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

Transcription

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

2 Outline Calculating H f, S, G f Components which contribute to H f, S, G f Calculating ΔH, ΔS, ΔG Calculating rate constants for chemical reactions Computing pk a values Computing electron affinities Computing redox potentials

3 Part 1: Thermodynamics

4 Calculating H f, S, G f H f = E SCF + ZPE + E solvation + H trans + H rot + H vib + H elec

5 Calculating H f, S, G f H f = E SCF + ZPE + E solvation + H trans + H rot + H vib + H elec H f (0 K) = E SCF + ZPE

6 Calculating H f, S, G f H f = E SCF + ZPE + E solvation + H trans + H rot + H vib + H elec H f (0 K) = E SCF + ZPE S = S trans + S rot + S vib + S elec

7 Calculating H f, S, G f H f = E SCF + ZPE + E solvation + H trans + H rot + H vib + H elec H f (0 K) = E SCF + ZPE S = S trans + S rot + S vib + S elec G f = H f - TS

8 Calculating H f, S, G f H f = E SCF + ZPE + H trans + H rot + H vib + H elec H f (0 K) = E SCF + ZPE S = S trans + S rot + S vib + S elec G f = H f - TS Components of enthalpy / entropy SCF energy Zero-point energy molecular translation molecular rotation molecular vibration electronics

9 Zero-point energy Energy Components (1) modes 1 ZPE= hωi 2 sum of energies for lowest vibrational level for each vibration harmonic oscillator approximation i

10 Zero-point energy Energy Components (1) modes 1 ZPE= hωi 2 sum of energies for lowest vibrational level for each vibration harmonic oscillator approximation i Translation U trans = 3/2 RT H trans = U trans + PV = U trans + RT = 5/2 RT S trans 3/2 2π MkBT V = R ln + 5/ 2 2 h NA particle in a 3-dimensional 3 box V in formula standard state must be defined standard state P P = 1 atm (V = 24.5 L at 298 K)

11 Rotation linear molecules linear rot linear rot Energy Components (2) H = U = RT S linear rot 2 8π IkBT = R ln σ h

12 Rotation linear molecules linear rot linear rot Energy Components (2) H = U = RT S linear rot 2 8π IkBT = R ln σ h non-linear molecules linear linear 3 Hrot = Urot = RT 2 2 3/2 linear π IAIBIC 8π kt B 3 Srot = R ln 2 + σ h 2 rigid-rotor rotor approximation I, I A, I B, I C moments of inertia σ symmetry number # of rotations that carry molecule into itself depends on point group (e.g. C 1 =1, C 2v =2, T d =12)

13 Energy Components (3) Vibration 3N 6(5) i vib = vib = hw k T i= 1 kb H U R harmonic oscillators hω i / B ( e 1) 3N 6(5) hωi Svib = R ln 1 e hwi / kbt i= 1 kt B ( e 1) hwi / kbt ( )

14 Energy Components (3) Vibration 3N 6(5) i vib = vib = hw k T i= 1 kb H U R harmonic oscillators hω i / B ( e 1) 3N 6(5) hωi Svib = R ln 1 e hwi / kbt i= 1 kt B ( e 1) hwi / kbt ( ) Electronic H elec = U elec = 0 elec = R ln (2S+1) S elec where 2S+1 is the spin multiplicity S = ½ * # of unpaired e -

15 Energy Components - Notes Independent of any QM calculation translational, electronic Depend on geometry only: rotational (provided an accurate geometry) Requiring an electronic structure calculation E SCF ZPE vibrational

16 Calculating ΔH, ΔS, ΔG H f = E SCF + ZPE + E solvation + H trans + H rot + H vib + H elec H f (0 K) = E SCF + ZPE S = S trans + S rot + S vib + S elec G f = H f - TS For a chemical reaction: A + B C + D ΔH = H f (C) + H f (D) - H f (A) H f (B) ΔS = S (C) S + S (D) S - S (A) S (B) ΔG = ΔH - TΔS

17 Transition State Theory Rate Constants k = kt B h e ΔG RT compare to Arrhenius expression E a k Ae RT =

18 Part 2: Applications of Thermodynamics

19 pk a Calculations (1) Calculate pk a values using a free energy cycle (Born-Haber cycle): AH (g) ΔG g A - (g) + H + (g) AH A- H+ AH (aq) ΔG a A - (aq) + H + (aq)

