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For the design equation for a plug flow reactor I don’t understand one of the steps. Can you please explain how FA is substituted to get the equation with dX ?

For the design equation for a plug flow reactor I don’t understand one of the steps. Can you please explain how FA is substituted to get the equation with dX ?

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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For the design equation for a plug flow reactor I don’t understand one of the steps. Can you please explain how FA is substituted to get the equation with dX ?
Со A Not secure problemsolving.engin.umich. problemsolving.engin.umich.edu/tentypes/hom rate of flow of A into the system F, (V) - Rearranging gives: Taking the limit as AV→ 0, we obtain: From the definition of conversion, FA is: Then substituting FA into the differential, we get: 4 Inserting our rate law (-rA-KCAO(1-X)) and dividing both sides by FAo. we get our PFR design equation: WC Mostly cloudy rate of flow of A out of the system rate of generation +of A by chemical reaction within the system + TAV = F, (V+AV) F(V+AV)-F (V) AV =r₁ dF =r₁ dv F₁ = FA - FAX dX -F TA dv dX_k₂CA (1-X) dV FA rate of accumulation = 0 of A within the system dN₁ dt = 0
Transcribed Image Text:Со A Not secure problemsolving.engin.umich. problemsolving.engin.umich.edu/tentypes/hom rate of flow of A into the system F, (V) - Rearranging gives: Taking the limit as AV→ 0, we obtain: From the definition of conversion, FA is: Then substituting FA into the differential, we get: 4 Inserting our rate law (-rA-KCAO(1-X)) and dividing both sides by FAo. we get our PFR design equation: WC Mostly cloudy rate of flow of A out of the system rate of generation +of A by chemical reaction within the system + TAV = F, (V+AV) F(V+AV)-F (V) AV =r₁ dF =r₁ dv F₁ = FA - FAX dX -F TA dv dX_k₂CA (1-X) dV FA rate of accumulation = 0 of A within the system dN₁ dt = 0
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