Problem:

The freezing point of a solution that contains 1.00 g of an unknown compound, (A), dissolved in 10.0 g of benzene is found to be 2.07 ^oC. The freezing point of pure benzene is 5.48 ^oC. The molal freezing point depression constant of benzene is 5.12 ^oC/molal. What is the molecular weight of the unknown compound?

Strategy:

1. Step 1: Calculate the freezing point depression of the solution.
   
   T_f = (Freezing point of pure solvent) - (Freezing point of solution)
   (5.48 ^oC) - (2.07 ^oC) = 3.41 ^oC
   
   
2. Step 2 : Calculate the molal concentration of the solution using the freezing point depression.
   
   T_f = (K_f) (m)
   m = (3.41 ^oC) / (5.12 ^oC/molal)
   m = 0.666 molal
   
   
3. Step 3: Calculate the molecular weight of the unknown using the molal concentration.
   
   m = 0.666 molal = 0.666 mol A / kg benzene
   
   moles A = (0.66 mol A / kg benzene) (0.100 kg benzene) = 6.66 X 10^-3 mol A
   
   molecular weight of A = (1.00 g A) / (6.66 X 10^-3 mol A)
   
   molecular weigh of A = 150. g/mol