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Unit 11 (Chp 5,8,19): Thermodynamics (∆H, ∆S, ∆G, K)
Chemistry, The Central Science, 10th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten Unit 11 (Chp 5,8,19): Thermodynamics (∆H, ∆S, ∆G, K) John D. Bookstaver St. Charles Community College St. Peters, MO 2006, Prentice Hall, Inc.
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Chapters 5,8: Energy (E), Heat (q), Work (w), and Enthalpy (∆H)
Chemistry, The Central Science, 10th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten Chapters 5,8: Energy (E), Heat (q), Work (w), and Enthalpy (∆H) John D. Bookstaver St. Charles Community College St. Peters, MO 2006, Prentice Hall, Inc.
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Energy (E) Enthalpy (H) (kJ) Entropy (S) (J/K) Free Energy (G) (kJ)
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Energy (E) What is it? ability to do work OR transfer heat
Work (w): transfer of energy by applying a force over a distance. (moving an object) Heat (q): transfer of energy by DT (high to low) unit of energy: joule (J) an older unit still in widespread use is… calorie (cal) 1 Cal = 1000 cal 1 cal = 4.18 J 2000 Cal ≈ 8,000,000 J ≈ 8 MJ!!!
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System and Surroundings
molecules to be studied (reactants & products) Surroundings: everything else (container, thermometer,…)
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1st Law of Thermodynamics
Energy is neither created nor destroyed. total energy of an isolated system is constant (universe) (no transfer matter/energy) (conserved) Internal Energy (E): E = KE PE (motions) (Thermal Energy) (attractions) (calculating E is too complex a problem) E = Efinal − Einitial released or absorbed
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Changes in Internal Energy
Energy is transferred between the system and surroundings, as either heat (q) or work (w). E = q + w E = ? E = (–) + (+) Surroundings E = + System q in (+) q out (–) E = q + w w on (+) w by (–)
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Changes in Internal Energy
Efinal > Einitial absorbed energy (endergonic) Efinal < Einitial released energy (exergonic)
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Work (w) The only work done by a gas at constant P is change in V by pushing on surroundings. PV = −w ΔV “–” b/c work done BY system ON surroundings Zn + H+ Zn2+ + H2(g)
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Enthalpy Enthalpy (H) is: H = E + PV H = E + PV E = q+w PV = −w
internal work done energy work done by system heat/work energy in or out of system H = E PV E = q+w PV = −w (change in) H or DH (at constant P) : H = E + PV H = (q+w) + (−w) H = q (change in) enthalpy IS heat absorbed/released H = heat
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CH4(g) + 2 O2(g) CO2(g) + 2 H2O(g)
Enthalpy of Reaction CH4(g) + 2 O2(g) CO2(g) + 2 H2O(g) enthalpy is… …the heat transfer in/out of a system (at constant P) H = E + PV H = q H = Hproducts − Hreactants exergonic exothermic endergonic endothermic
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Endothermic & Exothermic
Endothermic: H > 0 (+) H(+) = Hfinal − Hinitial products reactants Exothermic: H < 0 (–) H(–) = Hfinal − Hinitial reactants products H(–) is thermodynamically favorable
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Enthalpy of Reaction 2 H2(g) + O2(g) 2 H2O(g) Hrxn, is the enthalpy of reaction, or “heat” of reaction. units: kJ molrxn kJ/molrxn kJ∙molrxn Demo –242 kJ per 1 mol O2 (OR) H = –242 kJ/molrxn –242 kJ per 2 mol H2 Demo – Zn in narrow mouth Erlenmeyer flask. Add mL of 6 M H2SO4. Stretch out large balloon well and place over mouth. Blow some (not much) O2 into balloon and tie. (OR) –1 –121 kJ per 1 mol H2
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CH4(g) + 2 O2(g) CO2(g) + 2 H2O(g)
Enthalpy HW p. 207 #34,35,38,45 H depends on amount (moles, coefficients) Hreverse rxn = –Hforward rxn Hrxn depends on the state (s, l, g) of products & reactants H1 = –802 kJ if 2 H2O(g) because… 2 H2O(l) 2 H2O(g) H = +88 kJ/molrxn CH4(g) + 2 O2(g) CO2(g) + 2 H2O(g)
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Chp. 5,8: Calculate ∆H (4 Ways)