20 pk a Calculations (1) Calculate pk a values using a free energy cycle (Born-Haber cycle): AH (g) ΔG g A - (g) + H + (g) AH A- H+ AH (aq) ΔG a A - (aq) + H + (aq) Δ G =Δ G +ΔG ΔG A H AH g g g g ( ) H Δ G = P = 1 atm & T = 298K g + +

21 pk a Calculations (1) Calculate pk a values using a free energy cycle (Born-Haber cycle): AH (g) ΔG g A - (g) + H + (g) AH A- H+ AH (aq) ΔG a A - (aq) + H + (aq) Δ G =Δ G +ΔG ΔG A H AH g g g g ( ) H Δ G = P = 1 atm & T = 298K g Δ G =Δ G +Δ G +ΔG ΔG A H AH a g sol sol sol ( ) H Δ G = kcal/ mol experimental value sol

22 pk a Calculations (2) Calculate pk a values using a free energy cycle (Born-Haber cycle): AH (g) ΔG g A - (g) + H + (g) AH A- H+ AH (aq) ΔG a A - (aq) + H + (aq) K a = ΔG a / RT ( ) ( ΔG / log ) a RT a pk = log K = e a e

23 pk a Calculations (3) Accuracy depends mostly upon accuracy of the solvation energy of the ions and upon the accuracy of ΔG g

24 pk a Calculations (3) Accuracy depends mostly upon accuracy of the solvation energy of the ions approximately ±5 5 kcal/mol and upon the accuracy of ΔG g approximately ±5 5 kcal/mol expected accuracy of pk a values approximately ±5 5 units

25 pk a Calculations (3) Accuracy depends mostly upon accuracy of the solvation energy of the ions approximately ±5 5 kcal/mol and upon the accuracy of ΔG g approximately ±5 5 kcal/mol expected accuracy of pk a values approximately ±5 5 units prediction of relative pk a values can be more chemically meaningful

26 Electron Affinities ΔG X(g) + e - g (g) X - (g) one-electron reduction in the gas phase Electron Affinity = EA = Δ G =ΔG ΔG X X g g g

27 Redox Potential Calculations (1) Calculate redox potentials using free energy cycles X (g) + e - (g) ΔG g X - (g) o ΔG o = 0 o X (sol) + e - (sol) ΔG redox X - (sol) reduction potential

28 Redox Potential Calculations (1) Calculate redox potentials using free energy cycles X (g) + e - (g) ΔG g X - (g) X (g) ΔG g X + (g) + e - (g) o ΔG o = 0 o o o ΔG o = 0 X (sol) + e - (sol) ΔG redox X - (sol) X (sol) ΔG redox X + (sol) + e - (sol) reduction potential oxidation potential

29 Redox Potential Calculations (1) Calculate redox potentials using free energy cycles X (g) + e - (g) ΔG g X - (g) X (g) ΔG g X + (g) + e - (g) o ΔG o = 0 o o o ΔG o = 0 X (sol) + e - (sol) ΔG redox X - (sol) X (sol) ΔG redox X + (sol) + e - (sol) reduction potential oxidation potential e.g. reduction potential case Δ G =ΔG ΔG X X g g g Δ G =Δ G +ΔG ΔG E X X redox g sol sol ΔG = nf redox n=number of electrons F=Faraday constant=23.060kcal/v*mol

30 Redox Potential Calculations (2) Redox potentials typically reported relative to a standard electrode rode

31 Redox Potential Calculations (2) Redox potentials typically reported relative to a standard electrode rode standard hydrogen electrode (SHE) H + (aq) + e - ½ H 2 (g) reduction potentials: subtract 4.28 V oxidation potentials: add 4.28 V

32 Redox Potential Calculations (2) Redox potentials typically reported relative to a standard electrode rode standard hydrogen electrode (SHE) H + (aq) + e - ½ H 2 (g) reduction potentials: subtract 4.28 V oxidation potentials: add 4.28 V other standard electrodes based upon values relative to SHE example: standard calomel electrode (SCE) Hg 2 Cl 2 (s) + 2e - 2Hg(l) + 2Cl - (aq) E =+0.24 E V (vs. SHE) reduction potentials: subtract ( ) V oxidation potentials: add ( ) V