Asolution of 0.5 g of an unknown nonvolatile, nonelectrolyte solute is added to 100 ml of water and then placed across a semipermeable membrane from a volume of pure water. when the system reaches equilibrium, the solution compartment is elevated 5.6 cm above the solvent compartment. assuming that the density of the solution is 1.0 g / ml, calculate the molecular mass of the unknown.

Explanation:

The given data is as follows.

     Height = 5.6 cm = = 0.056, density = 1.0 g/ml, g = 9.8 m/s

As it is known that pressure is equal to height times density times acceleration due to gravity.

Mathematically,          P =

Now, putting the given values as follows.

                        P =

                           =

                           = 548.8 Pa

As 1 pascal equals 101325 atm. Hence, converting the given pressure into atmosphere as follows.

                          atm

                      =

 As the effect of concentration on osmotic pressure is as follows.

                         PV = inRT

    or,                   P =

                           P = iMRT

where,       M = molarity

                  R = gas constant = 0.0821

                  T = 298 K

                  i = 1 (for non-electrolyte)

Hence, calculate the molarity as follows.

                         P = iMRT

      =    

                             =

Also,    Molarity =

        =    

                                       = 22585.6 g/mol

Thus, we can conclude that molecular mass of the unknown is 22585.6 g/mol.