Question

2.) After the conversion above nearly reaches equilibrium, the mixture is pumped to a distillation column where form C is desired. The feed stream is 34% A, 24% B and 42% C by weight. The bottom exit stream is 10% A 20% B and 70% C, while the top exit stream only contains 20% C by weight and flows at 20 kg/hr. (a - 2 points) Arrange this information into a system of linear equations and assume the process runs at steady-state (In - Out = 0). (b - 2 points) Convert your system of equations into matrix form and use Gauss-Jordan Elimination to solve for the mass flow rates of each exit stream and the remaining composition of the top exit stream in terms of %A and %B by weight. (c - 2 points) Show that you obtain the same result using Cramer's Rule.

Answer 1

Distillate 20kg/ho D C 0.2 A ? Given data is fitted in disgram. م د B Flow of Distillete = 2018 Feed, F M N Assuming Steady state Total mazer balance: - A-0.34 B-0.24 C-0.42 A sool (9) Input output B 0-2 W co.7 Residue DtW → F-W =D = 20 e-component balance 0.42F = 0.2 * 20+ 0.7*W 10.42F -0.7W = 4 (b) Matrix form: do 0.42 -0.7 Gaur Jordan elimination method: 1 0.42 -0.7 4 final form echelon form into converting

20 Row operations are allowed R2 R2 -0.42R, 0 -0.28 ; -4.4 Rgt -2.8 20 0 15.714) Rp R+R2 0.35.714 o i 15.714 re feed flow 35.714 ks/ Residue flow = 15.714 ks/ho A - component balance: 35- 1/4* 0-3+ = IS 74* 0-4 + 20+ ZA - XA 0.5285 B - Component balance 15.714 * 0.2+ 20* 2B 35.714 *024 0.2715

(C) chamen's Rule : 4 0.42 -0.7 A х B IAI C -0.7+ 0.42= -0.28 A = 20 - A-10 4 -0.7 first is repland with constant matria Smilarly Ag =) (A2) = -4.4 10.42 4 (A) 35.714 -028 Feed rate (F) AL F = 35.714 ks/ Bottom rate (W) IAL A2) = -4.4 -0-28 Al 15.714 kg/ obtained results from Gauss Jordan elimination method has been verified with Cramer's rule matrix.

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