Problem:

1.60 g of naphthalene (C₁₀H₈) is dissolved in 20.0 g of benzene. The freezing point of pure benzene is 5.5 ^oC, and the freezing point of the mixture is 2.8 ^oC. What is the molal freezing point depression constant, K_f of benzene?

Strategy:

1. Step 1: Calculate the freezing point depression of benzene.
   
   T_f = (Freezing point of pure solvent) - (Freezing point of solution)
   (5.5 ^oC) - (2.8 ^oC) = 2.7 ^oC
   
   
2. Step 2 : Calculate the molal concentration of the solution.
   
   molality = moles of solute / kg of solvent
   moles of naphthalene = (1.60 g) (1 mol / 128 g) = 0.0125 mol naphthalene
   molality of solution = (0.0125 mol) / (0.0200 kg) = 0.625 m
   
   
3. Step 3: Calculate K_f of the solution.
   
   T_f = (K_f) (m)
   
   (2.7 ^oC) = (K_f) (0.625 m)
   
   K_f = 4.3 ^oC/m