 Enthalpy - Maple Help

Enthalpy Overview Thermodynamics is the study of the transfer of energy.  The internal energy of chemical system plus the product of its pressure and volume is known as enthalpy.  In this lesson we will explore the change in enthalpy for one of the simplest combustion reactions, the combustion of carbon monoxide to form carbon dioxide. Figure 1: Combustion reaction of carbon monoxide plus oxygen to form carbon dioxide. Enthalpy

Consider the unbalanced chemical reaction

CO (g)   +     O2     CO2 (g)

(a) Balance the chemical reaction for the combustion of carbon monoxide.

The enthalpy change of the reaction ΔH at standard temperature and pressure (298 K and 1 atm) can be computed from the enthalpies of the reactants and the products, which can be computed from quantum theory.  We will compute these enthalpies using the Thermodynamics command in the Quantum Chemistry package.

First, we set the Digits to 15 and load the Quantum Chemistry package

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 $\left[{\mathrm{AOLabels}}{,}{\mathrm{ActiveSpaceCI}}{,}{\mathrm{ActiveSpaceSCF}}{,}{\mathrm{AtomicData}}{,}{\mathrm{BondAngles}}{,}{\mathrm{BondDistances}}{,}{\mathrm{Charges}}{,}{\mathrm{ChargesPlot}}{,}{\mathrm{CorrelationEnergy}}{,}{\mathrm{CoupledCluster}}{,}{\mathrm{DensityFunctional}}{,}{\mathrm{DensityPlot3D}}{,}{\mathrm{Dipole}}{,}{\mathrm{DipolePlot}}{,}{\mathrm{Energy}}{,}{\mathrm{ExcitationEnergies}}{,}{\mathrm{ExcitationSpectra}}{,}{\mathrm{ExcitationSpectraPlot}}{,}{\mathrm{ExcitedStateEnergies}}{,}{\mathrm{ExcitedStateSpins}}{,}{\mathrm{FullCI}}{,}{\mathrm{GeometryOptimization}}{,}{\mathrm{HartreeFock}}{,}{\mathrm{Interactive}}{,}{\mathrm{Isotopes}}{,}{\mathrm{MOCoefficients}}{,}{\mathrm{MODiagram}}{,}{\mathrm{MOEnergies}}{,}{\mathrm{MOIntegrals}}{,}{\mathrm{MOOccupations}}{,}{\mathrm{MOOccupationsPlot}}{,}{\mathrm{MOSymmetries}}{,}{\mathrm{MP2}}{,}{\mathrm{MolecularData}}{,}{\mathrm{MolecularGeometry}}{,}{\mathrm{NuclearEnergy}}{,}{\mathrm{NuclearGradient}}{,}{\mathrm{OscillatorStrengths}}{,}{\mathrm{Parametric2RDM}}{,}{\mathrm{PlotMolecule}}{,}{\mathrm{Populations}}{,}{\mathrm{RDM1}}{,}{\mathrm{RDM2}}{,}{\mathrm{RTM1}}{,}{\mathrm{ReadXYZ}}{,}{\mathrm{Restore}}{,}{\mathrm{Save}}{,}{\mathrm{SaveXYZ}}{,}{\mathrm{SearchBasisSets}}{,}{\mathrm{SearchFunctionals}}{,}{\mathrm{SkeletalStructure}}{,}{\mathrm{Thermodynamics}}{,}{\mathrm{TransitionDipolePlot}}{,}{\mathrm{TransitionDipoles}}{,}{\mathrm{TransitionOrbitalPlot}}{,}{\mathrm{TransitionOrbitals}}{,}{\mathrm{Variational2RDM}}{,}{\mathrm{VibrationalModeAnimation}}{,}{\mathrm{VibrationalModes}}{,}{\mathrm{Video}}\right]$ (2.1)

The enthalpies of O2 and CO2 have been precomputed in Table 1.

Table 1: Enthalpies in kJ/mol for the combustion of CO

 CO O2 CO2 H ? -3.945 x 105 kJ/mol -4.949 x 105 kJ/mol

The enthalpy of CO can be computed as follows.  First, choose an initial guess for the equilibrium bond distance, i.e. 1.1 angstroms and define the geometry.

