Question

9.9 Table 9.9 lists measured values of gas-phase composition and total pressure for the binary two-phase methanol-benzene system at constant temperature and varied liquid-phase compo- sition. XA is the mole fraction of methanol in the liquid mixture, and ya is the mole fraction of methanol in the equilibrated gas phase. (a) For each of the 16 different liquid-phase compositions, tabulate the pyrtial pressures of A and B in the equilibrated gas phase. (b) Plot PA and Ps versus xA on the same graph. Notice that the behavior of the mixture is far from that of an ideal mixture. Are the deviations from Raoult's law positive or negative? (e) Tabulate and plot the activity coefficient Ys of the benzene as a function of xĂ using a pure-liquid reference state. Assume that the fugacity is equal to DR. and ignore the effects of variable pressure.

Answer 1

the (a) The partial pressures BA & B can be calculated from the giver dala wing formculae; PAYAP and Pop-PA Thus, the required table & is INA o.o207 oo314 o o43) oo613 oogs 4 o 18 o 3211 o o Y PA IPB о 29 894 o 2194 11. 44 5 29 514 o 239 14.999 24 - 232 o 31914 11. 168 24. 064 о. 43ot 21 140 28 - 14.g о. 46 4.2 | 24. 106 29 517 o s (7) | 24. 109 21 145 o 54 50 32 314 o 5590 | 33 5 4 8 26 461 o 518 3 134 1939 | 25 41 24 122 o62 1631 214 22 - 654 o6 6 8 139 964 19.357 o1525 | 41 . 15 13 536 o8 368 | 42.68 4 8 - 325 ! 4. 608 21 028 o o o o o o o o o o oooo o o 35 - 694 o 4 2 от o 54 20 o6164 o 1259 o 817) 0-9033 О. 9491 |

- -- -- r -- - 4 - ------- P (KPa) -- - I- ---------------- -- - -- -- - -- ok * 0.0 0.2 0.4 A 0.6 0.6 0.8 ta

(b) Positive deviation from Raoult's law. de to (c) Activity coefficient fe - 29.894 - also ff - PB Thus, the table is

1 O 0.0207 0.0317 0.0431 0.0613 0.0854 0.1811 0.3217 0.4201 0.5420 0.6 164 0 7259 0.8171 0.9033 0.9497 1.008. 1.009 1.016 1.024 1.043 1.133 1.333 1.527 1.861 2.156 2-765 3.540 4.682 5.536

YB vs X OLTI I III 0.0 0.2 0.4 0.6 0.8 1.0 ta
Since the mixture exhibits positive deviation from Raoult's law, the activity coefficients are greater than 1. When x_B=0, $\gamma _B$ reaches a limiting value. When x_B=1, i.e., for pure liquids, $\gamma _B$ =1 and it is the ideal case.