Question

Physical chemistry

. The osmotic of an aqueous solution at 351 K is 94 kPa and a density of 1,152 g/mL. Calculate the freezing point (in C) of the solution. The Kf for water is 1.86oC/m.

Answer 1

Answer – Given, osmotic pressure = 94 kPa , density = 1.152 g/mL , T = 351 K , Kf = 1.86^oC/m

First we need to calculate the concentration

We know

Osmotic pressure, π = MRT

So, M is molar concentration

So, M =   π / RT

We need the Osmotic pressure, π in atm

So, 1 kPa = 0.00986 atm

So, 94 kPa = ?

= 0.928 atm

So, M = 0.928 atm / 0.0821 L.atm.mol^-1.mol^-1* 351 K

          = 0.0322 M

We know, 0.0322 M means 0.0322 moles / L

So solution = 1.0 L = 1000 mL

So mass of solvent = 1000.0 mL * 1.152 g/mL

                               = 1152 g

                               = 1.152 kg

So molality = 0.0322 moles / 1.152 kg

                    = 0.0279 m

So, ∆Tf = Kf *m

             = 1.86^oC/m * 0.0279 m

             = 0.052^oC

So, Freezing point = 0.0^oC – 0.052^oC

                              = - 0.052^oC