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 ${\mathrm{mol_CO}}{≔}\left[\left[{"C"}{,}{0}{,}{0}{,}{0}\right]{,}\left[{"O"}{,}{0}{,}{0}{,}{1.10000000}\right]\right]$ (2.2)

Second, optimize the geometry of CO to find the minimum of the potential energy curve using the method density functional theory (DFT) with the default functional (B3-LYP) and the basis set cc-pVDZ.

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 $\left[\left[{"C"}{,}{0}{,}{0}{,}{0}\right]{,}\left[{"O"}{,}{7.46697480}{}{{10}}^{{-12}}{,}{1.43245335}{}{{10}}^{{-11}}{,}{1.13485718}\right]\right]$ (2.3)

(b) At what bond distance of CO does the minimum of the potential energy curve occur?  Is this distance shorter or longer than the initial guess of 1.1 angstroms?

Finally, we compute a table of thermodynamic properties for CO including the enthalpy.  By default, the command uses a temperature of 298 K.

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 ${\mathrm{thermo_CO}}{≔}{table}{}\left(\left[{\mathrm{entropy}}{=}{389.04949897}{}⟦\frac{{J}}{{\mathrm{mol}}{}{K}}⟧{,}{\mathrm{enthalpy}}{=}{-}{2.97353168}{}{{10}}^{{8}}{}⟦\frac{{J}}{{\mathrm{mol}}}⟧{,}{\mathrm{electronic_energy}}{=}{-}{2.97388047}{}{{10}}^{{8}}{}⟦\frac{{J}}{{\mathrm{mol}}}⟧{,}{{\mathrm{\theta }}}_{{B}}{=}{2.74504846}{}⟦{K}⟧{,}{\mathrm{heat_capacity}}{=}{20.81001215}{}⟦\frac{{J}}{{\mathrm{mol}}{}{K}}⟧{,}{\mathrm{zpe}}{=}{13100.56169779}{}⟦\frac{{J}}{{\mathrm{mol}}}⟧{,}{{\mathrm{\theta }}}_{{C}}{=}{2.74504846}{}⟦{K}⟧{,}{\mathrm{free_energy}}{=}{-}{2.97469163}{}{{10}}^{{8}}{}⟦\frac{{J}}{{\mathrm{mol}}}⟧{,}{\mathrm{energy}}{=}{-}{2.97355647}{}{{10}}^{{8}}{}⟦\frac{{J}}{{\mathrm{mol}}}⟧\right]\right)$ (2.4)

(c) What is the computed enthalpy of CO in kJ/mol?

We can convert the enthalpy from J/mol to kJ/mol using Maple's convert command

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 ${{H}}_{{\mathrm{CO}}}{≔}{-}{297353.16764574}{}⟦\frac{{\mathrm{kJ}}}{{\mathrm{mol}}}⟧$ (2.5)

(d) Using the enthalpy of CO in (c) and the precomputed enthalpy values in Table 1, calculate the change in enthalpy in the combustion of 1 mol of CO.

The precomputed values in Table 1 are as follows

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 ${{H}}_{{\mathrm{O2}}}{≔}{-}{394500.00000000}{}⟦\frac{{\mathrm{kJ}}}{{\mathrm{mol}}}⟧$
 ${{H}}_{{\mathrm{CO2}}}{≔}{-}{494900.00000000}{}⟦\frac{{\mathrm{kJ}}}{{\mathrm{mol}}}⟧$ (2.6)

Therefore, we can compute the change in enthalpy from

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 ${\mathrm{DeltaH}}{≔}{-}{296.83235426}{}⟦\frac{{\mathrm{kJ}}}{{\mathrm{mol}}}⟧$ (2.7)

(e) Is the reaction exothermic or endothermic?

(f) Compute the change in the enthalpy of the reaction in kJ/mol using enthalpies of formation at standard temperature and pressure (STP).

(g) Does your result in (f) agree with the quantum calculation in (d)?

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