Homework. Chap 5. Simple mixtures. Exercises: 5B.8(a), 5C.4(b), 5C.10(a), 5F.2(a)

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1 Homework Cha 5. Simle mitures Eercises: 5.8(a), 5C.4(b), 5C.10(a), 5F.2(a) Problems: 5.5, 5.1, 5.4, 5.9, 5.10, 5C.3, 5C.4, 5C.5, 5C.6, 5C.7, 5C.8, Itegrated activities: 5.5, 5.8, 5.10,

2 Cha 5. Simle mitures (mitures that do ot react) The artial roerties of mitures: Use artial molar quatities chemical otetial, artial molar V(), etc t equilibrium, μ of a secies is the same i every hase Hery s law & Raoult s law i terms of mole fractio Effect of solute o roerties of a solutio: Lowerig vaor of the solvet Elevatio of T b Colligative roerties Deressio of T f (deedig o # of solute) Osmotic μ of a real miture: i terms of activity 2

3 5 장 -1 수업목표. Simle mitures dg Vd SdT d Chemical otetial: d G J J, T, ' Δ mi G of two erfect gas: mi G l l 0 of liquids: l for gas: o l o Raoult s law: l Hery s law: K ( m K )? 3

4 5. The thermodyamic descritio of mitures 5.1 Partial molar quatities Partial molar V : V J V J, T, ' the chage i V er mole of added to a large V of the miture V For biary miture (, ), V V dv d d, T,, T, dv V d V d V V d 0 0 V d V d V d 0 0 V V V 4

5 5.1(b) Partial molar Gibbs eergy the chemical otetial for a substace i a miture For a biary miture, G J J G For a system of comoets,, etc, dg = Vd SdT becomes, T, dg Vd SdT d d T, Fudametal equatio of chemical thermodyamics t cost. T ad, dg d d dw d d add,ma ' No-easio work ca arise from the chagig comositio of a system 5

6 5.1(c) The wider sigificace of the chemical otetial G U V TS U G V TS du dg dv Vd SdT TdS du ( Vd SdT du TdS dv d d J G J d d ) dv Vd SdT TdS, T, ' t cost. S ad V, du d d J U J S, V, ' J H J S,, ' J J T, V, ' 6

7 5.1(d) The Gibbs-Duhem equatio d J J J of oe comoet of a miture caot chage ideedetly of of the other comoets. The same lie of reasoig alies to all artial molar quatities 0 For a biary miture, recall that dg d d G dg d d d d d d 0 d d 7

8 5.2 The thermodyamics of miig the miig is sotaeous ΔG < 0 (a) Δ mi G of erfect gases o o l l o μ o : stadard chemical otetial : i the uit of bar o o l l o o l l G i G f mig G f Gi l l l l G l l 0 mi,, 8

9 5.2 The thermodyamics of miig the miig is sotaeous ΔG < 0 (b) Other thermodyamic miig fuctios G l l 0 mi Recall that G T, S G T mi mis,, R l l 0 mi H mi G T mi S 0 For a erfect gas, drivig force for miig solely comes from S (o iteractio betwee molecules) 9

10 (Sulemet): () l() +(1-) l(1-) l()+(1-)l(1-) l()+(1-)l(1-)

11 5.2 The thermodyamics of miig G l l 0 mi miig two erfect gases S R l l 0 mi 11

12 E 5.3 (185) 3.0 mol of H 2 (g) ad 1.0 mol o N 2 (g) are i two equal comartmets at 25. Calculate G mi whe the artitio is removed. Let the iitial, N 2 efore miig:, fter miig: N, 2 H G N H H N N H o o H l l 2 H 2 H 2 N 2 N 2 N2 o o 3.0 mol l mol l G i H N 2 2 o 3 o G f 3.0 mol H l 1.0 mol N l mig G f Gi 3.0 mol l 1.0 mol l mol l l 6.9 kj

13 5.3 The chemical otetials of liquids For ure substaces: (at eq., μ liq = μ vaor ) o ( g) l ( l) o l I the resece of aother substace l o l l l l l 13

14 5.3(a) Ideal solutios l Eerimetally Raoult foud that Raoult s law For a ideal solutios: (obey Raoult s law throughout the comositio rage from ure to ure : good whe two comoets are structurally similar) l 14

15 For ideal solutios: l Strog deviatios from ideality by dissimilar liquids Eve some solutios deart sigificatly from Raoult s law, it is a good aroimatio for the roerties of the solvet if the solutio is dilute 15

16 E 5.4 (189) The vaor ressure of each comoet i a miture (acetoe + chloroform) were measured at 35 C C /kpa /kpa Cofirm that the miture coforms to Raoult s law for the major comoet ad Hery s law for the mior comoet. Fid the Hery s law costats. 16

: emirical costat K? Practically, m K m = mol/1 kg m O bis 5.

