The relationship between ΔG0 (the free energy change) and K (the equilibrium constant) is expressed by the equation
ΔG0 = -RTlnK.
Whether ΔG0 is negative or positive indicates that the reaction is spontaneous or non-spontaneous, respectively. In order for ΔG to be negative, then lnK must be positive, since both R and T are positive numbers. When ΔG is positive, then lnK must be negative. In order for lnK to be negative, K < 1.