1. Thermodynamics of Separation Operations
Chapter2
Exercises

2. Exercise2.1
MutuaJ solubility data for the ispOctane (l)/furfural(2) system "at 25°C are [Chem. Eng. ScL, 6, 116 (1957)]
Liquid Phase Ⅰ Liquid PhaseⅡ x
Compute:
(a) The distribution coefficients for isooctane and furfural
(b) The relative selectivity for isooctane relative to furfural
(c) The activity coefficient of isooctane in liquid phase 1 and the activity coefficient of furfural in liquid phase 2 assuming γ(1)2 =1.0 and γ(2)1 =1.0

3. Exercise2.2
A binary ideal gas mixture of A and B undergoes an isothermal separation at T0, the infinite surroundings tem­perature. Starting with Eq. (4), Table 2.1, derive an equation for the minimum work of separation, Wmin, in terms of mole fractions of the feed and the two products. Use your equation to prepare a plot of the dimensionless group, Wmin/RTonF, as a function of mole fraction of A in the feed for:
(a) A perfect separation
(b) A separation with SFA = 0.98, SFB = 0.02
(c) A separation with SRA =9.0 and SRB = 1/9
(d) A separation with SF = 0.95 for A and SPA.B = 361
How sensitive is Wmin to product purities? Does Wmin depend on the particular separation operation used?
Prove, by calculus, that the largest value of Wmin occurs for a feed with equimolar quantities of A and B.

4. Exercise2.3
A hydrocarbon vapor-liquid mixture at 250°F and 500 psia contains N2, H2S, CO2, and all the normal paraffins'^ from methane to heptane. Use Figure 2.8 to estimate the K-value of each component in the mixture. Which components will have a tendency to be present to a greater extent in the equilibrium vapor?

5. Exercise2.4
Use the R-K equation of state to estimate the partial fugacity coefficients of propane and benzene in the vapor mixture of Example 2.5.

6. Exercise2.5
Use a computer-aided, steady-state simulation program to estimate the k-values, using the P-R or S-R-K equation of state, of an equimolar mixture of the two butane isomers and the four butene isomers at 220°F and psia. Com­pare these values with the following experimental results [J. Chem. Eng. Data, 7, 331 (1962)]:
Component K-value
Isobutane
Isobutene
n-Butane
1-Butene
trans-2-Butene
cis-2-Butene

7. Exercise2.6
For the binary system ethanol(l)/isooctane(2) at 50°C, the infinite-dilution, liquid-phase activity coefficients are
γ1 *=21.17 andγ2 *= 9.84.
(a) Calculate the constants A12and A21in the van Laar equations.
(b) Calculate the constants andin the Wilson equations.
(c) Using the constants from (a) and (b), calculated γ1 and γ2 over the entire composition range and plot the calculated points as logγ versus x1.
(d) How well do the van Laar and Wilson predictions agree with the azeotropic point where x1= ,γ1 = 1.44, and γ2 = 2.18?
(e) Show that the van Laar equation erroneously predicts separation into two liquid phases over a portion of the com­position range by calculating and plotting a y-x diagram like Figure 2.22.