ThermodynamicsThermodynamics of of Separation Separation OperationsOperations

Chapter2Chapter2

Exercises

Exercise2.1 MutuaJ solubility data for the ispOctane (l)/furfural(2) syste

m "at 25°C are [Chem. Eng. ScL, 6, 116 (1957)] Liquid Phase Liquid PhaseⅠ Ⅱ x1 0.0431 0.9461 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 an

d the activity coefficient of furfural in liquid phase 2 assuming γ(1)2 =1.0 and γ(2)1 =1.0

Exercise2.2 A binary ideal gas mixture of A and B undergoes an isothermal separat

ion at T0, the infinite surroundings tem perature. 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 wit

h equimolar quantities of A and B.

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?

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.

Exercise2.5 Use a computer-aided, steady-state simulation program to e

stimate 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 276.5 psia. Com pare these values with the following experimental results [J. Chem. Eng. Data, 7, 331 (1962)]:

Component K-value Isobutane 1.067 Isobutene 1.024 n-Butane 0.922 1-Butene 1.024 trans-2-Butene 0.952 cis-2-Butene 0.876

Exercise2.6 For the binary system ethanol(l)/isooctane(2) at 50°C, the infinite-diluti

on, 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= 0.5941,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 com position range by calculating and plotting a y-x diagram like Figure 2.22.