What is the value of ∆G° when the equilibrium constant K is equal to 1?

When the equilibrium constant ( K ) is equal to 1, it signifies that at equilibrium, the concentrations of the reactants and products are equal, leading to no net change in the system. The relationship between the standard Gibbs free energy change ( \Delta G^\circ ) and the equilibrium constant ( K ) is given by the equation:

[ \Delta G^\circ = -RT \ln(K) ]

where ( R ) is the universal gas constant, ( T ) is the temperature in Kelvin, and ( K ) is the equilibrium constant.

When ( K = 1 ), the natural logarithm of ( K ) (i.e., ( \ln(1) )) equals 0. Substituting this into the equation gives:

[ \Delta G^\circ = -RT \cdot 0 = 0 ]

Thus, when ( K = 1 ), the standard Gibbs free energy change ( \Delta G^\circ ) is indeed zero. This indicates that the system is at equilibrium, and there is no tendency for the reaction to proceed in either the forward or reverse direction under standard conditions. This aligns with our understanding that a system at equilibrium