Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities

Transcription

1 Chemstry 163 Itroducto to Multcompoet Systems ad Partal Molar Quattes 1 the problem of partal mmolar quattes mx: 10 moles ethaol C H 5 OH (580 ml) wth 1 mole water H O (18 ml) get (580+18)=598 ml of soluto? o oly 594 ml for pure H O V HO T 98, P 1 bar, 0 V HO 18 ml but 10 mol V HO T 98, P 1 bar, ml 1

2 partal molar quattes (systems of varable composto) system of 1 moles substace 1, moles substace, Ω some extesve property of system (volume, free eergy, etc) total T, P, j partal molar Ω for compoet cotrbuto of substace to property Ω at T, P whe other compoets preset at cocetratos j molar Ω presece of other speces 3 sldes 4-7 are take from: apparetly o loger avalable ste from: Stephe. Cooke, Ph.D. Departmet of Chemstry Uversty of orth Texas 4 4

3 PRTIL MOLR QUTITIES I a system that cotas at least two substaces, the total value of ay extesve property of the system s the sum of the cotrbuto of each substace to that property. The cotrbuto of oe mole of a substace to the volume of a mxture s called the partal molar volume of that compoet. V f t costat T ad p V dv p, T,,... d V d... V V p, T, 5 5 PRTIL MOLR VOLUME dd of to mxture Very Large Mxture of ad V Composto remas essetally uchaged. I ths case: V p, T, ca be cosdered costat ad the volume chage of the mxture s V. Lkewse for addto of. The total chage volume s V + V. (Composto s essetally uchaged). Scoop out of the reservor a sample cotag of ad of ts volume s V + V. ecause V s a state fucto: V V V

4 PRTIL MOLR VOLUME Illustrato: What s the chage volume of addg 1 mol of water to a large volume of water? The chage volume s 18cm 3 V V H O H O p, T 18cm 3 dfferet aswer s obtaed f we add 1 mol of water to a large volume of ethaol. The chage volume s 14cm 3 V V H O H O p, T, (CH 3CH OH) 14cm PRTIL MOLR QUTITIES V s ot geerally a costat; t s a fucto of composto: 8 8 4

5 Gbbs-Duhem (later) X V V HO XHO T, P, HO T, P, HO 9 partal molar quattes bology 10 5

6 partal molar factods #1 total dfferetals 1. state fucto dfferetals for systems of varable composto (stll d wother =0) U U( S, V, 1,..., ) du TdS PdV d 1 SV,, j H H( S, P, 1,..., ) dh TdS VdP d 1 S, P, j ( T, V, 1,..., ) d SdT PdV d 1 TV,, j G GT (, P, 1,..., ) dgsdtvdp d 1 T, P, j 11 partal molar factods # the chemcal potetal. The partal molar Gbbs free eergy, the chemcal potetal, plays a cetral role G G T, P, j thus dg SdT VdP d 1 ad a very cute dervato gve ( see hadout): G H U T, P, j T, V, j S, P, j S, V, j ote: for,h,u these are OT partal molar quattes, H, ad U 1 6

7 factod #3: propertes of a system are sum of partal molar propertes 3. extesve property of a mult-compoet system s the sum of partal molar cotrbutos from each of the compoets V V V V total G 1 1 H H H H ote: H etc. G T, P, j S, P, j 13 factod #4: relatoshps amog partal molar quattes 4. Relatoshps amog thermodyamc quattes derved for oe-compoet systems ofte hold for partal molar quattes examples : G H TS G H TS or H U PV H U PV [proof class for G; studets do smlar proof for H] 14 7

8 factod #5: Gbbs Duhem 5. The Gbbs-Duhem relatoshp shows that partal molar quattes for substaces a mxture ca ot vary depedetly example: V for a two compoet mxture e.g. + H O X HO V V X X T, P, T, P, V V HO X T, P, T, P, H H O O [ote : the varato s wth respect to oe of the compoets ( both deomators)] [dervato doe class] 15 Gbbs-Duhem (slope of partal molar volume vs mole fracto) V X HO V HO X T, P, HO T, P, HO VHO X V X T, P, HO T, P, H H O O X 0 X + - HO

9 Ed of Lecture