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5. (Lecture L08) This problem is concerned with binary mixtures of n-octane and n-nonane at atmos pheric pressure a. Calculate and graph the Txy diagram b. Derive the formula for Hx(T,Xx), the liquid enthalpy, as a function of temperature and composition. c. Calculate the enthalpy of saturated liquid with n-octane mole fraction x 0.4 d. Derive the formula for Hy(T, y), the vapor enthalpy, as a function of temperature and composition e. Calculate the enthalpy of saturated vapor with n-nonane mole fraction y 0.7. Define reference states such that the liquid enthalpy is zero for each pure component at 398.75 K. Vapor pressure data for the components can be obtained from the Antoine's equation MatLab code in the Computer Code tab on the course website. Value for n-octane Property Normal boiling point in K Cp of liquid in J/(mol K) Cp of vapor in J/(mol K) AHvaP at normal boiling point in kJ/mol Value for n-nonane 398.75 423.95 310 373 258 289 36.91 34.41 407-Carylagueoualo.ecu-University at Buffale Mai function Psat %saturated vapor pressures from Antoine's equation for pure substances wwwcourses.sens buffalo.edulce407 onnelcomputer.codeiced -Psat Antoine databank i, T %data from Towler and Sinnott (2013), Appendix C %T entered in deqC, Psat given in mm Hg %components %i 1: water %i 2: n-butane 3: n-pentane 4: n-hexane 5: n-heptane 6: n-octane 7: n-nonane %i %i 8: n-decane 9: n-hexadecane %i 10: benzene 11: toluene %i = 12: ethylbenzene i 13: 1-propylbenzene (n-propylbenzene) %i (n-butylbenzene) 14: 1-butylbenzene 15: methanol 16: ethanol 17: 1-propanol (n-propanol) (n-butanol) &i 18: 1-butanol -- (n-pentanol) (n-octanol) 19: 1-pentanol 20: 1-octanol %i %i 21: L-1actic acid %i 22: L-lactide -46.13: 3816.44: c(1) = 18.3036: b( 1) a ( 1) 3816.44 c 1) 2154.90; c( 2) 2477.07; c 3) 2697.55; c( 4) 2911.32; c( 5) 3120.29; c( 6) 3291.45; c( 7) 3456.80; c( 8) 4214.91; c 9) 2788.51; c (10) 3096.52; c(11) 3279.47; c (12) -46.13; 18.3036; b( 1) a( 1) a 2) a( 3) a( 4) a( 5) a( 6) a( 7) a( 8) -34.42; 15.6782; b( 2) 15.8333; b( 3) 15.8366; b 4) 15.8737; b( 5) 15.9426 b( 6) 15.9671; b( 7) 16.0114 b8) 16.1841; b 9) 15.9008; b (10) 16.0137; b (11) 16.0195; b (12) 16.0062; b (13) 16.0793; b (14) 18.5875; b(15) 18.9119; b (16) 17.5439; b (17) 17.2160; b (18) 16.5270; b (19) 15.7428; b (20) 16.0785; b (21) 19.6150; b (22) -39.94; -48.78 -56.51; -63.63; -71.33; -78.67; - = - -118.70; = a( 9) -52.36; -53.67; a (10) a (11) a (12) a (13) a (14) a (15) a (16) a (17) a (18) a (19) -59.95; -66.01; -71.77; -34.29; -41.68; 3433.84; c (13) 3633.40; c (14) 3626.55; c (15) 3803.98; c(16) 3166.38; c(17) -80.15; -94.43; -105.00; 3137.02; c(18) 3026.89; c (19) 3017.81; c(20) 4276.57; c (21) 7279.91; c (22) =-137.10: a (20) a (21) a (22) -91.00; 0.00 = c (i))); Psat- exp (a (i) - b(i) / (T + 273.15 + end II function Psat Psat Antoine( i, T) = %saturated vapor pressures from Antoine's equation for pure substances Scomponents %i 1: benzene %i 2: toluene if i -1 ii 10; else ii 11 end Psat Psat Antoine_databank (ii, T) end Session >Psat Antoine (1, 80 .1) ans= 759.9559 >>Psat Antoine (2, 110.6) ans

