The ratio of rate constants for the forward and backward reactions gives us the equilibrium constant, $K_c$:

$$
\ce{A \underset{k_{-1}}{\overset{k_1}{<=>}}  P + Q}\quad \Longrightarrow \quad K_c = {k_1\over k_{-1}} = {C_P C_Q\over C_A}
$$

Per kinetic theory, rate constants depend only on temperature and the presence of any catalysts:

$$
k_i = A_i e^{-E_{a,i}\over RT}
$$

Thus, their ratio (i.e., the equilibrium constant, $K_c$) also must depend only on temperature:

So: **Why does $K_x$, the mole-fraction equilibrium constant, depend on pressure and volume?**