Gherman Group Meeting Thermodynamics and … · Gherman Group Meeting. Thermodynamics and Kinetics...

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Gherman Group Meeting Gherman Group Meeting Thermodynamics and Kinetics Thermodynamics and Kinetics and Applications and Applications June 25, 2009 June 25, 2009

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  • Gherman Group MeetingGherman Group Meeting

    Thermodynamics and KineticsThermodynamics and Kinetics and Applicationsand Applications

    June 25, 2009June 25, 2009

  • OutlineOutline

    Calculating HCalculating Hff, S, G, S, GffComponents which contribute to HComponents which contribute to Hff, S, G, S, GffCalculating Calculating HH, , SS, , GGCalculating rate constants for chemical reactions Calculating rate constants for chemical reactions

    Computing pKComputing pKaa valuesvaluesComputing electron affinitiesComputing electron affinitiesComputing redox potentialsComputing redox potentials

  • Part 1: ThermodynamicsPart 1: Thermodynamics

  • Calculating HCalculating Hff

    , S, G, S, GffHHff = E= ESCFSCF + ZPE + E+ ZPE + Esolvationsolvation + H+ Htranstrans + H+ Hrot rot + H+ Hvibvib + H+ Helecelec

  • Calculating HCalculating Hff

    , S, G, S, GffHHff = E= ESCFSCF + ZPE + E+ ZPE + Esolvationsolvation + H+ Htranstrans + H+ Hrot rot + H+ Hvibvib + H+ HelecelecHHff

    (0 K) = E(0 K) = ESCFSCF

    + ZPE + ZPE

  • Calculating HCalculating Hff

    , S, G, S, GffHHff = E= ESCFSCF + ZPE + E+ ZPE + Esolvationsolvation + H+ Htranstrans + H+ Hrot rot + H+ Hvibvib + H+ HelecelecHHff

    (0 K) = E(0 K) = ESCFSCF

    + ZPE + ZPE SS = S= Stranstrans + S+ Srot rot + S+ Svibvib + S+ Selecelec

  • Calculating HCalculating Hff

    , S, G, S, GffHHff = E= ESCFSCF + ZPE + E+ ZPE + Esolvationsolvation + H+ Htranstrans + H+ Hrot rot + H+ Hvibvib + H+ HelecelecHHff

    (0 K) = E(0 K) = ESCFSCF

    + ZPE + ZPE SS = S= Stranstrans + S+ Srot rot + S+ Svibvib + S+ SelecelecGGff = H= Hff -- TSTS

  • Calculating HCalculating Hff

    , S, G, S, GffHHff = E= ESCFSCF + ZPE + H+ ZPE + Htranstrans + H+ Hrot rot + H+ Hvibvib + H+ HelecelecHHff

    (0 K) = E(0 K) = ESCFSCF

    + ZPE + ZPE SS = S= Stranstrans + S+ Srot rot + S+ Svibvib + S+ SelecelecGGff = H= Hff -- TSTS

    Components of enthalpy / entropyComponents of enthalpy / entropySCF energySCF energyZeroZero--point energypoint energymolecular translationmolecular translationmolecular rotationmolecular rotationmolecular vibrationmolecular vibrationelectronicselectronics

  • Energy Components (1)Energy Components (1)

    ZeroZero--point energypoint energy

    sum of energies for lowest vibrational level for each vibrationsum of energies for lowest vibrational level for each vibrationharmonic oscillator approximationharmonic oscillator approximation

    modes 12 ii

    ZPE h=

  • Energy Components (1)Energy Components (1)

    ZeroZero--point energypoint energy

    sum of energies for lowest vibrational level for each vibrationsum of energies for lowest vibrational level for each vibrationharmonic oscillator approximationharmonic oscillator approximation

