Properties of Solutions

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

            K_f(C₂H₅OH) = 1.99°C/m          T°_b = 78.4°C

            C₆H₁₂O₆(s) C₆H₁₂O₆(l)

            ΔT_f = K_f x m x i

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

            ΔT_f = T°_f - T_f

            0.80°C = -114.6°C - T_f

            T_f = -115.4°C

            ΔT_b = K_b x m x i

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

            T_b = T°_b + ΔT_b = 78.4°C + 0.49°C = 78.9°C

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

           m₂ = 455 g CHCl₃                      K_f(CHCl₃) = 4.68°C/m              T°_f = -63.5°C

            C₁₀H₂₂(g) C₁₀H₂₂(l)

            m = n_solute/kg_solvent

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

            ΔT_f = K_f x m x i

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

            ΔT_f = T°_f - T_f

            1.45°C = -63.5°C - T_f

            T_f = -65.0°C

            ΔT_b = K_b x m x i

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

            T_b = T°_b + ΔT_b = 61.2°C + 1.12°C = 62.3°C

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

           n₂ = 0.15 mol KBr                                           K_f(H₂O) = 1.86°C/m          T°_f = 0.0°C

           m_water = 150 g H₂O

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

            KBr(s) K⁺(aq) + Br^-(aq)

            m = n_solute/kg_solvent

            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

            ΔT_f = K_f x m x i

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

            ΔT_f = T°_f - T_f

            9.3°C = 0.0°C - T_f

            T_f = -9.3°C

            ΔT_b = K_b x m x i

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

            T_b = T°_b - ΔT_b = 100.0°C + 2.6°C = 102.6°C