Question

What is the molality of a solution of naphthalene in benzene if the freezing point of pure benzene is 5.5°C and the freezing point of the solution is 4.0°C. The freezing point depression constant for benzene is 5.12°C m-1.

Answer 1

Ans. Depression in freezing point of a solution is given by-

            dT_f = K_f . m . i

            where, dT = depression in freezing point

     = freezing point of pure solvent – freezing point of solution

      = 5.5⁰C – 4.0⁰C = 1.5⁰C

                        K_f = Freezing point depression constant = 5.12⁰C m^-1

                        m = molality of the solution (moles of solute / kg solution)

                        i = van’t Hoff factor = 1 for non-ionizing solutes (naphthalene)

Putting the values in the above equation-

            1.5⁰C = 5.12⁰C m^-1 x m x 1

            Or, m = 1.5⁰C / (5.12⁰C m^-1) = 0.29296875 m

Hence, molality of naphthalene (solute) in benzene (solvent) is 0.293 m