a for save as PDF Chemstry 163B Introducton to Multcomponent Systems and Partal Molar Quanttes 1
the problem of partal mmolar quanttes mx: 10 moles ethanol C 2 H 5 OH (580 ml) wth 1 mole water H 2 O (18 ml) get (580+18)=598 ml of soluton? no only 594 ml for pure H 2 O V n HO 2 T 298, P 1 bar, n 0 V HO 2 18 ml but n 10 mol V n HO 2 T 298, P 1 bar, n 10 14 ml 2
partal molar quanttes (systems of varable composton) system of n 1 moles substance 1, n 2 moles substance 2, Ω some extensve property of system (volume, free energy, etc) total n T, P, n jn partal molar Ω for component contrbuton of substance to property Ω at T, P when other components present at concentratons n j molar Ω n presence of other speces 3
sldes 4-7 are taken from: http://www.chem.unt.edu/faculty/cooke/3510/3510_chap7.ppt apparently no longer avalable ste from: Stephen. Cooke, Ph.D. Department of Chemstry Unversty of orth Texas 4 4
PRTIL MOLR QUTITIES In a system that contans at least two substances, the total value of any extensve property of the system s the sum of the contrbuton of each substance to that property. The contrbuton of one mole of a substance to the volume of a mxture s called the partal molar volume of that component. V f t constant T and p V dv n p, T, n, n B... dn V n B dn B... V V n p, T, n 5 5
PRTIL MOLR VOLUME dd n of to mxture Very Large Mxture of and B V Composton remans essentally unchanged. In ths case: V n p, T, n can be consdered constant and the volume change of the mxture s n V. Lkewse for addton of B. The total change n volume s n V + n B V B. (Composton s essentally unchanged). Scoop out of the reservor a sample contanng n of and n B of B ts volume s n V + n B V B. Because V s a state functon: V V n V B n B... 6 6
PRTIL MOLR VOLUME Illustraton: What s the change n volume of addng 1 mol of water to a large volume of water? The change n volume s 18cm 3 V V H O 2 nh 2O p, T 18cm 3 dfferent answer s obtaned f we add 1 mol of water to a large volume of ethanol. The change n volume s 14cm 3 V V H O 2 nh 2O p, T, n(ch CH OH) 3 2 14cm 3 7 7
PRTIL MOLR QUTITIES V s not generally a constant; t s a functon of composton: 8 8
Gbbs-Duhem (later) X V V HO 2 XH2O n n T, P, n T, P, n H2O H2O http://www.chem.unt.edu/faculty/cooke/3510/3510_chap7.ppt 9
partal molar quanttes n bology 10
partal molar factods #1 total dfferentals 1. state functon dfferentals for systems of varable composton (stll d wother =0) U U( S, V, n1,..., n) du TdS PdV dn n 1 1 S, V, n n H H( S, P, n1,..., n) dh TdS VdP dn n 1 S, P, n n ( T, V, n1,..., n) d SdT PdV dn n G( T, P, n,..., n ) dg SdT VdP 1 T, V, n n G n 1 T, P, n jn j j j dn 11
partal molar factods #2 the chemcal potental 2. The partal molar Gbbs free energy, the chemcal potental, plays a central role G G n T, P, n jn thus dg SdT VdP dn 1 and a very cute dervaton gve ( see handout) : G H U n n n n T, P, n n T, V, n n S, P, n n S, V, n n j j j j note: for,h,u these are OT partal molar quanttes, H, and U 12
factod #3: propertes of a system are sum of partal molar propertes 3. n extensve property of a mult-component system s the sum of partal molar contrbutons from each of the components V nv nv n V total G 1 1 2 2 H H H n H note : H etc. n G n n T, P, n n S, P, n n j j 13
factod #4: relatonshps among partal molar quanttes 4. Relatonshps among thermodynamc quanttes derved for one-component systems often hold for partal molar quanttes examples : G H TS G H TS or H U PV H U PV [proof n class for G; students do smlar proof for H] 14
factod #5: Gbbs Duhem 5. The Gbbs-Duhem relatonshp shows that partal molar quanttes for substances n a mxture can not vary ndependently X H O 2 X V V X B B nb n T, P, n B T, P, n VHO V 2 X n n T, P, n T, P, n H2O [note : the varaton s wth respect to one of the components ( n n both denomnators)] H2O [dervaton done n class] 15
Gbbs-Duhem (slope of partal molar volume vs mole fracton) V X H2O VH 2O n X n T, P, n T, P, n H2O H2O VHO X 2 V n X n T P n H O T, P, n,, 2 H H 2O 2O + X 0 X 2 - HO 0 http://www.chem.unt.edu/faculty/cooke/3510/3510_chap7.ppt 16
End of Lecture 17 17