Partial Molar Properties of solutions

Transcription

1 Paral Molar Properes of soluos A soluo s a homogeeous mxure; ha s, a soluo s a oephase sysem wh more ha oe compoe. A homogeeous mxures of wo or more compoes he gas, lqud or sold phase The properes of a soluo are o addve properes, meas volume of soluo s o he sum of pure compoes volume. Whe a subsace becomes a par of a soluo looses s dey bu sll corbues o he propery of he soluo. The relaoshps for pure compoe are o applcable o soluos. Whch eeds modfcao because of he chage hermodyamc properes of soluo.

2 A mole of compoe a parcular soluo a specfed emperaure ad pressure has go a se of properes assocaed wh lke. V, H, U, S... ec These properes are parally resposble for he properes of soluo ad s kow as paral molar propery The PMP of a parcular compoe a mxure measures he corbuo of ha compoe o he mxure propery. The paral molar value expresses how ha propery (volume, pressure, ehalpy, eropy) depeds o chages amou of oe compoe

3 I s defed as M = Paral molar propery of compoe. M = Toal value of ay exesve hermodyamc propery of he soluo = Toal umber moles a soluo =Number of moles of compoe he soluo j P T j P T M M M,,,, Iesve propery, value depeds oly o he composo a he gve Temp ad Pressure 3

4 Physcal Sgfcace of Paral Molar Properes To udersad he physcal meag of molar properes, cosder a ope beaker coag huge volume of waer, f oe mole of waer s added o, he volume crease s 8x 0-6 m 3. If he same amou of waer s added o pure ehaol he volume creased was approxmaely 4 x 0-6 m 3. V cm Ths s he paral molar volume of H O pure ehaol. V (ehaol) cm V (H O) cm Addo of 50.0 cm 3 of waer o 50.0 cm 3 of ehaol a 0 o C ad am gves a soluo of 96.5 cm 3. 4

5 The Paral molar propery chages wh composo. The ermolecular forces also chages Resuls chage hermodyamc propery. V w V w V = Paral molar volume of he waer ehaol waer soluo = Molar volume of pure waer a same emperaure ad pressure =Toal volume of soluo whe waer added o ehaol waer mxure ad allowed for suffce me so ha he emperaure remas cosa 5

6 The paral molar volumes of he compoes of a mxure vary wh he composo of he mxure, because he evrome of he molecules he mxure chages wh he composo. I s he chagg molecular evrome (ad he coseque alerao of he eracos bewee molecules) ha resuls he hermodyamc properes of a mxure chagg as s composo s alered 6

7 Paral molar properes ad properes of he soluo Le M be he molar propery of a soluo, ( may be Volume free eergy, hea capacy he oal propery of he soluo M M 3,,3 represes umber of cosues Thermodyamc propery s a f T,P,,, 3 j 7

8 For small chage he pressure ad emperaure ad amou of varous cosues ca be wre as P T p T p T d M d M dt T M dp P M dm j,,,,,,, 3 3,,,,... T M f T P j 8

9 A cosa emperaure ad pressure dp ad dt are equal o zero. The above equao reduces o dm M P.T, j d dm Md 9

10 dm Md M s a esve propery depeds o composo ad relave amou of cosues. All cosue properes a cosa emperaure ad pressure are added o gve he propery of he soluo dm Md M d M 3d3 dm Mx M x M 3 x3 x mole fraco of compoe he soluo d d x d d x d 0

11 dm Mx M x M 3 x3 d Iegrag yelds M Mx M x M3x3 M M M 3 3 M M a cosa emp ad press, he oal propery s equal o he sum of paral molar propery of he speces ad s mole fraco; s o equvale o mole fraco ad pure compoe propery For bary sysem M x M, Volume s he propery V x V x V

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13 Problem A 30% mole by mehaol waer soluo s o be prepared. How may m 3 of pure mehaol (molar volume = x 0-6 m 3 /mol) ad pure waer (molar volume = x 0-6 m 3 /mol) are o be mxed o prepare m 3 ( 000 L)of desred soluo. The paral molar volume of mehaol ad waer 30% soluo are x 0-6 m 3 /mol ad x 0-6 m 3 /mol respecvely. 3

14 Mehaol = 0.3 mole fraco Waer = 0.7 mole fraco V x V xv V = 0.3 x x x x 0-6 =4.05 x 0-6 m 3 /mol Toal moles for m 3 soluo mol 4

15 Number of moles of mehaol m 3 soluo = x 0 3 x 0.3 = x 0 3 mol Number of moles of waer m 3 soluo = x 0 3 x 0.7 = x 0 3 mol Volume of pure mehaol o be ake = 4.97 x 0 3 x 40.7 x0-6 =.077 m 3 Volume of pure waer o be ake = 58.7x0 3 x 8.068x0-6 =.059 m 3 To prepare m3 ( 000L), 30% mol mehaol-waer soluo, oe should add.077 m3 ( 07.7 L) of pure mehaol ad.059 m3 5 (05.9 L)of pure waer

16 Esmao of Paral molar properes for a bary mxure paral molar volume paral molar ehalpy paral molar eropy Aalycal Mehod : f he volume of a soluo s kow as fuco of s composo, paral dffereao wh respec o he amou of ha cosue. V V T, P, j 6

