A biochemical engineer isolates a bacterial gene fragment and dissolves a 11.8 mg sample of the material in enough water to make 36.1 mL of solution. The osmotic pressure of the solution is 0.340 torr at 25°C.

Question

A biochemical engineer isolates a bacterial gene fragment and dissolves a 11.8 mg sample of the material in enough water to make 36.1 mL of solution. The osmotic pressure of the solution is 0.340 torr at 25°C. 
 (a) What is the molar mass of the gene fragment?(in g/mol)
 (b) If the solution density is 0.997 g/mL, how large is the freezing point depression for this solution (Kf of water=1.86°C/m)? (in degrees C)

DrBob222 · Answer

pi = MRT
Use pi in atm; i.e., 340/760 = ?atm.
Solve for M = molarity.
Then M = mols/L soln. You know L and you know M, solve for mols.
Then mol = grams/molar mass. You know grams and mols, solve for molar mass.

b.
delta T = Kf*m
You know M, you want m.
Use density to convert volume to grams of solution, and recognize that grams soln = g solute + grams solvent. Subtract to find grams solvent, convert to kg then to m and calculate delta T.