1) Bond Energies 2) Hess’s Law 3) Standard Heats of Formation (Hf ) 4) Calorimetry (lab)
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Overlap and Bonding E internuclear distance
When bonds/attractions form, energy is _________. released – + + – + + What repulsive forces? What attractive forces? E Where is energy being released? internuclear distance
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Potential Energy of Bonds
High PE chemical bond Low PE (energy released when bonds form) High PE (energy absorbed when bonds break) + +
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Bond Enthalpy (BE) p.330 BE: ∆H for the breaking of a bond (all +)
aka… bond dissociation energy
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Enthalpy of Reaction (∆H)
BE: ∆H for the breaking of a bond (all +) To determine H for a reaction: compare the BE of bonds broken (reactants) to the BE of bonds formed (products). Hrxn = (BEreactants) (BEproducts) (bonds broken) (bonds formed) (released) (stronger) H(+) = BEreac − BEprod (NOT on equation sheet) H(–) = BEreac − BEprod (stronger)
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Enthalpy of Reaction (∆H)
CH4(g) + Cl2(g) CH3Cl(g) + HCl(g) Hrxn = [4(C—H) + (Cl—Cl)] [3(C—H) + (C—Cl) + (H—Cl)] = (4x ) (3x ) Hrxn = 104 kJ/molrxn HW p. 339 #66, 68
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Chp. 5,8: Calculate ∆H (4 Ways)
1) Bond Energies Hrxn = (BEreactants) (BEproducts) 2) Hess’s Law 3) Standard Heats of Formation (Hf ) 4) Calorimetry (lab) (NOT given) (+ broken) (– formed)
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(NOT on equation sheet)
Hess’s Law H = Hfinal − Hinitial prod. react. Hrxn is independent of path taken Hrxn = sum of H of all steps (NOT on equation sheet) Hoverall = H1 + H2 + H3 …
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Calculation of H by Hess’s Law
C3H8(g) + 5 O2(g) 3 CO2(g) + 4 H2O(l) ∆Hcomb = ? Given: + 3 C(gr.) + 4 H2(g) C3H8(g) ∆H1= –104 kJ C(gr.) + O2(g) CO2(g) ∆H2= –394 kJ H2(g) + ½ O2(g) H2O(l) ∆H3= –286 kJ 3( ) 3( ) 4( ) 4( ) Used: C3H8(g) 3 C(gr.) + 4 H2(g) ∆H1= +104 kJ 3 C(gr.) + 3 O2(g) 3 CO2(g) ∆H2= –1182 kJ 4 H2(g) + 2 O2(g) 4 H2O(l) ∆H3= –1144 kJ ∆Hcomb = –2222 kJ C3H8(g) + 5 O2(g) 3 CO2(g) + 4 H2O(l)
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Standard Enthalpy of Formation (Hf )
heat released or absorbed by the formation of a compound from its pure elements in their natural states. o (25oC , 1 atm) o Hf = 0 for all elements in natural state 3 C(gr.) + 4 H2(g) C3H8(g) ∆Hf = –104 kJ o o o Hf = 0 Hf = 0 Hf = –104 kJ H = Hfinal − Hinitial Recall… …therefore ---> prod. react.
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Calculation of H by Hf’s
…we can use Hess’s law in this way: H = nHf(products) – nHf(reactants) n (mol) is the stoichiometric coefficient. “sum” (on equation sheet)
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Calculation of H by Hf’s
C3H8(g) + 5 O2(g) 3 CO2(g) + 4 H2O(l) ∆Hcomb = ? H = nHf(products) – nHf(reactants) Appendix C (p ) H = [3(Hf CO2) + 4(Hf H2O)] – [1(Hf C3H8) + 5(Hf O2)] H = (3 ∙ – ∙ –285.83) – (– ∙ 0) H = (–2323.7) – (–103.85) H = – kJ HW p. 209 #60,63,66, 72,73
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Chp. 5,8: Calculate ∆H (4 Ways)
1) Bond Energies Hrxn = (BEreactants) (BEproducts) 2) Hess’s Law Hoverall = Hrxn1 + Hrxn2 + Hrxn3 … 3) Standard Heats of Formation (Hf ) H = nHf(products) – nHf(reactants) 4) Calorimetry (lab) (NOT given) (+ broken) (– formed) (NOT given) (given)
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Calorimeter nearly isolated
Calorimetry We can’t know the exact enthalpy of reactants and products, so we calculate H by calorimetry, the measurement of heat flow. By reacting (in solution) in a calorimeter, we indirectly determine H of system by measuring ∆T & calculating q of the surroundings (calorimeter). Calorimeter nearly isolated (on equation sheet) heat (J) q = mcT mass (g) [of sol’n] Tf – Ti (oC) [of surroundings]
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Specific Heat Capacity (c)
(or specific heat) energy required to raise temp of 1 g by 1C. (for water) c = 4.18 J/goC J of heat Metals have much lower c’s b/c they transfer heat and change temp easily.
