperature.

Terms in free energy

• Standard free energy formation:

Standard free energy formation is defined as the Gibbs free energy change when 1 mole of a pure substance is formed from its elements in its standard state.

• Standard free energy Change:

Standard free energy change is defined as the change in Gibbs free energy from the reaction carried out under standard conditions.

Example for standard free energy

H2 + 3N2 → 2NH3

The reaction takes place at 298 K.  ∆G = -32.7 kJ/mol. Find Kp.

Answer: ∆G= -RT In Kp

In Kp = – ∆G/RT

           = – (-32.7 x 103J/mol) / (8.314 J/K mol x 298 K)

           = 13.2

      Kp = 5.4 x 105

Conclusion

Comparing the equilibrium constant (K) with the reaction quotient (Q) will help decipher how a reaction will achieve equilibrium. When a system is in equilibrium, ∆G =0 and ∆G0 denote that all products and reactants are in the standard state.

Therefore ∆G0 = -RT InK

The equilibrium constant, K of a gas involved in a reaction is described in terms of its concentration.

• ΔG0 < 0, then K > 1, it means products are more favoured
• ΔG0 > 0, then K < 1, it means  Reactants are more favoured
• If ΔG0 = 0, then K = 1, it means both reactant and product are not favoured.