SANDARD fr hemcal Rxns prducts G p G reactants r But, we d NO knw G!!! rrect, but nt applcable! prducts G f G reactants f f (element) 0 f standard Gbbs free energy f frmatn Free Energy Prblems: 5. Prf. Zv. Kren 0.07.00
G prducts p NON-Standard nsder the : G reactants r cg aa + bb c + dd dg But, accrdng t Lews: D ag G A G bg B Rna G Rna d G D Rna a G A Rna b G B Rna c D A B cg dgd aga bgb R cna dna D ana A bna B c d a a D RnQ Q Reactn Qutent. Recall: a a b sl/lq a A a B Reactn Istherm At equlbrum at cnst. & P, G = 0: eq But G = f() nly, Q eq = f() nly. S, f =cnst., then Q eq =cnst.: Q eq K a And ths, flks, s hw the hermdynamc Equlbrum nstant, K a, was Brn! a RnQ, etc. RnK (a unfyng eqn.) Nte: K a G S H Fr gases: a =f K a = K f (= K P, fr deal gases). f 0 bar/atm, f,p n bar/atm Fr slutns: a M K a K M Free Energy Prblems: 0, 8, 9. Prf. Zv. Kren 0.07.00
Krchhff-ype Equatns fr Gustav Rbert Krchhff 84 (Köngsberg, Prussa; nw Kalnngrad, Russa) 887 (Berln, Germany) f() ΔS ΔH Accrdng t ΔS : Frm: G p Gr prducts reactants d dg p dgr Sprducts ( Sreactants) d prducts d reactants d d ΔSd I ΔS d ΔSd Accrdng t ΔH : ΔS d d d ΔH d ΔH d d I ΔH http://www-grups.dcs.stand.ac.uk/~hstry/mathematcans/krchhff.html d ΔH d Gbbs-Helmhltz Equatn: Free Energy Prblems: 6 9, 6 3. [(G/)/] P = H/ 3 Prf. Zv. Kren 0.07.00 &
Bent Paul Emle lapeyrn 799 864 (Pars) http://www-grups.dcs.st-and.ac.uk/~hstry/mathematcans/lapeyrn.html http://www.annales.rg/archves/x/clapeyrn.html 4 Prf. Zv. Kren 0.07.00
Henr Lus le hateler 850 (Pars) 936 (Mrbel-les-Echelles) http://en.wkpeda.rg/wk/image:lechateler.jpg 5 Prf. Zv. Kren 0.07.00
G fr Physcal ransfrmatns equlbrum A (phase ) A (phase ), [P, ]: G = 0 Recall: Stresses: dp d d(g) = 0 Le hateler s Prncple A (phase ) new A (phase ), [P+dP, +d]: G = 0 equlbrum dp d Recall: dg = VdP Sd (fr a pure substance) d(g) = (V)dP (S)d (fr a prcess) Here: 0 = (V)dP (S)d S V H V dp d H V lapeyrn Equatn alculatns wth lapeyrn Eqn. (fr prmarly sl lq equlbra): H H H () dp d (P P ) n fr cnst. V V V () P - P - dp d H V H V Ntes fr bth methds: Watch the unts!!! V d 6 Prf. Zv. Kren 0.07.00
Phase Dagram & lapeyrn dp d H V Slpe f each curve can be explaned by lapeyrn s eqn. Als, nte Le hateler s Prncple n peratn P fusn curve meltng pnt curve freezng pnt curve S L H O crtcal pnt vaprzatn curve blng pnt curve lqud vapr-pressure curve sublmatn curve sld vapr-pressure curve trple pnt V,G 7 Prf. Zv. Kren 0.07.00
Vapr-Phase Physcal Equlbra sublmatn (s v) & vaprzatn (l v) (Recall: he ntegrated lapeyrn eqn s best suted fr nn-vapr equlbra) Frm lapeyrn: Integratns: P n P np R R dp d dnp d H V ΔH R sub. vap. V P vapr pressure f sld/lqud H H d d f f [H] [H] V v V s/ lausus-lapeyrn Eqn. H R H R I (see prevus curves) lnp V v R/P @ P = atm, = nb. y-ntercept = I = H/R nb (fr [H]) slpe = H/R P vs. s nt as nterestng as lnp vs. / / 8 Prf. Zv. Kren 0.07.00
Phase ranstns fr a Pure Substance n Lght f G Fr a pure substance: chemcal ptental G (Recall: Gravtatnal (r alttudnal) ptental, electrc ptental, etc.) Snce G < 0 fr a spntaneus prcess, the phase wth the lwest G (r ) at a specfed s the mst stable ne at that. When =, phases and are n cal equlbrum. [P] Effect f P () n vs. (NO fr water) Shft f due t ncrease n P: (/P) = V (mpare wth P vs. phase dagram) Nte: bp >> mp sld stable lqud stable gas stable mp bp ( s nt necessarly lnear) Slpes: (/) P = S: S g >> S l > S s (cntnued) 9 Prf. Zv. Kren 0.07.00 mp ld mp new bp ld bp new
(fr water) Effect f P () n vs. Shft f due t ncrease n P: (/P) = V (mpare wth P vs. phase dagram) Nte: bp >> mp mp new mp ld bp ld bp new 0 Prf. Zv. Kren 0.07.00
he hemcal Ptental Recall: Gravtatnal (r alttudnal) ptental, electrc ptental, etc. Fr OPEN Systems (fnally) (cmpstns may vary) nsder a Mxture: G = G(P,,n,n, ) G G G G dg dp d dn dn P,n P,n n n Defne: μ G n P,,n j n P,,n n P,,n n hemcal Ptental f substance n a mxture: expresses hw G f the system changes as substance s added (r remved) frm the system. dg VdP Sd μ dn Fundamental Equatn f hemcal hermdynamcs Free Energy Prblems: 3 53. Prf. Zv. Kren 0.07.00