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Calorimetry q = mcT – q = Hrxn in J of surroundings (thermometer)
HW p. 208 #49, 52, 54 in J of surroundings q = mcT (thermometer) – q = Hrxn (in kJ/mol) of system When 4.50 g NaOH(s) is dissolved 200. g of water in a calorimeter, the temp. changes from 22.4oC to 28.3oC. Calculate the molar heat of solution, ∆Hsoln (in kJ/mol NaOH). q = ( )(4.18)(28.3–22.4) qsurr = 5040 J H = –5.04 kJ mol Hsys = –5.04 kJ 4.50 g NaOH x 1 mol = mol NaOH 40.00 g = –44.8 kJ mol
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Chp. 5,8: Calculate ∆H (4 Ways)
1) Bond Energies Hrxn = (BEreactants) (BEproducts) 2) Hess’s Law Hoverall = Hrxn1 + Hrxn2 + Hrxn3 … 3) Standard Heats of Formation (Hf ) H = nHf(products) – nHf(reactants) 4) Calorimetry (lab) q = mc∆T (surroundings or thermometer) –q = ∆H ∆H/mol = kJ/mol (molar enthalpy) (NOT given) (+ broken) (– formed) (NOT given) (given) (given)
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Chapter 19: Thermodynamics (∆H, ∆S, ∆G, K)
Chemistry, The Central Science, 10th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten Chapter 19: Thermodynamics (∆H, ∆S, ∆G, K) John D. Bookstaver St. Charles Community College St. Peters, MO 2006, Prentice Hall, Inc.
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Energy (E) Enthalpy (H) (kJ) Entropy (S) (J/K) Free Energy (G) (kJ)
ΔH = ΔE + PΔV internal work by energy system (KE + PE) (–w) ΔE = q + w PΔV = –w (at constant P) ΔH = q (heat) ΔH = ? ΔS = ? ΔG = ?
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Big Idea #5: Thermodynamics
Bonds break and form to lower free energy (∆G). Chemical and physical processes are driven by: a decrease in enthalpy (–∆H), or an increase in entropy (+∆S), or both.
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1st Law of Thermodynamics
Energy cannot be created nor destroyed (is conserved) or…total energy of the universe is constant. Hsystem = –Hsurroundings OR Huniv = Hsystem + Hsurroundings = 0 if (+) then (–) = 0 if (–) then (+) = 0
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Thermodynamically Favorable
Thermodynamically Favorable (spontaneous) processes occur with no outside intervention. If Favorable in one direction, then UNfavorable in reverse.
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Thermodynamically Favorable
Processes that are favorable (spontaneous) at one temperature… …may not be at other temperatures. HW p. 837 #7, 11 melting freezing
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Entropy (S) S = Sfinal Sinitial (okay but oversimplified)
disorder/randomness (more correct) dispersal of matter & energy among various motions of particles in space at a temperature in J/K. “The energy of the universe is constant.” “The entropy of the universe tends toward a maximum.” (ratio of heat to temp) S = ∆H T S = Sfinal Sinitial S = + therm fav S = – therm UNfav (more dispersal) (less dispersal) (structure/organization)
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Entropy (S) S = ∆H T change in entropy (S) depends on…
height AND weight (a part) S = ∆H T (the rest) change in entropy (S) depends on… …heat (∆H)…AND…temp. (T) same ∆H diff. ∆S System A (100 K) 50 J System B (25 K) 50 J Surroundings (100 K) Visualize a 1 ft tall dog. Now, that dog is a 100 lb. dachshund! Surroundings (25 K) ∆S = ____J/K +0.5 ∆S = ____J/K +2.0 (loud restaurant, less disturbed) (quiet library, more disturbed) Cough!