Answer 1

Answeas n octane and n-nohane As the Rabuld's las follows P P A octane n - PA=Vapou puessune of Vapous poie Ssure of h- nonane p Total prHessute 1 atm (given) ba A CtT T: Keluin 4.04-1355. I T-63.6 4.06-1430 y legP T-71.4

aAcending EquaHion to 4.06-1420.y . 013 (Io)4:04-135S Tr.6 (1- Xa 4t(lo T-11.4 ) pet by the quation () is in vasuia ble TSKA We Can values of T torne sponeling getting ahol 0 to XA b En halpy of Liguid mix ture 4Hmik 2 X; Hi Ha) AHmi x (x, H Hmik ton ideal A Hmik Hmin C pdt 398.75 H 344.75) 4 Ot 3lo (7-39f, 75) 7-39.15) 2 6313 (31ont 313 x.)T- 396-7s)

Enthalpy of Satuna ted Liguid = 0.4 XA focom ) Caltulate ) C ur2-398.75) -(310 X 0.4 3 73 x0. 6 Hmis 4608.35 J/mol 2 dEnthalpy of vapous mintusie H V H Vap H(3 8.75) 398.75 (T-39 f. 7)+34.4txiDoo oo + s H l43.95-391.75+ 9 /7-4393 +36 91 Xlo00 2 04 373 y H Hmin 289 T-ob0 27 34.41 sf (7- 398.a5) x l000 1- y - 0.3 T2 412 k y 0.7 h hohane 131.9 J/mol Hmix

T Pa PA Xa Pb Ха T Ха 399.5 0.5015954066 0.9992971777 0.9999665044 1.013359679 1.012647468 0.9998519917 399.5 400.5 401.5 1.041689295 0.5171311863 0.9453076889 0.9847169003 0.9720798621 400.5 0.9998975788 0 8927872004 09558502569 401.5 0.9998267002 402.5 0.9997538342 403.5 404.5 0.9996020002 405.5 0.9995229615 406.5 0.9994417941 0.5330496299 1.070636157 0.9435836692 402.5 403.5 404.5 405.5 408.5 407.5 408.5 409.5 410.5 1.100209428 0.5493574629 0.8416826445 0.9260271792 0.9141433161 1.130418322 0.5660614708 07919431266 0.8952270203 0.8837384208 0.999678946 1.161272116 0.5831684979 0.7435198284 0.8634288424 0.8523483143 0.6006854489 0.696365903 0.8308114162 1.192780135 0.8199520397 1.224951757 .6186192864 0.6504364064 0.7967532192 0.7865283506 1.257796413 0.6369770317.60568819160.7618324347 0.7520557105 407.5 0.9993584619 1.291323583 0.6557657637 0.5620798378 0.7258269504 0.7165122906 408.5 0.9992729286 1.325542801 0.6749926191 0.5195715723 0.6887143573 0.6798759697 409.5 0.9991851575 0.4781251984 0.6504719484 0.9990951115 1.360463647 0.6946847914 0.6421243321 410.5 411.5 0.99900a27536 412.5 0.9989o80461 413.5 411.5 1.396095752 0.7147895307 0.6110767178 0.4377040164 0.6032346671 412.5 413.5 414.5 1.432448793 0.7353741431 0.3982727778 0.5705053594 0.5631839678 1.469532496 0.7584259904 0.3597976006 0.528734266 0.5219489299 0.9988109512 0.7779524895 1.507356632 0.3222459223 0.485739528 0.4795059506 414.5 0.9987114308 0 4414969327 415.5 0.9986094466 416.5 417.5 418.5 0.9982883236 419.5 0.9981760951 420.5 0.9980612071 421.5 0.9979436197 0.2855864381 415.5 1.545931017 0.7999811118 0.4358311281 1.585265513 416.5 0.822459383 0.2497890479 0.3959819632 0.3909002598 0.99850496 417.5 1.625370026 0.2148248042 0.3491697974 0.3446888425 0.998397932 0.845454882 0.1806658629 418.5 1.686254501 0.8689552413 0.3010353072 0.2971720703 419.5 420.5 421.5 422.5 423.5 1.70792893 0.8929681453 0.1472854362 0.2515530575 0.2483248346 1.750403342 0.917501331 0.1146577481 0.2006973055 0.1981217231 1.79368781 0.9425625864 0.08275799104 0.1484419997 O.1465370185 0.9978232925 0.09354469837 422.5 1.837792443 0.9681597504 0.05156228594 0.09476077945 1.882727391 0.9943007125 0.0210478429 0.03962697380.03911843415 423.5 0.9977001853