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1 Plottng P-x-y dagram for bnary system Acetone/water at temperatures 25,100,and 200 C usng UNIFAC method and comparng t wth expermental results. Unfac Method: The UNIFAC method s based on the UNIQUAC equaton, for whch the actvty coeffcents are gven by the formula lnγ () =lnγc () + lnγr () (1) where c() s combnatoral term to account for molecular sze and shape dfferences, and r() s a resdual term to account for molecular nteractons. Functon c() contans pure speces parameters only, whereas functon r() ncorporates two bnary parameters for each par of molecules.for a multcomponent system, lnγc () = 1 J () + ln (J ()) 5 q () 1 J () + ln J () L () L () (2) lnγr () = q () 1 θ (k) β (k) e (k) ln β (k) k s (k) s (k) (3) where r () J () = ( r (j) x (j)) j (4) q () L () = ( q (j) x (j)) j (5) where r () = k v () R (k) (6) k Non-Commercal Use Only

2 q () = k v () Q (k) (7) k e (k) = v () Q (k) k q () (8) θ (k) = ( x () q () e (k)) ( x (j) q (j)) j (9) s (k) = ( θ (m) τ (mk)) (10) m τ (mk) = exp a (mk) T (11) T --- Temperature β (k) = ( e (m) τ (mk)) (12) m Subscrpt dentfes speces, and j s a dummy ndex runnng over all speces. Subscrpt k dentfes subgroups, and m s a dummy ndex runnng over all subgroups.the quantty () s the number of subgroup parameters of type k n a molecule of speces. Values of the subgroup parameters R(k) and Q(k) and of the group nteracton parameters a(mk) come from tabulatons n the lterature. v k From tables of Appendx G n Smth and Van Ness Subgroups for acetone are 1 CH 3 (k=1) and 1 COCH 3 (k=19) Subgroups for water s the molecule tself (k=17). In our problem Non-Commercal Use Only

3 In our problem k R(k) Q(k) v (1) v (2) k k CH COCH H O Calculatons From equatons 6 and 7 r r r1 = r2 = 0.92 q q q1 = q2 = 1.4 From the above values usng equaton 8 e(k) table s prepared e (k) sample calculaton for e(19,1) k = 1 = = Non-Commercal Use Only

4 Interacton parameters from tables a ( 1, 1) =a ( 19, 19) =a ( 17, 17) =0 a ( 1, 19) =476.4 a ( 19, 1) =26.76 a ( 1, 17) = a ( 17, 1) = a ( 19, 17) = a ( 17, 19) = bar 10 5 joule Pa R gas mole K acetone water Expermental values of lqud phase composton (x1exp25), vapor phase composton (y1exp25) of acetone and total pressure of the system are gven as shown below. At 25C 0 16 Non-Commercal Use Only

5 x1exp y1exp Pexp bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar Calculaton of actvty coeffcents by UNIFAC-method x2exp25 1 x1exp25 r r From equatons 6 and 7 q q J1 r1 r1 x1exp25 + r2 x2exp25 J2 r2 r1 x1exp25 + r2 x2exp25 From equaton 4 = J = J Non-Commercal Use Only

6 q1 L1 q1 x1exp25 + q2 x2exp25 = L L2 = L2 q2 q1 x1exp q2 x2exp25 From equaton 5 x1exp25 q Non-Commercal Use Only

7 x1exp25 q x1exp25 q θ1 x1exp25 q1 + x2exp25 q2 θ19 x1exp25 q1 + x2exp25 q2 θ17 x2exp25 q2 1 x1exp25 q1 + x2exp25 q2 From equaton 9 = θ = θ = θ From equaton 10 s1 θ1 1 + θ θ τ (mk) 's n equaton 10 are calculated from equaton 11 Sample calculaton s19 θ θ θ τ ( 1, 19) = s17 θ θ θ17 1 exp = Non-Commercal Use Only

8 = s = s = s lnγc1 J1 J1 1 J1 + ln J1 5 q1 1 + ln L1 L1 From equaton 2 lnγc2 J2 J2 1 J2 + ln J2 5 q2 1 + ln L2 L Non-Commercal Use Only

9 lnγr1 q1 1 θ ln θ ln s1 s θ s19 s19 s17 lnγr2 q2 1 θ θ s1 θ17 1 ln s19 1 s17 s17 From equaton 3 = lnγr = lnγr2 β (k) 's are calculated by equaton 12. = lnγc β ( 1, 19) = = lnγc2 sample calculaton = γ1 exp lnγc1 + lnγr1 γ2 exp lnγc2 + = γ = γ lnγr2 Non-Commercal Use Only

10 γ γ Psat bar Psat bar from lterature at 25 C Pcal25 x1exp25 γ1 Psat1 + x2exp25 γ2 Psat2 y1cal25 x1exp25 γ1 Psat1 Pcal25 = y1cal Pcal25 =? bar Non-Commercal Use Only

11 rms 2 Pexp25 Pcal25 Root mean square error calculaton. rms =? bar Pexp25 bar 2 0 Pexp25 bar -2 Non-Commercal Use Only

12 Pcal25 bar -6-4 Pcal25 bar x1exp25 y1exp25 x1exp25 y1cal25 Smlar calculatons were carred on at 100 and 200 C At 100C x1exp Non-Commercal Use Only