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Entropy Example: melting 1 mol of ice at 0oC. Shand = ?
Hhand = –6000 J 6000 J Hice = J Sice = ?
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Entropy S = ∆H T +Hice = –Hhand Huniv = 0 Suniv = +
+Sice > –Shand The melting of 1 mol of ice at 0oC. Hfusion T (1 mol)(6000 J/mol) 273 K Sice = = = +22.0 J/K (gained by ice) Assume the ice melted in your hand at 37oC. Hfusion T (1 mol)(–6000 J/mol) 310 K Shand = = = –19.4 J/K (lost by hand) Suniv = Ssystem + Ssurroundings Suniv = (22.0 J/K) + (–19.4 J/K) = (ice) (hand) Suniv +2.6 J/K
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Universe (isolated system)
1st Law: J = J Huniv = 0 Suniv = + 2nd Law: +22 J/K > –19 J/K 5290 J (usable E) (usable E) 6000 J + (dispersed E) 710 J (in hand) (in ice) +2.6 J/K x 273 K = (∆Suniv) (T) Universe (isolated system) Initial Energy “dispersed” energy (unusable) Free energy (useful for work) Final Energy
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2nd Law of Thermodynamics
Suniv = Ssystem + Ssurroundings For thermodynamically favorable (spontaneous) processes… … +∆S gained always greater than –∆S lost, so… Suniv = Ssystem + Ssurroundings > 0 2nd Law of Thermodynamics (formally stated): All favorable processes increase the entropy of the universe (Suniv > 0) HW p. 837 #20, 21
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Entropy (Molecular Scale)
Ludwig Boltzmann described entropy with molecular motion. Motion: Translational , Vibrational, Rotational He envisioned the molecular motions of a sample of matter at a single instant in time (like a snapshot) called a microstate.
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Entropy (Molecular Scale)
S = k lnW Boltzmann constant 1.38 1023 J/K microstates (max number possible) Entropy increases (+∆S) with the number of microstates in the system. < < <
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Entropy (Molecular Scale)
S : dispersal of matter & energy at T The number of microstates and, therefore, the entropy tends to increase with… ↑Temperature (motion as KEavg) ↑Volume (motion in space) ↑Particle number (motion as KEtotal) ↑Particle Size (motion of bond vibrations) ↑Particle Type (mixing)
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Entropy (Molecular Scale)
S : dispersal of matter & energy at T Maxwell-Boltzmann distribution curve: ∆S > 0 by adding heat as… …distribution of KEavg increases (T)
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Entropy (Molecular Scale)
S : dispersal of matter & energy at T Entropy increases with the freedom of motion. S(s) < S(l) < S(g) S(s) < S(l) < S(aq) < S(g) gas solid T more microstates (s) + (l) (aq) V H2O(g) H2O(g)
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Standard Entropy (So) Standard entropies tend to increase with increasing molecular size. larger molecules have more microstates
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Entropy Changes (S) In general, entropy increases when
liquids or solutions form from solids moles of gas increases total moles increase Predict the sign of S in these reactions: 1. Pb(s) + 2 HI(aq) PbI2(s) + H2(g) 2. NH3(g) + H2O(l) NH4OH(aq) S = + S = –
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3rd Law of Thermodynamics
The entropy of a pure crystalline substance at absolute zero is 0. (not possible) S = k lnW S = k ln(1) S = 0 increase Temp. only 1 microstate 0 K S = 0 > 0 K S > 0
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Standard Entropy Changes (∆So)
HW p. 838 #29, 31, 40, 42, 48 Standard entropies, S. (Appendix C) So = nSo(products) – nSo(reactants) (on equation sheet) n (mol) is the stoichiometric coefficient.
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dispersal of matter & energy at T
Energy (E) Enthalpy (H) (kJ) Entropy (S) (J/K) Free Energy (G) (kJ) ΔH = ΔE + PΔV internal work by energy system (KE + PE) (–w) (disorder) microstates dispersal of matter & energy at T ΔE = q + w PΔV = –w (at constant P) ∆Suniv = + ΔH = q (heat) ΔS = ΔH T ΔS = ? ΔG = ?
