17 (8) up Tup Use this result in Eq. 4 to produce the second term in the Taylor series expansion for f(b) about f(a) dn up Tup Repeat this entire procedure to extend the representation for f(b) to obtain the third term in the Taylor series expansion and thus illustrate how one obtains a representation for f(b) that involves only the function and its derivatives evaluated at x=a . Keep in mind that the only mathematical tools used in this derivation are the definition of the definite integral and the rule for differentiating a product'. 5-32. A gas mixture leaves a solvent recovery unit as illustrated in Figure 5.32. The partial pressure of benzene in this stream is 80 mm Hg and the total pressure is 750 mm Hg. The volumetric analysis of the gas, on a benzene-free basis, is 15% CO,, 4% O, and the remainder is nitrogen. This gas is compressed 2 to 5 atm and cooled to 100 F. Calculate the percentage of benzene condensed in the process. Assume that CO2, 02 and N2 are insolub le in benzene, thus the liquid phase is pure benzene. 9. Stein, S.K. and Barcellos, A. 1992, Calculus and Analytic Geometry, Chapters 3 and 5, McGraw-Hill, Inc., New York.
compressor and heat exchanger 160 Chapter 5 gas in equilibrium with liquid benzene at 100 F cr wovig >4 solvent recovery unit condensed benzene Figure 5.32. Recovery-condenser system by Eq. 11 in Example 5.8.
Vapor pressure of benzene in gas mixture before compression is given as 80 mmHg.
Total pressure of the gas mixture before compression is given as 750 mmHg.
Mole fraction of benzene in the gas mixture before compression on benzene-free basis will be:
Partial preassure of Benzene Partial pressure of benzene-free gas (x3 ) initial 80 mmHg (750-80) mmHg =0.12
This can also be written as:
Moles of benzene (x3)mitaMoles of benzene-free gas Moles of benzene 0.12= Moles of benzene-free gas Moles of benzene 0.12 x (Moles of benzene-free gas)
When this gas is cooled and compressed to 100 ̊F and 5 atm (3800 mmHg) , liquid...
100 32 C 100 F = 1.8 =37.78 C
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