    TranslationTranslationUUtranstrans = 3/2 RT H= 3/2 RT Htranstrans = U= Utranstrans + PV = U+ PV = Utranstrans + RT = 5/2 RT+ RT = 5/2 RT

    particle in a 3particle in a 3--dimensional boxdimensional boxV in formula V in formula standard state must be definedstandard state must be defined

    standard state Pstandard state P = 1 atm (V= 1 atm (V = 24.5 L at 298 K)= 24.5 L at 298 K)

    modes 12 ii

    ZPE h=

    3/ 2

    2

    2ln 5/ 2BtransA

    Mk T VS Rh N

    = +

  • Energy Components (2)Energy Components (2)

    RotationRotationlinear moleculeslinear molecules

    2

    2

    8ln 1

    linear linearrot rot

    linear Brot

    H U RT

    Ik TS Rh

    = =

    = +

  • Energy Components (2)Energy Components (2)

    RotationRotationlinear moleculeslinear molecules

    nonnon--linear moleculeslinear molecules

    rigidrigid--rotor approximationrotor approximationI, II, IAA, I, IBB, I, ICC moments of inertiamoments of inertia symmetry numbersymmetry number

    # of rotations that carry molecule into itself# of rotations that carry molecule into itselfdepends on point group (e.g. Cdepends on point group (e.g. C11=1, C=1, C2v2v=2, T=2, Tdd=12)=12)

    2

    2

    8ln 1

    linear linearrot rot

    linear Brot

    H U RT

    Ik TS Rh

    = =

    = +

    3/ 22

    2

    32

    8 3ln2

    linear linearrot rot

    A B Clinear Brot

    H U RT

    I I I k TS Rh

    = =

    = +

  • Energy Components (3)Energy Components (3)

    VibrationVibration

    harmonic oscillatorsharmonic oscillators

    ( )

    ( ) ( )

    3 6(5)

    /1

    3 6(5)/

    /1

    1

    ln 11

    i B

    i B

    i B

    Ni

    vib vib hw k Ti B

    Nhw k Ti

    vib hw k Ti B

    hH U Rk e

    hS R ek T e

    =

    =

    = =

    =

  • Energy Components (3)Energy Components (3)

    VibrationVibration

    harmonic oscillatorsharmonic oscillators

    ElectronicElectronicHHelecelec = U= Uelecelec = 0= 0SSelecelec = R ln (2S+1)= R ln (2S+1)

    where 2S+1 is the spin multiplicitywhere 2S+1 is the spin multiplicityS = S = * # of unpaired e* # of unpaired e--

    ( )

    ( ) ( )

    3 6(5)

    /1

    3 6(5)/

    /1

    1

    ln 11

    i B

    i B

    i B

    Ni

    vib vib hw k Ti B

    Nhw k Ti

    vib hw k Ti B

    hH U Rk e

    hS R ek T e

    =

    =

    = =

    =

  • Energy Components Energy Components --

    NotesNotes

    Independent of any QM calculationIndependent of any QM calculationtranslational, electronictranslational, electronic

    Depend on geometry only:Depend on geometry only:rotational (provided an accurate geometry)rotational (provided an accurate geometry)

    Requiring an electronic structure calculationRequiring an electronic structure calculationEESCFSCFZPEZPEvibrationalvibrational

  • Calculating Calculating H, H, S, S, GG

    HHff = E= ESCFSCF + ZPE + E+ ZPE + Esolvationsolvation + H+ Htranstrans + H+ Hrot rot + H+ Hvibvib + H+ HelecelecHHff

    (0 K) = E(0 K) = ESCFSCF

    + ZPE + ZPE SS = S= Stranstrans + S+ Srot rot + S+ Svibvib + S+ SelecelecGGff = H= Hff -- TSTS

    For a chemical reaction: A + B For a chemical reaction: A + B C + DC + DHH = H= Hff(C) + H(C) + Hff(D) (D) -- HHff(A) (A) HHff(B)(B)SS = S= S(C) + S(C) + S(D) (D) -- SS(A) (A) SS(B)(B)GG = = HH -- TTSS