17 5.3(b) Ideal-dilute solutios Dilute solutio solvet: a slightly modified ure liquid solute: etirely differet from its ure state Ideal-dilute solutios, but Hery s law K? : emirical costat K? Practically, m K m = mol/1 kg m O bis 5.4 (190) the molar solubility of O 2 i water at 25 O 21 kpa mol kg K kpa kg mol O 2 O 2 H2O O O m m kg L mm 17

18 5 장 -2 수업목표. The roerties of solutio Miig ideal solutios: mi G l l Colligative roerties (deeds oly o # of solute articles) l T T b f va fus 2 H H 2 K K b f m m M r 1000 m Osmotic ressure, Π: va t Hoff eq: Real solutio: J 1 J 18

19 G 5. The roerties of solutios 5.1 Liquid mitures (a) Ideal solutios (miscible all the time) i l T l G R f G l l mi S R l l mi mi H 0 Same as that for two ideal gases (E ave of - iteractios i the miture is the same as E ave of - ad - iteractios i the ure liquids) 19

20 Real solutios iteractios are all differet: miscible, immiscible, artially miscible 5.1(b) Ecess fuctios ad regular solutios Ecess fuctios: X E mi X H 0 mi mi X ideal the etet to which the solutios are oideal Ideal solutios (miscible all the time) Regular solutios: S E = 0, H E 0 20

5.2 Colligative roerties deeds oly o the # of solute articles reset, ot their idetity E, T b, T f, osmotic ressure (Π) ssumtios: the solute is oly i liquid solvet (ot volatile, ot dissolved i the

21 5.2 Colligative roerties deeds oly o the # of solute articles reset, ot their idetity E, T b, T f, osmotic ressure (Π) ssumtios: the solute is oly i liquid solvet (ot volatile, ot dissolved i the solid solvet) (a) Commo features of colligative roerties l Whe solute is reset, the disorder of the liquid is higher tha that of the ure liquid, ad there is a decreased tedecy to acquire the disorder characteristic of the vaor. 21

22 5.2(b) T b T K m b b t T b, ( g) ( l) ( l) l ( g) ( l) vag l vah TvaS vah 1 1 R T T va T T va T 2 T H H R T T R b 2 H va T M r Sice m (see et slid e) 1000 l l 1 va S T va vas T vah T 0 Pure solvet: 0 va H T vah T va va va R R H T va S T S T S ! for l 1 H Tb H va H 2 2 va M r m 1000 K m b where 2 H Kb va M r

23 m 1 edi r m : i 1 kg of for 1 kg of : m M r m 1 molal water solutio ( m 1): for 1 kg of 1000 kg of for 1 kg of 1000 M 1, :1 kg 1000 M kg of water: 55.6 M 18 r r M r 18 1 m

24 T 2 5.2(c) T f K m f f fush where K f 2 H fus M r 1000 t Tf, ( s) ( l) ( l) l ( s) ( l) fusg l d fusg l dt d l 1 d fusg 1 fush 2 dt R dt T R T l 1 T fush d l dt 1 T 2 R T T fush 1 dt T 2 R T fush 1 1 l l 1 R T T fush 1 1 fush T T R T T R TT fush T 2 R T 2 T H fus 24

25 5.2(d) Solubility l fush 1 1 R Tf T Highly questioable No solvet roerties ( s) ( l) ( l) l ( s) ( l) fusg l d fusg l dt d l 1 d fusg 1 fush 2 dt R dt T R T l 1 T fush d l dt 0 T 2 R f T T fush 1 dt T 2 R f T l fush 1 1 R T Tf fush T T R TT f f 25

26 5.2(e) Osmosis ( ush i Greek) the sotaeous assage of a ure solvet ito a solutio searated from it by a semiermeable membrae Osmotic ressure, Π: that must be alied to the solutio to sto the iflu of solvet 26

27 Osmotic ressure, Π: that must be alied to the solutio to sto the iflu of solvet va t Hoff eq: ( ) ( ) ( ) l ( ) ( ) V m, m, m, m, l V d V l l 1 V V V d Real solutio: J 1 J : Osmotic virial coefficiet 27

28 E 5.2 (200) Π of solutios of PVC i cycloheae at 298 K are measured. The ressure are eressed i terms of the heights of solutio ( = g cm -3 ) i balace with Π. Determie the molar mass of the olymer. M M c/(g dm -3 ) h/cm (h/c)/(cm g -1 dm 3 ) h R c 2 c T gm gm Plot h/c vs, c get itercet g J K mol 298 K cm g 2 3 kg m 9.81 m s m kg kg mol dm 1 J J 1 J c, gh M c c gh 1 M M h c 1 c gm M 2 gm gm c 28

PhysChem05 CHEMICAL POTENTIAL CHEMICAL POTENTIAL CHEMICAL POTENTIAL CHEMICAL POTENTIAL CHEMICAL POTENTIAL I. CHEMICAL POTENTIAL OF AN IDEAL GAS

PhysChem05 CHEMICAL POTENTIAL CHEMICAL POTENTIAL CHEMICAL POTENTIAL CHEMICAL POTENTIAL CHEMICAL POTENTIAL I. CHEMICAL POTENTIAL OF AN IDEAL GAS he cocet of calculatio of the chemical otetial i oe- ad multi-comoet systems I. Chemical otetial of a ideal gas II. Chemical otetial of real gases. Fugacity III. Chemical otetial of liquids IV. Chemical