Question

A tau protein is being studied. It is believed to have a mass between 55,000 and 62,000 g/mol. You have been given the task of determining its actual molecular mass. If you assume a mass of 58,500 g/mol, and were to dissolve 5.00mg in 1.00mL water, calculate the freezing point depression, boiling point elevation, the vapor pressure change (from 23.76 Torr at 25C), the osmotic pressure, and the height of a column of water corresponding to this osmotic pressure. Which method would you use to experimentally determine the molecular mass of this polymer. Why?

Answer 1

moles = mass / molar mass = 5 mg / 58500 = 5 x 10^-3 / 58500 = 8.55 x10^-8

mass of solvent water = density x volume = 1 x 1 = 1 g = 10^-3 kg

molality   = moles / mass of solvent

             = 8.55 x10^-8 / 10^-3

           = 8.55 x10^-5 m

freezing point depression   (delta Tf) = Kf x m = 1.86 x 8.55 x10^-5 = 1.59 x 10^-4 oC

T0 -Tf= 0.000159

0 - 0.000159 = Tf

Tf = - 0.000159 oC

water freezing point decreases to -0.000159 oC

boiling point elevation = Kb x m

                                    = 0.52 x 8.55 x10^-5

                                  = 0.0000445 oC

Tb - To = 0.0000445 oC

Tb = 100 + 0.0000445

Tb = 100.0000445 oC

boiling point increases from 100 to 100.0000445oc

Ps -Po / Po = (5x 10^-3 / 58,500) x 18 / 1

                  = 1.54 x 10^-6

Ps -23.76 / 23.76 = 1.54 x 10^-6

Ps = 23.76003655

vapour pressure change = 23.76003655 torr