Chemstry 163B 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 HO T 98, P 1 bar, 0 HO 18 ml but 10 mol HO T 98, P 1 bar, 10 14 ml
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: http://www.chem.ut.edu/faculty/cooke/3510/3510_chap7.ppt apparetly o loger avalable ste from: Stephe. Cooke, Ph.D. Departmet of Chemstry Uversty of orth Texas 4 4
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. f t costat T ad p d p, T,, B... d B d B... p, T, 5 5
PRTIL MOLR OLUME dd of to mxture ery Large Mxture of ad B Composto remas essetally uchaged. I ths case: p, T, ca be cosdered costat ad the volume chage of the mxture s. Lkewse for addto of B. The total chage volume s + B B. (Composto s essetally uchaged). Scoop out of the reservor a sample cotag of ad B of B ts volume s + B B. Because s a state fucto: B B... 6 6
PRTIL MOLR OLUME Illustrato: What s the chage volume of addg 1 mol of water to a large volume of water? The chage volume s 18cm 3 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 H O H O p, T, (CH 3 CH OH) 14cm 3 7 7
PRTIL MOLR QUTITIES s ot geerally a costat; t s a fucto of composto: 8 8
Gbbs-Duhem (later) X HO XHO T, P, T, P, HO HO http://www.chem.ut.edu/faculty/cooke/3510/3510_chap7.ppt 9
partal molar quattes bology 10
partal molar factods #1 total dfferetals 1. state fucto dfferetals for systems of varable composto (stll d wother =0) U U( S,, 1,..., ) du TdS Pd d 1 1 S,, H H( S, P, 1,..., ) dh TdS dp d 1 S, P, ( T,, 1,..., ) d SdT Pd d G( T, P,,..., ) dg SdT dp 1 T,, G 1 T, P, j j j j d 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 dp d 1 ad a very cute dervato gve ( see hadout) : G H U T, P, T,, S, P, S,, j j j j ote: for,h,u these are OT partal molar quattes, H, ad U 1
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 total G 1 1 H H ote : H etc. G H T, P, S, P, H j 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 P H U P [proof class for G; studets do smlar proof for H] 14
factod #5: Gbbs Duhem 5. The Gbbs-Duhem relatoshp shows that partal molar quattes for substaces a mxture ca ot vary depedetly X H O X HO B B B T, P, B T, P, T, P, T, P, HO X [ote : the varato s wth respect to oe of the compoets X ( both deomators)] HO [dervato doe class] 15
Gbbs-Duhem (slope of partal molar volume vs mole fracto) X H O H O X T, P, T, P, HO HO X HO X T P H O T, P,,, H H O O + X 0 - X HO 0 http://www.chem.ut.edu/faculty/cooke/3510/3510_chap7.ppt 16
Ed of Lecture 17 17