17 Aalycal mehod Cosder bary soluo moles of compoe ad moles of compoe Le V = he oal volume V = he molar volume Dff wr o... Keepg, T, P V T, P, V V ( ) V V V V ( ) bu mole fraco x by defo dff w.. r x rearragg V V x x x V x d dx 7 x

18 V V x V x V V x V x V or V V ( x) x 8

19 Molar Volume, V m3/kmol Tage -Iercep mehod Wdely used mehod o esmae PMP of boh compoes a bary sysem The molar volume V s ploed agas mole fraco of oe of he compoes, (Le x, he mole fraco compoe ) Draw he age o he curve a he desred mole fraco The ercep wh vercal axs gves pure compoe volume, A x =(x =0) V, bu V=0 X =0(x =), bu V=0 V B BD V ; P AC V F legh BD BE ED; E V BE s he slope of he age a P*PE A V BE ( x C D ) x 0 X mole fraco of comp ED = V, he molar volume a he mole fraco x, 9

20 Tage -Iercep mehod BD V AC V ; legh BD BE ED; BD V ( x BD V AC FC FA V ) V x x V x V A F C 0 X mole fraco of comp P V B E D 0

21 Lmg cases: For fe dluo of compoe whe a age s draw a x =0, wll gve he paral molar propery of compoe a fe dluo ( M Tage s draw a x =0 or x = wll gve fe dluo he paral molar propery of compoe M ) ( )

22 Problem The Gbbs free eergy of a bary soluo s gve by G 00x 50x xx( 0x x cal ) mol (a) Fd he paral molar free eerges of he compoes a x=0.8 ad also a fe dluo. (b) Fd he pure compoe properes G 00x 50x xx( 0x x Subsue x x dg G G ( x ) G dx x ) cal mol 3 G 9x 8x 49x x V V V ( x) x V V V ( x ) ; V V x 7 6x 49 x x 50 V

23 3 G 8x 35x 6x 0 G dg 3 G x 50 dx G 8x 8x To fd he paral molar properes of compoes ad x =0.8, x = = 0. G G ( x ) dg dx 3 G 8x 35x 6x G 8x 8x G G cal mol cal mol 3

24 A fe dluo G Gax 0 G 0 cal mol G 60 cal G G ax or x =0 mol To fd he pure compoe propery G G ax G Gax 0 G 00 G 50 cal mol cal mol 4

25 Problem The ehalpy a 300K ad bar of a bary lqud mxure s H 400 x 600 x x x [ 40 x 0 x ] Where H s J/mol. For he saed emperaure deerme.expresso erms of H ad H erms of x..numercal Values of pure compoe ehalpes. 3. Numercal values for paral molar properes a fe dluo. 5

26 Soluo: Subsue H 400 x 600 x x x [ 40 x 0 x x x 3 H 0x 80x 600 ] H H H ( x ) dh dx 3 H H x dh dx 3 40x 60x 40 H 40x 600 6

27 A fe dluo H Hax 0 H 40 J mol H H ax or x =0 H 640 J mol To fd he pure compoe propery H Hax H 400 J mol H H ax 0 H 600 J mol 7

28 Chemcal Poeal of speces I s wdely used as a hermodyamc propery. I s used as a dex chemcal equlbrum, same as pressure ad emperaure. The chemcal poeal of compoe The chemcal poeal of a subsace s a esve propery. G G T, P, Iesve properes are spaally uform uder equlbrum codos. Temperaure grades lead o hea coduco o acheve hermal equlbrum. Pressure grades lead o flud flow o acheve mechacal equlbrum. Dffereces bewee phases leads o he dffuso of compoe bewee phases (or chemcal reacos) o acheve chemcal equlbrum. j 8

29 Toal Gbbs free eergy, G G f P, T,, k G G G k dg dp dt d P T T, P, P, T, j dg G P T, dp G T P, dt G s ce, d T, P, j 9

30 For closed sysem here wll be o exchage of cosues ( s cosa) dt S dp V dg a cosa emperaure T G V P a cosa pressure P G S T 30

31 dg V dp S dt d fudameal relaoshp for chages he free eergy of a soluo A cosa emperaure ad pressure T, P dg d he chage free eergy s erely because of he chages he umber of mol For bary soluo he molar free eergy of he soluo G G x x Leads o GIBBS DUHEM relao 3

32 Effec of emperaure ad pressure o chemcal poeal Effec of emperaure: G G T, P, j () dffereag equao () wh respec o T a cosa P T P, G T () 3

33 dg VdP SdT (3) G wh respec o T a cosa P dffereag aga w r G S G T S T T P, P, j I a useful form P S s paral molar eropy of compoe T T P, T T T d U ( V ) VdU UdV V 33

34 T S T G H I erms of paral molar properes TS G H T S H H T S T S ( T) T P, H T Ths equao represes he effec of emperaure o chemcal poeal. 34

35 Effec of Pressure: j P T G G,, (4) dffereag equao (4) wh respec o P a cosa T T Pd G P, (5) SdT VdP dg (3) G wh respec o P a cosa T V P G T 35

36 dffereag aga w r T V V P G j, T V P, Ths equao represes he effec of pressure o chemcal poeal. The rae of chage of chemcal poeal wh pressure s equal o he paral molar volume of he cosue. 36