Chapter 6 : Gibbs Free Energy
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1 Wnter 01 Chem 54: ntrductry hermdynamcs Chapter 6 : Gbbs Free Energy Defntn f G, A Mawell Relatns Gbbs Free Energy G(,) (ure substances) Gbbs Free Energy fr Mtures ΔG f deal mng Chemcal Equlbrum and Equlbrum Cnstant K p emperature Dependence f K Chemcal Equlbrum: Calculatng Equlbrum Cmpstn rncple f LeChateler Use and Sgnfcance f ΔG, ΔA Chapter 6 : Gbbs Free Energy Defntn f G, A Fr sngle substances du q w Fr reversble prcess rev rev du q w du ds d (crrect relatn always) s nternal pressure f gas. du : epressed n term f functns f state,,, U, H, G, A Defne: H U A U S A arbet (wrk): Helmhltz free energy G H S U S G Gbbs free energy Dfferental frms: du ds d dh du d ds d d d ds d da du d S ds d ds Sd Sd d dg dh d S ds d ds Sd Sd d 64
2 Wnter 01 Chem 54: ntrductry hermdynamcs Fr eact dfferentals F F df d dy y y F F y y y y f true then F(, y ) ests U S H S A G S S ; ; ; ; U S H A G S U( S, ) H( S, ) A(, ) G(, ) Mawell Relatns U H A G S S S S S S 1 ; 1 Dervatns usng Mawell: du ds d ds du d 1 ds du d 1 U U ds d d d C 1 U A) ds d d Chapter 6 : Gbbs Free Energy 65
3 Wnter 01 Chem 54: ntrductry hermdynamcs B) S S ds d d S 1 U S U C S usng Mawell relatn OR U S S ds d d C ds d d C d d We have used all f these relatns wthut dervatn befre. A) B) dh ds d ds dh d dh ds d 1 H H ds d d d C 1 H ds d d S S ds d d S C S 1 H (Mawell) Chapter 6 : Gbbs Free Energy 66
4 Wnter 01 Chem 54: ntrductry hermdynamcs H C ds d d Gbbs Free Energy G(,) (ure substances) G ndependent f path, a functn f state, depends nly n, and, f f Changes n Changes n G wth dg Sd d G H S U S G Fr lquds and slds Fr (deal) gases G wth S G changes n and f G f G d d G nr f G nr ln f G f G d Sd f But S always depends n, nt cnvenent, use a trck G 1 G 1 G S 1 1 G S G H G S G 1 H Chapter 6 : Gbbs Free Energy 67
5 Wnter 01 Chem 54: ntrductry hermdynamcs f G f f G f H ( ) H d assume H( ) H( f ) (cnstant H, apprmatn) G f G 1 1 H f f G f G 1 1 H f f retend we have abslute Gbbs free energy, but n thermdynamcs ths s never the case. We always nly cnsder changes n G, H. Calculate G r, analgus t r H G f G r H r fund n tables alng wth abslute S rg r H f assumed t be cnstant (small errr) n real lfe yu need t knw (we wll d t n an eercse) G, dn t use ths frmula, use dependence f H. r Gbbs Free Energy fr Mtures We have varus speces: # f mles fr each: n1, n, n G G G dg d d dn n 1, n, n 1,, n n 1 Chapter 6 : Gbbs Free Energy 68
6 Wnter 01 Chem 54: ntrductry hermdynamcs G G dn n dn n,, n n,, n n dg Sd d dn dn dn dg Sd d dn G n,, n j n dn : the change n G when addng dn mles f speces, whle keep and, n j n cnstant. ( =chemcal ptental f speces and has unts kj/ml) Understand better fr pure substance, mlecule AG ( ), G naga, m (true because G s a functn f,, and, dn t change wth the sze f system) G na, G A, m ure substance A : mlar Gbbs free energy at partcular, A What s the physcal sgnfcance f? dg Sd dg dn dn dn d 1dn1 dn dg 1 mass balance dn dg 0 Always at cnstant, f dn 0 then 0 hases: Matter flws frm phase wth hgh chemcal ptental t phase wth lw chemcal ptental Analgy mlecules flw frm t, dn 0 Chemcal ptental strngly depends n cncentratn At equlbrum fr any speces lume changes (changng between phases) untl pressure s equal (equal ) Chapter 6 : Gbbs Free Energy 69
