$5$ milli-moles of a solid $A$ was dissolved in $5$ moles of $H_2O$. On adding to the solvent,$A$ starts polymerising into another insoluble solid following zero order kinetics. On adding $6$ milli-moles of another solid solute $C$ (after $20$ minutes) the polymerisation completely stops. The insoluble solid polymer is removed and the resulting solution was cooled to a temperature less than $-0.186\,^{\circ}C$ (melting point of solution) to cause solidification of some liquid water. Calculate the value of $'X'$ if rate constant for polymerisation reaction is represented as $10^{-X}\,moles/minute$. $[K_f(H_2O) = 1.86\, K\, Kg\,mol^{-1}]$