What happens when K is less than 1 in terms of ∆G°?

When the equilibrium constant ( K ) is less than 1, it indicates that the products of the reaction are less favored compared to the reactants at equilibrium. In thermodynamic terms, this is associated with a positive standard Gibbs free energy change (( \Delta G^\circ )) for the corresponding reaction.

The relationship between the equilibrium constant and the standard Gibbs free energy change is given by the equation:

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

Here, ( R ) is the ideal gas constant, ( T ) is the temperature in Kelvin, and ( K ) is the equilibrium constant. When ( K < 1 ), the natural logarithm of ( K ) becomes negative (( \ln K < 0 )). Substituting this negative value into the equation leads to:

[ \Delta G^\circ = -RT \cdot (\text{a negative value}) = \text{a positive value} ]

As a result, ( \Delta G^\circ ) is greater than 0 when ( K < 1 ), confirming that the reaction is non-spontaneous under standard conditions.

Understanding the implications of different values of ( K )