Sol_HW_6_v3_KS_12oct - Chemical Engineering 150B- Fall 2005...

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Chemical Engineering 150B- Fall 2005 Problem Set #6 Solutions Problem 1. (15 points) Consider an isothermal, isobaric ideal binary gas mixture of A and B being separated below into k streams: where n is the molar flow rate. Derive an expression for the minimum (reversible) work of separation in terms of gas constant, R, temperature T o , and mole fractions of A and B. [Hint: Try reading Seader, Chapter 1 and using Tables 2.1/2.4.] From Table 2.1 you can use the expression (4) to calculate the minimum work of separation: Since the temperature is constant, the enthalpy change is zero. Now use Table 2.4 to get the s in terms of mole fractions, where s for an ideal gas solution at constant temperature and pressure reduces to: 1 C ii i sR y l n y = =− Combining the above two equations, we arrive at the final answer: [] 1 k min o k k,A k,B o in A A B B k W R T nyl n y yl n y R T ny l n y y l n y = =+ + ⎡⎤ ⎣⎦ Through complicated mathematics, we can show that regardless of values for y between 0 and 1, W min is always positive. Since W min is independent of the process, this implies that the separation of a mixture into essentially pure species, or other mixtures of differing compositions, always require the transfer of energy to the mixture or a degradation of its energy. y A y B y 1,A y 1,B . . . y 2,A y 2,B y k,A y k,B n in n 1 n 2 n k 4 pt 8 pt 3 pt
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Problem 2. (30 Points) In petroleum refineries, a mixture of paraffins and cycloparaffins is commonly reformed in a fixed-bed catalytic reactor to produce blending stocks for gasoline and aromatic precursors for making petrochemicals. A typical multi-component product from catalytic reforming is a mixture of ethylbenzene with the three xylene isomers. If this mixture is separated, these four chemicals can be subsequently processed to make styrene, phthalic anhydride, isophthalic acid, and terephthalix acid.
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Sol_HW_6_v3_KS_12oct - Chemical Engineering 150B- Fall 2005...

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