Determine the expected value of T _ f for 1 ~m CaCl ₂ solution if 1 m urea solution has T _ f value ' x ' K .

Step-by-step solution

The freezing point depression T_f is a colligative property given by T_f = i K_f m , where i is the van't Hoff factor, K_f is the cryoscopic constant, and m is the molality. For urea, a non-electrolyte with i = 1 , the observed depression is T_ f, urea = x = 1 K_f 1 , so K_f = x . Calcium chloride dissociates as CaCl ₂ Ca ²⁺ + 2 Cl ^- , giving i = 3 . Thus, for 1 m CaCl ₂ , T_ f, CaCl ₂ = 3 K_f 1 = 3x . The expected freezing point depression is 3x K .