Calculate van't Hoff factor of aqueous solution of 0.18 m electrolyte that freezes at -0.54^ C ( K _ f for solvent =1.86 ~K ~kg ~mol ⁻¹ )

Step-by-step solution

The van't Hoff factor i is determined using the freezing point depression formula: T_f = i K_f m Given molality m = 0.18 , m , solution freezing point T_f = -0.54^ C , cryoscopic constant K_f = 1.86 , K , kg , mol ⁻¹ , and pure water freezing point T_f^0 = 0^ C , the depression is: T_f = T_f^0 - T_f = 0 - (-0.54) = 0.54 , K Solving for i : i = T_f K_f m = 0.54 1.86 0.18 = 0.54 0.3348 1.6129 This value approximates to 1.612 , corresponding to option C. Final answer: C