Concept:
The thermodynamic equilibrium constant ($K_{eq}$) dictates the ratio of product concentrations to reactant concentrations when a reversible chemical reaction reaches a state of balance.
Step 1: The equilibrium constant is fundamentally linked to the standard Gibbs free energy change of the reaction via the equation: $\Delta G^\circ = -RT \ln(K_{eq})$.
Step 2: In this equation, '$R$' is the universal gas constant, and $\Delta G^\circ$ is a fixed value for a specific reaction under standard conditions. The only operating variable that remains is Temperature ($T$).
Step 3: While changing the concentration, pressure, or volume will shift the position of the equilibrium left or right (Le Chatelier's principle), the actual numerical value of the equilibrium constant $K_{eq}$ itself remains unchanged.
Step 4: Therefore, for a specific given chemical reaction, the equilibrium constant is a function of temperature and temperature alone.