7 Wnter 01 Chem 54: ntrductry hermdynamcs Chemcal ptental s equal between dfferent cmpnents n a system: Fundamental prncple f chemcal equlbrum, at cnstant, Hw t calculate G fr mtures (deal mtures) deal mtures: deal gases, dlute slutn (n electrlyte), cmpnents d nt nteract substantally deal gas, pure cmpund, change f G(, f ) G(, ) nr ln nr dg d d f G nr ln G(, ) (, ) (, ) R ln n Lkewse fr an deal gas n a mture (artal ) ttal (, ) (, ) R ln ttal (, ) R ln ttal (, ) R ln R ln ttal Snce (, ) (, ) R ln (,, ) (, ) R ln ttal (,, ) (, ) R ln where (, ) s the chemcal ptental f the pure substance Chapter 6 : Gbbs Free Energy 70
8 Wnter 01 Chem 54: ntrductry hermdynamcs ΔG f deal mng G(, ) G, nr ln Fr pure substances Mtures ttal G(, ) G,, G, nr ln G, nr ln Mlar Gbbs free energy = chemcal ptental,,, (,, ), R ln G(,, ) G, nr ln G are chemcal ptentals fr pure substances (cnstant ) Eample at equlbrum H H pure m H, ln pure R H, ln m R H H pure m ln ln H H pure m tal pressure s dfferent n tw cmpartments! pure H m H ttal pure ttal m H m Ar Ar Chapter 6 : Gbbs Free Energy 71
9 Wnter 01 Chem 54: ntrductry hermdynamcs Eample m Ne G m G G n R ln G 0 ln Ne Ne Ar nne nttal Ne nar nttal Ar n R G Ar Ar Ne ln G n R ln R m ttal Ne Ne Ar Ar ln G n R ln general epressn fr mng Gm nttal R ln m ttal Ne Ne Ar Ar G Ar What s Calculate Sm? Smng 0 1; ln 0 lm ln always G m dg Sd d dn G S, n S m nr ln Sm nr ln S m 0 spntaneus drectly: f change : S nr ln at cnstant ttal ttal Sm nner ln nar R ln Nettal Arttal S n R ln ln m ttal Ne Ne Ar Ar Chapter 6 : Gbbs Free Energy 7
10 Wnter 01 Chem 54: ntrductry hermdynamcs Eample G n R ln 0 m ttal S nr ln 0 m Hm Gm Sm 0 (deal mes nly) G H S H G S G nr ln ln nr ln S n Rln ttal What abut? 1) G nr ln? ) G 0? Mlecules are ndstngushable n prncple. Gbbs parad? G 0, we knw. Gd understandng f ths nly frm Quantum Mechancs Chapter 6 : Gbbs Free Energy 7
11 Wnter 01 Chem 54: ntrductry hermdynamcs Chemcal Equlbrum and Equlbrum Cnstant K p Cnsder a generc reactn n the gas phase G r n A n B n C n D A ( g) B ( g) C ( g) D ( g) G n n n n r C C D D A A A B,, R ln G, r fr reactants; nfr prducts n rg, R ln rg, R ln rg rg R ln, pure substance at ; = prduct f all factrs, analgus t r f G G fr sums. Q Reactns Qutent: change durng a reactn, Q s an nstantaneus quantty Back t ntal reactn A B C D Q nc nd na nb C D A B Q nc C D A B nd na nb Chapter 6 : Gbbs Free Energy 74
12 Wnter 01 Chem 54: ntrductry hermdynamcs G G R lnq r r Rules: - f ntally 0 the reactn wll prceed t the rght, prduct CD, wll ncrease r G G r ncreases untl t s 0 - f ntally 0 reactn wll prceed t reactants, AB, ncreases r G At equlbrum Q Kequlbrum cnstant G G R ln K 0 r r emperature Dependence f K ln K rg R ln K 1 G 1 H R R r r f ln K f 1 r H d d R f rh f 1 ln K d R assume H s ndependent f r rh 1 1 ln K ( f ) ln K ( ) R f Eample: CO H O CO H ( g) ( l) ( g) ( g) Chapter 6 : Gbbs Free Energy 75
