Calculating Reaction Thermodynamics for Combustion of Methane
Copyright (c) RDMCHEM LLC 2019
Overview
Initialize
Calculate Thermodynamics of Reactants and Products
Calculate ΔS, ΔH, and ΔG
Hydrocarbon resources constitute the largest source of energy production, contributing to over 85% of the world's energy! Consider the combustion of methane:
Rxn (1)
In this activity, you will calculate the ΔHrxn, ΔGrxn, and ΔSrxn from first principles and then compare your calculated results with values determined using Hess's Law and enthalpies of formation data:
Table 1: Thermodynamic values at 298 K and 1 atm
S (J/molK)
ΔHf (kJ/mol)
ΔGf (kJ/mol)
CH4
186.16
-74.85
-50.79
O2
205.03
0
CO2
-393.52
-394.38
213.69
H2O
-241.82
-228.59
188.72
restart;withQuantumChemistry:Digits≔15:withScientificConstants:withLinearAlgebra:
You will calculate ΔS, ΔH, and ΔG for Rxn (1) using the following expression:
ΔF =∑iniFproduct,i− ∑jnjFreactant,j
where F refers to values of S, H, or G, and n refers to stoichiometric coefficients in Rxn (1). In this section, you will use the Thermodynamics function to calculate S, H, and G for each reactant and product. For each, you will need to enter the following information:
name = "methane", "oxygen", "carbondioxide", or "water" (do not use spaces between carbon and dioxide).
symm_num = 12 for methane, = 2 for oxygen, carbon dioxide, and water.
energy_method = HartreeFock, DensityFunctional, Coupled Cluster, etc.
energy_basis = "sto-3g", "6-31g", "cc-pvdz", etc.
freq_method = HartreeFock or DensityFunctional (Note, only Hartree-Fock seems to work in a timely manner)
energy_basis = "sto-3g", "6-31g", "cc-pvdz", etc. (Note, only sto-3g seems to work in a timely manner)
freq_scaling = float (0.8905 for HF, 0.9613 for DFT)
molec_name≔oxygen;
molec_name≔oxygen
molec_label≔2; # methane = 1, oxygen = 2, carbon dioxide = 3, water = 4
molec_label≔2
symm_num≔2;
symm_num≔2
energy_method≔HartreeFock;
energy_method≔HartreeFock
energy_basis≔sto-3g;
energy_basis≔sto-3g
freq_method≔HartreeFock;
freq_method≔HartreeFock
freq_basis≔sto-3g;
freq_basis≔sto-3g
frequency_scaling≔0.8905;
frequency_scaling≔0.89050000
molec_spin≔0; # zero for all but oxygen, which is a triplet so molec_spin = 1
molec_spin≔0
molec≔MolecularDatamolec_name,geometry3d;
molec≔O,−0.61600000,0,0,O,0.61600000,0,0
data≔Thermodynamicsmolec,energy_method,basis=energy_basis,symmetry_number=symm_num,freq_scaling=frequency_scaling,spin=2⋅molec_spin;
data≔tableelectronic_energy=−3.87395968108Jmol,energy=−3.87368491108Jmol,enthalpy=−3.87366013108Jmol,θC=1.99753627K,zpe=10634.27017022Jmol,free_energy=−3.87481576108Jmol,θB=1.99753627K,entropy=387.60228332JmolK,heat_capacity=20.90118890JmolK
enthalpymolec_label≔ data'enthalpy'1000.;
enthalpy2≔−387366.01251576Jmol
gibbsmolec_label≔data'free_energy'1000.;
gibbs2≔−387481.57613653Jmol
entropymolec_label≔data'entropy';
entropy2≔387.60228332JmolK
Repeat for each reactant and product before moving onto next section.
Calculate DS, DH, and DG
ΔS≔entropy3+2⋅entropy4−entropy1−2⋅entropy2;
ΔS≔entropy3+2entropy4−entropy1−775.20456663JmolK
ΔH≔enthalpy3+2⋅enthalpy4−enthalpy1−2⋅enthalpy2;
ΔH≔enthalpy3+2enthalpy4−enthalpy1+774732.02503151Jmol
ΔG≔gibbs3+2⋅gibbs4−gibbs1−2⋅gibbs2;
ΔG≔gibbs3+2gibbs4−gibbs1+774963.15227306Jmol
Compare with values determined using Hess's law and S, ΔHf, and ΔGf from Table 1:
expDH≔−393.52 +2⋅−241.82−−74.85;
expDH≔−802.31000000
expDG≔−394.38 +2⋅−228.59−−50.79;
expDG≔−800.77000000
expDS≔213.69+2⋅188.72−186.16−2⋅205.03;
expDS≔−5.09000000
entropy2
387.60228332JmolK
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