If .455g of thyroxine is dissolved in 10g of benzene, the freezing point of the solution is 5.144 deg. C.?

Question

Pure benzene freezes at 5.444 deg C and has a value for the molal freezing point depression constant of Kf of 5.12 C/m. What is the molar mass of thyroxine?

Answer 1

Delta T = kf m

delta T = 5.444-5.144= 0.3

0.3 = 5.12 m

m = 0.3 / 5.12=0.0586

10 g= 0.001 Kg

m= moles thyroxine/ Kg benzene

0.0586 = moles/ 0.001

moles= 0.0000586

moles = g /MM = 0.455 /MM = 0.0000586

MM =0.455 / 0.0000586 = 7765 g/mol

Answer 2

ΔTf =Kf*m

m= molality = mole solute /kg solvent = 1000* mole solute / g solvent = 1000* grams solute /(MW solute*grams solvent)
so if for simplicity
g= grams solute
G= grams solvent , we have

m= 1000*g /(MW*G) and
ΔTf =Kf*1000*g / (MW*G) =>

MW = Kf*1000*g / (ΔTf*G) =>
MW = 5.12*1000*0.455 / ((5.444-5.144)*10) = 776.53