The equilibrium constant K is tied to standard Gibbs free energy through \( \Delta G^\circ = -RT \ln K \), and \( \Delta G^\circ \) is fixed by the reaction itself once temperature is set, it does not care about the total pressure or volume you squeeze the system into. Changing pressure or volume can push a gas reaction toward more or fewer moles, but the ratio of products to reactants at the new equilibrium still obeys the same K. Adding a catalyst only helps both directions reach equilibrium sooner, it never changes where equilibrium settles. So temperature is the only variable that genuinely resets the value of K.