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# 4a - Fundamentals of Material Balances II Outline Examples...

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Fundamentals of Material Balances II

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Examples of material balance Degree-of-freedom (DOF) analysis Independent equations General procedure for single unit MB calculation DOF analysis for multiple-unit processes Recycle & bypass Why recycle/bypass? DOF for recycle systems Outline:
Example 1 A solution contains 50% benzene, 30% toluene and 20% xylene by weight at a temperature of 100°C. The vapors are in contact with solution. Calculate the total pressure and the molar percentage compositions of the liquid and the vapor. The vapor pressure and molecular weights are as follows Components Vapor pressure at 100 ° C Mol. wt Benzene 1340 mm of Hg 78 Toluene 560 mm of Hg 92 Xylene 210 mm of Hg 106

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Solution: Basis: 100 kg of solution Molar percentage composition of liquid Constituents Amount kg Mol. Wt. Mol. Mol % Benzene 50 78 50/78 = 0.641 55.45 Toluene 30 92 30/92 = 0.326 28.20 Xylene 20 106 20/106 = 0.189 16.35 Total 100 1.156 100.00 Calculation of partial pressure By Rault’s law p = V.P. x Mol. Fraction in liquid Where p = Partial Pressure p benzene = 1340 x 0.5545 = 743.0 mm Hg p toluene = 560 x 0.2820 = 157.9 mm Hg p xylene = 210 x 0.1635 = 34.3 mm Hg Total Pressure = εp = 743.0 + 157.9 + 34.3 = 935.2 mm of Hg
Vapor composition = ure Vaporpress P y = Where y = mol. Fraction in vapor % 45 . 79 7945 . 0 2 . 935 743 = = % 88 . 16 1688 . 0 2 . 935 9 . 157 = = % 67 . 3 0367 . 0 2 . 935 3 . 34 = = y benzene = y toluene = y xylene =

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Degree-of-freedom (DOF) analysis Material balances can be very frustrating if you start attempting a question and not enough information is available Degree-of-freedom (DOF): Carried out before lengthy calculations Use the properly drawn and labelled flowchart to determine if you have enough information Steps required: Count # of unknown variables ( n var ) Count # of independent equations ( n eqn ) Determine DOF: n df = n var n eqn
Independent equations Material balances : For non-reactive process, not more than n ms independent material balance may be written n ms = # of molecular species in a process (e.g. CH 4 , O 2 ) E.g. Benzene (B) & toluene (T) enter & leave a distillation column, balances can be written on B, T, total mass, atomic C @ H, etc., but at most 2 balances would be independent.

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Energy balances (leave this until Energy Balance) Process specification (e.g. 40% of inlet leave as condensate, i.e. m 2 = 0.4 m
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4a - Fundamentals of Material Balances II Outline Examples...

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