Gibbs Energy of Formation of Ethanol - Maple Help

Gibbs Energy of Formation of Ethanol

Introduction

This application will calculate the Gibbs energy of formation of ethanol (C2H5OH) at any temperature, employing thermodynamic data from the ThermophysicalData[Chemicals] package. The results are compared with values from the literature (at various temperatures)

This chemical reaction describes how ethanol is formed from carbon, hydrogen and oxygen (in their stable states).

2 C (gr) + 3 H2 (g) + 0.5 O2 (g) → C2H5OH (g)

Literature values of the Gibbs energy of formation are normally only tabulated at standard temperature, or for a small number of temperatures. However, the ThermophysicalData:-Chemicals package contains temperature-dependent curve fits for enthalpy and entropy. This means that Maple will help you calculate the Gibbs energy of formation of ethanol at any temperature (assuming that the enthalpy and entropy are within the bounds of the fitted data).

Reference:  CRC Handbook of Chemistry and Physics, 94th Edition, 5-49, Haynes, William M.

 > restart: with(ThermophysicalData:-Chemicals): with(plots):

Thermodynamic Data

Enthalpies at temperature T

 > h_C2H5OH := Property("Hmolar", "C2H5OH(g)", "temperature" = T): h_C      := Property("Hmolar", "C(gr)",     "temperature" = T): h_O2     := Property("Hmolar", "O2(g)",     "temperature" = T): h_H2     := Property("Hmolar", "H2(g)",     "temperature" = T):

Entropies at temperature T

 > s_C2H5OH := Property("Smolar", "C2H5OH(g)", "temperature" = T): s_C      := Property("Smolar", "C(gr)",     "temperature" = T): s_O2     := Property("Smolar", "O2(g)",     "temperature" = T): s_H2     := Property("Smolar", "H2(g)",     "temperature" = T):

Gibbs Energy of Formation of C2H5OH

Change in enthalpy at temperature T

 > DeltaH := h_C2H5OH - (2*h_C + 3*h_H2 + 0.5*h_O2):

Change in entropy at an arbitrary temperature T

 > DeltaS := s_C2H5OH - (2*s_C + 3*s_H2 + 0.5*s_O2):

Hence the Gibbs energy of formation at temperature T

 > DeltaG := DeltaH - DeltaS*T
 ${-}\left({\mathrm{Property}}{}\left({"Smolar"}{,}{"C2H5OH\left(g\right)"}{,}{"temperature"}{=}{T}\right){-}{2}{}{\mathrm{Property}}{}\left({"Smolar"}{,}{"C\left(gr\right)"}{,}{"temperature"}{=}{T}\right){-}{3}{}{\mathrm{Property}}{}\left({"Smolar"}{,}{"H2\left(g\right)"}{,}{"temperature"}{=}{T}\right){-}{0.5}{}{\mathrm{Property}}{}\left({"Smolar"}{,}{"O2\left(g\right)"}{,}{"temperature"}{=}{T}\right)\right){}{T}{+}{\mathrm{Property}}{}\left({"Hmolar"}{,}{"C2H5OH\left(g\right)"}{,}{"temperature"}{=}{T}\right){-}{2}{}{\mathrm{Property}}{}\left({"Hmolar"}{,}{"C\left(gr\right)"}{,}{"temperature"}{=}{T}\right){-}{3}{}{\mathrm{Property}}{}\left({"Hmolar"}{,}{"H2\left(g\right)"}{,}{"temperature"}{=}{T}\right){-}{0.5}{}{\mathrm{Property}}{}\left({"Hmolar"}{,}{"O2\left(g\right)"}{,}{"temperature"}{=}{T}\right)$ (3.1)

Hence at 300 K, the Gibbs energy of formation is

 > eval(DeltaG, T = 300 * Unit(K))
 ${-}{167.3017990}{}⟦\frac{{\mathrm{kJ}}}{{\mathrm{mol}}}⟧$ (3.2)

Comparison with Literature Data

This list contains values for the Gibbs Energy of Formation of C2H5OH  from the CRC Handbook of Chemistry and Physics. The first column is temperature (in K), the second is the Gibbs Energy of Formation (in kJ/mol)

 > data:= [[298.15, -167.874],  [300,    -167.458],  [400,    -144.216],  [500,    -119.82 ],  [600,    -94.672 ],  [700,    -69.023 ],  [800,    -43.038 ],  [900,    -16.825 ],  [1000,    9.539  ],  [1100,    36     ],  [1200,    62.52  ],  [1300,    89.07  ],  [1400,    115.63 ],  [1500,    142.185]]:

We will now plot the literature values against those calculated by Maple

 > CRC_data   := plot(data, style = point, symbol = solidcircle, legend = "Data from CRC Handbook"): maple_data := plot(DeltaG/1000, T = 298.15...1500, legend = "Calculated from ThermophysicalData:-Chemicals"):

 > display(CRC_data, maple_data, title = "Gibbs Energy of Formation of Ethanol", labels = ["Temperature (K)","Gibbs Energy of Formation (kJ/mol)"], labeldirections = [horizontal, vertical], titlefont = [Arial, 15], labelfont = [Arial], axesfont=  [Arial], size = [800, 400], legendstyle = [font = [Arial]])