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When the Gibbs free energy change (ΔG) becomes more negative, it indicates that the reaction is becoming more thermodynamically favorable. The relationship between ΔG and the equilibrium constant (K) is described by the equation:

\[

\Delta G = -RT \ln K

\]

where R is the universal gas constant and T is the temperature in Kelvin. When ΔG is more negative, it means that the value of -RT ln K is also becoming more negative.

To achieve a more negative value of ΔG, K must increase. The reason for this is that as K increases, the natural logarithm of K (ln K) also increases, leading to a larger magnitude of -RT ln K, thus making ΔG more negative. A higher value of K corresponds to a greater ratio of products to reactants at equilibrium, signifying that the formation of products is favored.

This phenomenon illustrates a fundamental principle in thermodynamics: a lower free energy (more negative ΔG) corresponds to a higher tendency for the reaction to proceed, leading to a larger equilibrium constant. Therefore, as ΔG decreases toward more negative values, the equilibrium constant K increases accordingly.