13 y1exp r r Pexp bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar bar x2exp100 1 x1exp100 q q J1 r1 r1 x1exp100 + r2 x2exp100 J2 r2 r1 x1exp100 + r2 x2exp100 = J = J Non-Commercal Use Only

14 q1 L1 q1 x1exp100 + q2 x2exp100 L2 q2 q1 x1exp100 + q2 x2exp100 = L = L Non-Commercal Use Only

15 x1exp100 q θ1 x1exp100 q1 + x2exp100 q2 θ19 x1exp100 q x1exp100 q1 + x2exp100 q2 = θ θ17 = θ19 x2exp100 q2 x1exp100 q1 + x2exp100 q = θ s1 θ1 1 + θ θ s19 θ θ θ Non-Commercal Use Only

16 s17 θ θ θ17 1 = s = s = s lnγc1 J1 J1 1 J1 + ln J ln L1 L1 lnγc2 J2 J2 1 J2 + ln J ln L2 L2 Non-Commercal Use Only

17 lnγr1 q1 1 θ ln θ ln s1 s θ s19 s19 s17 lnγr2 q θ1 + + θ19 s1 θ17 1 ln s19 1 s17 s17 = lnγc = lnγc = lnγr = lnγr γ1 exp lnγc1 + lnγr1 γ2 exp lnγc2 + lnγr γ1 = γ2 = Non-Commercal Use Only

18 γ1 = γ2 = Psat bar Psat bar Pcal100 x1exp100 γ1 Psat1 + x2exp100 γ2 Psat2 y1cal100 x1exp100 γ1 Psat1 Pcal100 = y1cal Pcal100 =?bar Non-Commercal Use Only

19 rms 2 Pexp100 Pcal100 rms =? bar Non-Commercal Use Only

20 Pexp100 bar 2 0 Pexp100 bar -2 Pcal100 bar -6-4 Pcal100 bar x1exp100 y1exp100 x1exp100 y1cal100 At 200C x1exp y1exp Pexp bar bar bar bar bar bar bar bar bar bar bar Non-Commercal Use Only

21 bar bar bar bar bar bar x2exp200 1 x1exp200 r r q q J1 r1 r1 x1exp200 + r2 x2exp200 J2 r2 r1 x1exp200 + r2 x2exp200 = J = J Non-Commercal Use Only

22 L1 q1 q1 x1exp200 + q2 x2exp200 L2 q2 q1 x1exp200 + q2 x2exp200 = L = L Non-Commercal Use Only

23 x1exp200 q θ1 x1exp200 q1 + x2exp200 q2 θ19 x1exp200 q x1exp200 q1 + x2exp200 q2 = θ θ17 x2exp200 q2 x1exp200 q1 + x2exp200 q2 = θ = θ s1 θ1 1 + θ θ s19 θ θ θ Non-Commercal Use Only

24 s17 θ θ θ17 1 = s = s = s lnγc1 J1 J1 1 J1 + ln J ln L1 L1 lnγc2 J2 J2 1 J2 + ln J ln L2 L2 Non-Commercal Use Only

25 lnγr1 q1 1 θ ln θ ln s1 s θ s19 s19 s17 lnγr2 q2 1 θ θ s1 θ17 1 ln s19 1 s17 s17 = lnγc = lnγc = lnγr = lnγr γ1 exp lnγc1 + lnγr1 γ2 exp lnγc lnγr2 Non-Commercal Use Only

26 = γ = γ Psat bar Psat bar Pcal200 x1exp200 γ1 Psat1 + x2exp200 γ2 Psat2 y1cal200 x1exp200 γ1 Psat1 Pcal200 = y1cal Pcal200 =?bar Non-Commercal Use Only

27 rms 2 Pexp200 Pcal200 rms =? bar Non-Commercal Use Only

28 4 Pexp200 bar 2 0 Pexp200 bar -2 Pcal200 bar -6-4 Pcal200 bar x1exp200 y1exp200 x1exp200 y1cal200 = x1exp Non-Commercal Use Only

29 = y1cal = Pcal25? bar = x1exp = y1cal = Pcal100?bar = x1exp Non-Commercal Use Only

30 = y1cal Pcal200 =?bar Pcal augment ( Pcal25, Pcal100, Pcal200) Pcal =? bar Non-Commercal Use Only

31 x augment ( x1exp25, x1exp100, x1exp200) y augment ( y1cal25, y1cal100, y1cal200) 0 16 j z T z, j j Pcal Non-Commercal Use Only

32 bar x T Pcal bar y T Conclusons 1) Ths metod s more accurate when compared to the other methods avalable.ths can be seen by comparng the "root mean square" values of dfferent methods wth ths method at same temperature. 2) Ths method s most accurate at low temperatures. 3) Ths method doesn't requre the knowledge of expermental values of x (lqud phase composton) and y (gas phase composton) to plot phase equlbrum plot. We can select our own x values and fnd correspondng y values to construct phase equlbrum plot. The only values needed are the saturaton pressures of the components whch can be estmated from Redel correspondng states method. 4) Ths method doesn't requre the knowledge of crtcal temperature and crtcal pressure values. 5) Ths method just requres the knowledge of structure of the compound to plot the phase dagrams of the compounds.based on the structure, the compound s dvded nto subgroups and calculatons are performed. Non-Commercal Use Only