Excess Enthalpy and Excess Gibbs Free Energy
for Benzene/n-Heptane, Benzene/n-Nonane 
and Benzene/n-Dodecane at 298.15K
Author's Data: Housam BINOUS
Department of Chemical Engineering
National Institute of Applied Sciences and Technology
Tunis, TUNISIA
Email: binoushousam@yahoo.com

Reference: Binary interaction parameters were taken from DISTIL by Hyprotech Ltd.

Off[General::"spell1"]

The Wilson model is used to compute the activity coefficients.

Off[General::"spell1"]

A12 = V2/V1 Exp[-d1/(Rcal T)]; 
    A21 = V1/V2 Exp[-d2/(Rcal T)];

Rcal = 1.987; Rjoul = 8.314;

γ1[x_, T_] := 
      Exp[-Log[
              x + A12 (1 - x)] + (1 - 
                x) (A12/(x + A12 (1 - x)) - 
                A21/(A21 x + 1 - x))]

γ2[x_, T_] := 
      Exp[-Log[
              1 - x + A21 (x)] + (x) (A21/(1 - x + 
                      A21 (x)) - 
                A12/(A12 (1 - x) + x))]

Excess Enthalpy and excess Gibbs free energy.

GEX[x_] := 
      Rjoul T Log[γ1[x, T]] x + 
        Rjoul T Log[γ2[x, T]] (1 - x)

HEX[x_] := -T^2 D[GEX[x]/T, {T, 1}]

HEX2[x_] := -Rjoul T^2 x D[Log[γ1[x, T]], {T, 1}] - 
        Rjoul T^2 (1 - x) D[Log[γ2[x, T]], {T, 1}]

Benzene/n-heptane mixture at 298.15K

V1 = 89.4; V2 = 147.5;

d1 = 162.9398; d2 = 213.87930;

plt1 = 
      Plot[GEX[x] /. T -> 298.15, {x, 0, 1}, 
        PlotStyle -> {Thickness[0.01], Hue[0.1]}, 
        DisplayFunction -> Identity, Frame ->  True]

plt2 = 
      Plot[HEX[x] /. T -> 298.15, {x, 0, 1}, 
        PlotStyle -> {Thickness[0.01], Hue[0.1]}, 
        DisplayFunction -> Identity, Frame ->  True]

plt2b = 
      Plot[HEX2[x] /. T -> 298.15, {x, 0, 1}, 
        PlotStyle -> {Thickness[0.01], Hue[0.5]}, 
        DisplayFunction -> Identity, Frame ->  True]

Show[plt2, plt2b, 
      DisplayFunction ->  $DisplayFunction]

Benzene/n-Nonane mixture at 298.15K

V1 = 89.4; V2 = 178.6;

d1 = 167.941629; d2 = 267.059890;

plt3 = 
      Plot[GEX[x] /. T -> 298.15, {x, 0, 1}, 
        PlotStyle -> {Thickness[0.01], Hue[0.2]}, 
        DisplayFunction -> Identity, Frame ->  True]

plt4 = 
      Plot[HEX[x] /. T -> 298.15, {x, 0, 1}, 
        PlotStyle -> {Thickness[0.01], Hue[0.2]}, 
        DisplayFunction -> Identity, Frame ->  True]

Benzene/n-dodecane mixture at 298.15K

V1 = 89.4; V2 = 228.6;

d1 = 161.7481816; d2 = 313.18543;

plt5 = 
      Plot[GEX[x] /. T -> 298.15, {x, 0, 1}, 
        PlotStyle -> {Thickness[0.01], Hue[0.3]}, 
        DisplayFunction -> Identity, Frame ->  True]

plt6 = 
      Plot[HEX[x] /. T -> 298.15, {x, 0, 1}, 
        PlotStyle -> {Thickness[0.01], Hue[0.3]}, 
        DisplayFunction -> Identity, Frame ->  True]

Excess Gibbs free energy at 298.15K

Show[plt1, plt3, plt5, 
      DisplayFunction ->  $DisplayFunction]

Excess Enthalpy at 298.15 K

Show[plt2, plt4, plt6, 
      DisplayFunction ->  $DisplayFunction]