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Big Idea #5: Thermodynamics
Bonds break and form to lower free energy (∆G). Chemical and physical processes are driven by: a decrease in enthalpy (–∆H), or an increase in entropy (+∆S), or both.
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Thermodynamically Favorable
Chemical and physical processes are driven by: decrease in enthalpy (–∆Hsys) increase in entropy (+∆Ssys) causes (+∆Ssurr) (+) (+) Suniv = Ssystem + Ssurroundings > 0 Thermodynamically Favorable: (defined as) increasing entropy of the universe (∆Suniv > 0) ∆Suniv > 0 (+Entropy Change of the Universe)
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(∆Suniv) ↔ (∆Gsys) Hsystem
For all thermodynamically favorable reactions: Suniverse = Ssystem + Ssurroundings > 0 (Boltzmann) Hsystem T Suniverse = Ssystem + (Clausius) multiplying each term by T: –TSuniverse = –TSsystem + Hsystem rearrange terms: –TSuniverse = Hsystem – TSsystem Gsystem = Hsystem – TSsystem (Gibbs free energy equation)
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(∆Suniv) & (∆Gsys) –TSuniv = Hsys – TSsys Gsys = Hsys – TSsys
(Gibbs free energy equation) Gibbs defined TDSuniv as the change in free energy of a system (Gsys) or G. Free Energy (G) is more useful than Suniv b/c all terms focus on the system. If –Gsys , then +Suniverse . Therefore… –G is thermodynamically favorable. “Bonds break & form to lower free energy (∆G).”
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(not react to completion)
Gibbs Free Energy (∆G) ∆G : free energy transfer of system as work –∆G : work done by system (–w) favorably +∆G : work done on system (+w) to cause rxn (not react to completion) +DG –DG
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Q & ∆G (not ∆Go) [P] R P Q = [R] Q < K Q > K +DG –DG –DG Q = K
–DG (release), therm. fav. +G (absorb), not therm. fav. DG = 0, system at equilibrium. (Q = K) (not react to completion) can cause with electricity/light Q > K +DG –DG –DG Q = K Gmin 0 DG = 0 DGo (1 M, 1 atm) Q = 1 = K (rare)
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Standard Free Energy (∆Go) and Temperature (T)
(on equation sheet) (consists of 2 terms) DG = DH – TS free energy (kJ/mol) enthalpy term (kJ/mol) entropy term (J/mol∙K) units convert to kJ!!! max energy used for work energy transferred as heat energy dispersed as disorder The temperature dependence of free energy comes from the entropy term (–TS).
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Standard Free Energy (∆Go) and Temperature (T)
DG = DH TS Thermodynamic Favorability ∆Go = (∆Ho) ∆So – T( ) ( ) –T( ) (high T) – (low T) + (fav. at high T) (unfav. at low T) + + = ( ) – T ( ) + + – (unfav. at ALL T) + = ( ) – T( ) + (fav. at ALL T) – = ( ) – T( ) – + (high T) + (low T) – ( ) –T( ) (unfav. at high T) (fav. at low T) – – = ( ) – T ( ) – –
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+ = Energy (E) Enthalpy (H) (kJ) Entropy (S) (J/K)
Free Energy (G) (kJ) ΔH = ΔE + PΔV internal work by energy system (KE + PE) (–w) (disorder) microstates –T∆Suniv as: ΔHsys & ΔSsys at T dispersal of matter & energy at T max work done by favorable rxn ΔE = q + w PΔV = –w (at constant P) ∆Suniv = + ΔH = q (heat) ΔS = ΔH T ΔG = ΔH – TΔS ΔG = ? sys sys –T∆Suniv
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Calculating ∆Go (4 ways)
Standard free energies of formation, Gf : Gibbs Free Energy equation: From K value (next few slides) From voltage, Eo (next Unit) DG = SnG(products) – SnG(reactants) f (given equation) HW p. 840 #52, 54, 60 DG = DH – TS (given equation) (may need to calc. ∆Ho & ∆So first) (given equation) (given equation)
