Page 71 - Separation process principles 2

36 Chapter 2 Thermodynamics of Separation Operations

at equilibrium: Vapor molar enthalpy (datum = ideal gas at 298.15 K and 1
I
n, kmolh 0 kPa): From (2-36) for ethylbenzene, i
i
Component Vapor Liquid i
h;,, = -43098.9(350.65 - 298.15)
I
Ethylbenzene (EB) 76.51 27.3 1
Styrene (S) 61.12 29.03
Based on the property constants given below, and assuming that the
ideal-gas, ideal-liquid-solution model of Table 2.4 is suitable at this
low pressure, estimate values of vv, pv, hV, sv, VL, PL, hL, and s~
in SI units, and the K-values and relative volatility.

= 7,351,900 Jhol I
Property Constants for (2-35), (2-38), (2-39)
(In all cases, T is in K)
Similarly, I
Ethylbenzene Styrene

M, kghol 106.168 104.152
From (2), Table 2.4, for the mixture, 1
C&, Jlkmol-K:
a0 R -43,098.9 -28,248.3
hV = yih~ (0.5559)(7,351,900)
=
a1 R 707.151 615.878
a2 R -0.48 1063 -0.4023 1 + (0.4441)(6,957,100) = 7,176,800 Jhol
a3 R 1.30084 x 9.93528 x
Vapor molar entropy (datum = pure components as vapor at
a4 R 0 0
298.15 K, 101.3 kPa): From (2-37), for each component, j
P, Pa:
i
k~ 86.5008 130.542
k2 -7,440.61 -9,141.07 lr ($) dT = 22,662 Jlkmol-K for ethylbenzene
k3 0 0
and 21,450 Jfkmol-K for styrene
k4 0.00623 121 0.0143369
k5 -9.87052 -17.0918
From (3), Table 2.4, for the mixture,
k6 4.13065 x lo-'8 1.8375 x
k7 6 6
p~. kg/m3:
A 289.8 299.2
B 0.268 0.264
To K 617.9 617.1
=
R = 8.314 kJ/kmol-K or k~a-rn~hol-~ 8,314 Jlkmol-K
Note that the terms for the pressure effect and the mixing effect are
significant for this problem.
SOLUTION
Liquid molar volume and density. From (2-38), for ethylbenzene,
Phase mole-fraction compositions and average molecular
weights: From yi = (niv)/nv,xi = (niL)/nL,

Ethylbenzene Styrene

Similarly,
psL = 853.0 kg/m3
From (I), Table 2.4,
vsL = 0.1221 m3ho~

From (4), Table 2.4, for the mixture,

Vapor molar volume and density: From (I), Table 2.4,

Liquid molar enthalpy (datum = ideal gas at 298.15 K): Use (5)
in Table 2.4 for the mixture. For the enthalpy of vaporization of