  • Rate ConstantsRate Constants

    Transition State TheoryTransition State Theory

    compare to Arrhenius expressioncompare to Arrhenius expression

    GB RTk Tk eh

    =

    aERTk Ae

    =

  • Part 2: Applications of ThermodynamicsPart 2: Applications of Thermodynamics

  • pKpKaa

    Calculations (1)Calculations (1)Calculate pKCalculate pKaa values using a free energy cycle (Bornvalues using a free energy cycle (Born--Haber cycle):Haber cycle):

    AH (g) A- (g) + H+ (g)

    AH (aq) A- (aq) + H+ (aq)

    Gg

    Ga

    GsolAH GsolA- GsolH+

  • pKpKaa

    Calculations (1)Calculations (1)Calculate pKCalculate pKaa values using a free energy cycle (Bornvalues using a free energy cycle (Born--Haber cycle):Haber cycle):

    AH (g) A- (g) + H+ (g)

    AH (aq) A- (aq) + H+ (aq)

    Gg

    Ga

    GsolAH GsolA- GsolH+

    ( )0.00999 @ 1 & 298

    A H AHg g g g

    Hg

    G G G G

    G hartrees P atm T K

    +

    +

    = +

    = = =

  • pKpKaa

    Calculations (1)Calculations (1)Calculate pKCalculate pKaa values using a free energy cycle (Bornvalues using a free energy cycle (Born--Haber cycle):Haber cycle):

    AH (g) A- (g) + H+ (g)

    AH (aq) A- (aq) + H+ (aq)

    Gg

    Ga

    GsolAH GsolA- GsolH+

    ( )

    ( )

    0.00999 @ 1 & 298

    264.0 / experimental value

    A H AHg g g g

    Hg

    A H AHa g sol sol sol

    Hsol

    G G G G

    G hartrees P atm T K

    G G G G G

    G kcal mol

    +

    +

    +

    +

    = +

    = = =

    = + +

    =

  • pKpKaa

    Calculations (2)Calculations (2)Calculate pKCalculate pKaa values using a free energy cycle (Bornvalues using a free energy cycle (Born--Haber cycle):Haber cycle):

    AH (g) A- (g) + H+ (g)

    AH (aq) A- (aq) + H+ (aq)

    Gg

    Ga

    GsolAH GsolA- GsolH+

    ( ) ( )/

    /log log

    a

    a

    G RTa

    G RTa a

    K e

    pK K e

    =

    = =

  • pKpKaa

    Calculations (3)Calculations (3)AccuracyAccuracy

    depends mostly upon accuracy of the solvation energy of the ionsdepends mostly upon accuracy of the solvation energy of the ions

    and upon the accuracy of and upon the accuracy of GGgg

  • pKpKaa

    Calculations (3)Calculations (3)AccuracyAccuracy

    depends mostly upon accuracy of the solvation energy of the ionsdepends mostly upon accuracy of the solvation energy of the ionsapproximately approximately 5 kcal/mol5 kcal/mol

    and upon the accuracy of and upon the accuracy of GGggapproximately approximately 5 kcal/mol5 kcal/mol

    expected accuracy of pKexpected accuracy of pKaa values approximately values approximately 5 units5 units

  • pKpKaa

    Calculations (3)Calculations (3)AccuracyAccuracy

    depends mostly upon accuracy of the solvation energy of the ionsdepends mostly upon accuracy of the solvation energy of the ionsapproximately approximately 5 kcal/mol5 kcal/mol

    and upon the accuracy of and upon the accuracy of GGggapproximately approximately 5 kcal/mol5 kcal/mol

    expected accuracy of pKexpected accuracy of pKaa values approximately values approximately 5 units5 units

    prediction of relative pKprediction of relative pKaa values can be more chemically meaningfulvalues can be more chemically meaningful

  • Electron AffinitiesElectron Affinities

    X (g) + e- (g) X- (g)Gg

    one-electron reduction in the gas phase

    X Xg g gElectron Affinity EA G G G

    = = =

  • Redox Potential Calculations (1)Redox Potential Calculations (1)Calculate redox potentials using free energy cyclesCalculate redox potentials using free energy cycles

    X (g) + e- (g) X- (g)

