Properties of Solutions

 

56(a) m = 0.40 m C6H12O6                      Kb(C2H5OH) = 1.22°C/m          T°f = -114.6°C

            Kf(C2H5OH) = 1.99°C/m          T°b = 78.4°C

 

            C6H12O6(s) C6H12O6(l)

            ΔTf = Kf x m x i

            ΔTf = 1.99°C/m x 0.40 m x 1 = 0.80°C

            ΔTf = T°f - Tf

            0.80°C = -114.6°C - Tf

            Tf = -115.4°C

 

            ΔTb = Kb x m x i

            ΔTb = 1.22°C/m x 0.40 m x 1 = 0.49°C

            Tb = T°b + ΔTb = 78.4°C + 0.49°C = 78.9°C

 

      (b) m1 = 20.0 g C10H22                         Kb(CHCl3) = 3.63°C/m             T°b = 61.2°C

           m2 = 455 g CHCl3                      Kf(CHCl3) = 4.68°C/m              f = -63.5°C

 

            C10H22(g) C10H22(l)

            m = nsolute/kgsolvent

            m = 20.0 g C10H22 x 1 mol C10H22/142.32 g C10H22/(455 g x 1 kg/103 g) = 0.309 m

            ΔTf = Kf x m x i

            ΔTf = 4.68°C/m x 0.309m x 1 = 1.45°C

            ΔTf = T°f - Tf

            1.45°C = -63.5°C - Tf

            Tf = -65.0°C

 

            ΔTb = Kb x m x i

            ΔTb = 3.63°C/m x 0.309m x 1 = 1.12°C

            Tb = T°b + ΔTb = 61.2°C + 1.12°C = 62.3°C

 

      (c) n1 = 0.45 mol CH2(OH)CH2(OH)                       Kb(H2O) = 0.51°C/m          T°b = 100.0°C

           n2 = 0.15 mol KBr                                           Kf(H2O) = 1.86°C/m          T°f = 0.0°C

           mwater = 150 g H2O

 

            CH2(OH)CH2(OH)(l) CH2(OH)CH2(OH)(aq)

            KBr(s) K+(aq) + Br-(aq)

            m = nsolute/kgsolvent

            m = (0.45 mol CH2(OH)CH2(OH) + 0.15 mol K+ + 0.15 mol Br-)/(150g x 1 kg/103 g) = 5.0 m

            ΔTf = Kf x m x i

            ΔTf = 1.86°C/m x 5.0 m x 1 = 9.3°C

            ΔTf = T°f - Tf

            9.3°C = 0.0°C - Tf

            Tf = -9.3°C

 

            ΔTb = Kb x m x i

            ΔTb = 0.51°C/m x 5.0 m x 1 = 2.6°C

            Tb = T°b - ΔTb = 100.0°C + 2.6°C = 102.6°C