The freezing point depression of a $0.1\,\text{M}$ solution of weak acid (HX) is $-0.20^\circ\text{C}$. What is the value of equilibrium constant for the reaction $\text{HX(aq)} \rightleftharpoons \text{H}^\text{+(aq)} + \text{X}^\text{-}\text{(aq)}$? [Given: $K_f$ for water $= 1.8\,\text{kg·mol}^{-1}\,\text{K}$, molality $=$ molarity]