    Gsolo GsoloGo = 0

    X (sol) + e- (sol) X- (sol)

    Gg

    Gredox

    reduction potential

  • Redox Potential Calculations (1)Redox Potential Calculations (1)Calculate redox potentials using free energy cyclesCalculate redox potentials using free energy cycles

    X (g) + e- (g) X- (g)

    Gsolo GsoloGo = 0

    X (sol) + e- (sol) X- (sol)

    Gg

    Gredox

    X (g) X+ (g) + e- (g)

    Gsolo Gsolo Go = 0

    X (sol) X+ (sol) + e- (sol)

    Gg

    Gredox

    reduction potential oxidation potential

  • Redox Potential Calculations (1)Redox Potential Calculations (1)Calculate redox potentials using free energy cyclesCalculate redox potentials using free energy cycles

    X (g) + e- (g) X- (g)

    Gsolo GsoloGo = 0

    X (sol) + e- (sol) X- (sol)

    Gg

    Gredox

    X (g) X+ (g) + e- (g)

    Gsolo Gsolo Go = 0

    X (sol) X+ (sol) + e- (sol)

    Gg

    Gredox

    reduction potential oxidation potential

    e.g. reduction potential case

    n=number of electrons F=Faraday constant=23.060kcal/V*mol

    X Xg g g

    X Xredox g sol sol

    redox

    G G G

    G G G G

    GEnF

    =

    = +

    =

  • Redox Potential Calculations (2)Redox Potential Calculations (2)

    Redox potentials typically reported relative to a standard electRedox potentials typically reported relative to a standard electroderode

  • Redox Potential Calculations (2)Redox Potential Calculations (2)

    Redox potentials typically reported relative to a standard electRedox potentials typically reported relative to a standard electroderode

    standard hydrogen electrode (SHE)standard hydrogen electrode (SHE)HH++ (aq) + e(aq) + e-- HH22 (g)(g)reduction potentials: subtract 4.28 Vreduction potentials: subtract 4.28 Voxidation potentials: add 4.28 Voxidation potentials: add 4.28 V

  • Redox Potential Calculations (2)Redox Potential Calculations (2)

    Redox potentials typically reported relative to a standard electRedox potentials typically reported relative to a standard electroderode

    standard hydrogen electrode (SHE)standard hydrogen electrode (SHE)HH++ (aq) + e(aq) + e-- HH22 (g)(g)reduction potentials: subtract 4.28 Vreduction potentials: subtract 4.28 Voxidation potentials: add 4.28 Voxidation potentials: add 4.28 V

    other standard electrodes based upon values relative to SHEother standard electrodes based upon values relative to SHEexample: standard calomel electrode (SCE) example: standard calomel electrode (SCE)

    HgHg22

    ClCl22

    (s) + 2e(s) + 2e--

    2Hg(l) + 2Cl2Hg(l) + 2Cl--(aq) E(aq) E=+0.24 V (vs. SHE)=+0.24 V (vs. SHE)reduction potentials: subtract (4.28+0.24) Vreduction potentials: subtract (4.28+0.24) Voxidation potentials: add (4.28+0.24) Voxidation potentials: add (4.28+0.24) V

    Slide Number 1OutlinePart 1: ThermodynamicsCalculating Hf, S, GfCalculating Hf, S, GfCalculating Hf, S, GfCalculating Hf, S, GfCalculating Hf, S, GfEnergy Components (1)Energy Components (1)Energy Components (2)Energy Components (2)Energy Components (3)Energy Components (3)Energy Components - NotesCalculating H, S, GRate ConstantsPart 2: Applications of ThermodynamicspKa Calculations (1)pKa Calculations (1)pKa Calculations (1)pKa Calculations (2)pKa Calculations (3)pKa Calculations (3)pKa Calculations (3)Electron AffinitiesRedox Potential Calculations (1)Redox Potential Calculations (1)Redox Potential Calculations (1)Redox Potential Calculations (2)Redox Potential Calculations (2)Redox Potential Calculations (2)