Chemstry 163B Free Energy and Equlbrum E&R ( ch 6) 1
ΔG reacton and equlbrum (frst pass) 1. ΔG < spontaneous ( natural, rreversble) ΔG = equlbrum (reversble) ΔG > spontaneous n reverse drecton. ΔG = ΔHΔS here ΔG ΔG reacton 3. ΔGº all reactants and products n standard states 4. Gf Gf Appendx A at 98.15K (reacton where reactants are elements n ther most stable form and n ther standard states, =1 atm, [conc]=1m, etc) G ( ) ( ) f O g G f C gr 5. G H S reacton f G H S reacton reacton reacton NOE n -1 Appendx A: G H n kj mol BU S n J K 1 : mol 1 f and f
goals of lecture 6. Bref hello to thermodynamcs of multcomponent systems (n s vary) 7. ΔG reacton for non-standard state concentratons, pressures ΔG reacton = ΔGº reacton + R ln 8. K eq and ΔGº reacton 9. ΔG reacton = ΔGº reacton + R ln s extensve 1. Varaton of K eq wth 3
6. molar free energy and partal molar free energy (chemcal potental) NO N O 4 multcomponent mxture n moles NO ; NO n moles N O NO 4 4 G (,, n, n ) NO N O mxture NO N O 4 4 G G G G dg d d dn dn n n NO, n, n, n, n NO,, n n,, n NO NO4 NO NO4 N O N 4 4 4 NO N O NO G NO NO mxture 4 = partal molar Gbbs free energy n NO,, nno 4 or chemcal potental more generally G (,, n,..., n ) mxture dg d d dn Sd Vd dn N N G G G, n, n 1 n,, n 1 j 1 N 4
6. molar free energy and partal molar free energy (chemcal potental) NO N O 4 multcomponent mxture n moles NO ; NO n moles N O NO 4 4 NO G NO NO mxture 4 = partal molar Gbbs free energy n NO,, nno 4 or chemcal potental G molar Gbbs free energy of pure NO G G NO NO f NO molar Gbbs free energy of NO n envronment where other molecules are prese nt NO thermodynamcs of multcomponent systems E&R secton 6.4 (later) 5
G for now G reacton G reacton G G reacton reacton 6
7. ΔG reacton as a functon of pressure, concentraton 7. How does ΔG reacton (Δμ) vary as the concentraton of reactants and products vares? example : 'concentraton' of gas = partal pressure X where X total G dg Sd Vd V s mole fracton of speces for deal gas: total n total n V R V R 7
7. ΔG reacton as a functon of concentraton G V for deal gas total n total n V R V R G V G R G G 1bar d Vd d ' ' ' ' ' 1 bar 1 bar 1 bar G G 1bar R ln 1 bar 8
7. ΔG reacton as a functon of concentraton (deal gas) G G 1bar R ln 1 bar G G R ln 1 bar G G R ln 1 bar later R ln 1 bar 9
7. ΔG reacton as a functon of concentraton G G R ln 1 bar G G reacton Greacton G R ln Greacton G R ln 1 bar 1 bar Greacton Greacton R ln 1 bar R ln R ln R ln 1 bar 1 bar 1 bar for 'persnckety' unts notaton R R mol J K mol 1 1 [ ] [ untless] 1
7. ΔG reacton as a functon of concentraton reacton quotent G G R ln reacton reacton n q q q prod 1 bar n r 1 bar r rreact 1 bar s UNILESS 1 bar s, sd t state for n a A +n b B n c C +n d D for solutes n soln HW6 prob 39 c a n n n C D 1 bar 1 bar A B 1 bar 1 bar c [ C] [ D] [] 1 M 1 M a 1M [ A] [ B] 1 M 1 M C C n n n d B n 'lke' an equlbrum constant n d b s UNILESS 1 M s std state for solute 11
7. and unts (persncketyness) G G R ln reacton reacton reacton quotent C 1 bar [] 1M s UNILESS Greacton Greacton R ln 1 bar Greacton Greacton 1 mol R ln 1 mol 1 bar 1 mol Greacton Greacton 1 mol R ln 1 bar Greacton Greacton R ln 1 bar untless exponent 1 R1 mol R J K 1
7. ΔG reacton as a functon of concentraton G G R ln reacton reacton [] C 1 bar 1 M evaluates ΔG for ANY set of pressures, concentratons ΔGº gves free energy change for standard condtons, R ln corrects ΔG for actual s and [conc s] at equlbrum ΔG=? 13
8. ΔG reacton at equlbrum at equlbrum ΔG= G reacton eq G reacton R ln at gven constant K eq R ln eq G R ln K eq Keq e G R eq G G R ln reacton reacton [] C 1 bar 1 M G G R ln any concentratons for eq reacton K eq for reacton that satsfy equlbrum concentratons G reacton R ln K eq 14
9. ΔG reacton = ΔGº + R ln s extensve ΔG 1 ΔG n a A + n b B n c C + n d D n a A + n b B n c C + n d D ΔG?=? ΔG 1 n n n n C D C D 1 bar 1 bar 1 bar 1 bar c d c A B A B 1 bar 1 bar 1 bar 1 bar 1 n n n n a b a b 1 d G G R ln 1 1 1 G G R ln G G R ln G R ln 1 1 1 G G 1 1 15
1. varaton of K eq wth (ΔG rxn ), reacton carred out sothermally a Vary : (ΔG rxn ) 1, vs (ΔG rxn ), Need G Grxn and 16
1. varaton of K eq wth dg Sd Vd G S but remember S() a few manpulatons whch lead to smpler fnal relatonshps G G R ln G R ln K rxn rxn rxn G G G R ln R ln K G 1 G G eq eq 17
18 1. varaton of K eq wth 1 G G G S G G H S S G H G
1. varaton of K eq wth G H G Rln K ln K H R ln K H R 19
1. varaton of K eq wth ln K H R ln K 1 H d ln K d R 1 1 H 1 1 H 1 1 ln K R R K H 1 1 ln K R 1 1 1 1
1. varaton of K eq wth K H 1 1 ln K R 1 1 1 endothermc, H ln K K 1 K K 1 hgher moves equlbrum to rght (products) reactants + heat products K exothermc H ln K K 1 K 1 hgher moves equlbrum to left (reactants) reactants products + heat Le Chateler's rncple for heat 1
goals of lecture 6. Bref hello to thermodynamcs of multcomponent systems (n s vary) 7. ΔG reacton for non-standard state concentratons, pressures ΔG reacton = ΔGº reacton + R ln 8. K eq and ΔGº reacton 9. ΔG reacton = ΔGº reacton + R ln s extensve 1. Varaton of K eq wth
End of Lecture 3