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Free Energy (∆G) & Equilibrium (K)
Under any conditions, standard or nonstandard, the free energy change can be found by: G = G + RT lnQ Q = [P] [R] RT is “thermal energy” RT = ( kJ)(298) = 2.5 kJ at 25oC At equilibrium: Q = K G = 0 therefore: 0 = G + RT lnK rearrange: G = –RT lnK
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Free Energy (∆G) & Equilibrium (K)
G = –RT ln K (on equation sheet) If G in kJ, then R in kJ……… R = J∙mol–1∙K–1 = kJ∙mol–1∙K–1 –∆Go RT = ln K –∆Go RT Solved for K : (NOT on equation sheet) K = e^
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Free Energy (∆G) & Equilibrium (K)
G = –RT ln K ∆Go = –RT(ln K) K @ Equilibrium – + = –RT ( ) > 1 product favored (favorable forward) + – = –RT ( ) < 1 reactant favored (unfavorable forward)
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+ = Energy (E) Enthalpy (H) (kJ) Entropy (S) (J/K)
Free Energy (G) (kJ) ΔH = ΔE + PΔV internal work by energy system (KE + PE) (–w) (disorder) microstates –T∆Suniv as: ΔHsys & ΔSsys at a T dispersal of matter & energy at T max work done by favorable rxn ΔE = q + w PΔV = –w (at constant P) K > 1 means –∆Gsys & +∆Suniv ∆Suniv = + ΔH = q (heat) ΔS = ΔH T ΔG = ΔH – TΔS sys sys –T∆Suniv
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p. 837 #6 What does x quantify? ΔGo What is significant at this point?
G of Reactants What does x quantify? ΔGo What is significant at this point? G of Products ΔG = 0 (at equilibrium)
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p. 837 #4 In what T range is this favorable? What happens at 300 K?
ΔG = ΔH – TΔS T > 300 K ΔH = TΔS so… ΔG = ΔH – TΔS ΔG = 0 (at equilibrium) HW p. 841 #62, 63, 76
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∆Go & Rxn Coupling Rxn Coupling:
Unfav. rxns (+∆Go) combine with Fav. rxns (–∆Go) to make a Fav. overall (–∆Gooverall ). goes up if coupled (zinc ore) (zinc metal) (NOT therm.fav.) ZnS(s) Zn(s) + S(s) ∆Go = +198 kJ/mol S(s) + O2(g) SO2(g) ∆Go = –300 kJ/mol ZnS(s) + O2(g) Zn(s) + SO2(g) ∆Go = –102 kJ/mol (therm.fav.)
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∆Go & Biochemical Rxn Coupling
(weak bond broken, stronger bonds formed) ATP ADP ATP + H2O ADP + H3PO4 ∆Go = –31 kJ/mol Alanine + Glycine Alanylglycine ∆Go = +29 kJ/mol (amino acids) (peptide/proteins) ATP + H2O + Ala + Gly ADP + H3PO4 + Alanylglycine ∆Go = –2 kJ/mol
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∆Go & Biochemical Rxn Coupling
Overall Rxn: Glu + Pi Glu-6-P ATP ADP + Pi Glu + ATP Glu-6-P + ADP +14 (not fav) –31 (fav) –17 (fav) Overall Reaction: 1st of 10 steps of Glycolysis is phosphorylation of glucose at C-6 (ends with ATP production). ∆Govr ∆Govr = ∆G1 + ∆G2
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∆Go & Biochemical Rxn Coupling
Glucose (C6H12O6) ATP Proteins + O2 (oxidation) Free Energy (G) –∆G (fav) +∆G (not fav) –∆G (fav) +∆G (not fav) ADP CO2 + H2O Amino Acids
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Thermodynamic vs Kinetic Control
Kinetic Control: (path 2: A C ) A thermodynamically favored process (–ΔGo) with no measurable product or rate while not at equilibrium, must have a very high Ea . A B ∆Go = +10 Ea = +20 (kinetic product) (initially pure reactant A) path 1 (low Ea , Temp , time) B A A C ∆Go = –50 Ea = +50 (thermodynamic product) Free Energy (G) +10 kJ path 2 –50 kJ C (–∆Go, Temp, Q<<K, time)
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Thermodynamic vs Kinetic Control
Thermodynamic Product: ___ E Kinetic Product: ___ D Rxn A E will be under ______________ control at low temp and Q > K . kinetic (high Ea) Pain
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