13 Wnter 01 Chem 54: ntrductry hermdynamcs R ln K G r n G ( CO ) n G ( H ) n G ( H O) n G ( CO) f f f f H H r f Q : gases nly, lquds and slds has lttle pressure dependence CO H CO at equlbrum Chemcal Equlbrum: Calculatng Equlbrum Cmpstn K ma A mb B mc C md D (reactants) m (prducts) m m : stchmetrc ceffcents (here) n : actual number f mles fr speces Can we calculate n fr each at chemcal equlbrum? Can we calculate r? Hw d we d t? Etent f reactn n n n beng the ntal number f mles fr mlecule Fr any value f yu get number f mles n wth mles f reactn Eample: N H NH Fr any mle f N that reacts, gan mles f NH and lse mles f H ntal # f mles has t be gven, n ths eample, we start wth mles f H, 1 mle f N and 0.1 mles f NH Chapter 6 : Gbbs Free Energy 76
14 Wnter 01 Chem 54: ntrductry hermdynamcs n n ma / mn N H mn NH mn 0.05 n.1 ttal Fr all n 0, fr all n n : (reactants) 0 ma n ma : (prducts) 0 mn n n dn d mn bunded dg Sd d dn at cnstant, dg dn d G, Fr spntaneus pssble prcess: ntally G dg G f rg,,, G r, d 0 0 Always d 0 : t the rght Chapter 6 : Gbbs Free Energy 77
15 Wnter 01 Chem 54: ntrductry hermdynamcs G f rg,, G f rg,, 0 0 d 0 : t the left chemcal equlbrum G, G r,, R ln, R ln G, R ln R ln r,, R ln, R ln G, R ln r rg, R ln G, R lnq r Q Q ; ( ) Chapter 6 : Gbbs Free Energy 78
16 Wnter 01 Chem 54: ntrductry hermdynamcs N H NH D n n 1 ttal Q Q Q NH N H Q 0 as 0.05 Q as mn mn rg, here s always precsely ne pnt at whch ln Q : chemcal equlbrum R ln Q : mathematcally ncreases between mn and ma Chapter 6 : Gbbs Free Energy 79
17 Wnter 01 Chem 54: ntrductry hermdynamcs rncple f LeChateler Easy t understand frm thermdynamcs: dln K Change n : H d R f H 0, K ncreases wth ncreasng prduct, requres heat (lwers ) f H 0, K decreases wth ncreasng reactant, requres heat (lwers ) K K K K K n gas ; K K ngas a) n gas 0 mre gas n prduct sde K decreases, reactn t the left decreases number f gas mlecules, reduces b) n gas 0, K ncreases, prducts ncreases n gas mles f gas decreases, decreases Chapter 6 : Gbbs Free Energy 80
18 Wnter 01 Chem 54: ntrductry hermdynamcs Use and Sgnfcance f ΔG, ΔA dq Clausus 0 rev q q 0 q ds 0 ds q du w du w ds 0 q rev ds Cnsder a cnstant prcess 0 ds d S ds Sd du d S w 0 d U S w A U S da w 0 w da Same reasnng fr G : epansn nn epansn nn epansn d U S w w d U S d w et cnstrant et cnstant nn epansn nn epansn d U S d w 0 d U S w 0 U S G dg w nn epansn Chapter 6 : Gbbs Free Energy 81
19 Wnter 01 Chem 54: ntrductry hermdynamcs Cmbustn f Octane: G = -596 kj/ml A = -585 kj/ml G A, s very small H = kj/ml Heat engne: heat frm burnng ctane cld ht wrk q heat H 1 w H Fuel cell: React ctane t generate electrcty nn Ma w G 0.98 H Mre effcent (knwn snce 1880!!) r 1 Chapter 6 : Gbbs Free Energy 8
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