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It is proposed to react 1 t/h of a pure liquid A to a desired product B. Byproducts C and D are formed through series and parallel reactions as follows: A B k3 B D C k1= k2= k3= 0.1 min¹ Assuming an average density of 800 kg/m³, estimate the size of a mixed-flow reactor that will give the maximum yield of B. Hint: First derive the expressions for the concentration of A and B in the reactor outlet (CA and CB) as functions of reactor volume, then maximize CB/C4,0 with respect to reactor volume (C4,0 is the concentration of A at the reactor inlet).

It is proposed to react 1 t/h of a pure liquid A to a desired product B. Byproducts C and D are formed through series and parallel reactions as follows: A B k3 B D C k1= k2= k3= 0.1 min¹ Assuming an average density of 800 kg/m³, estimate the size of a mixed-flow reactor that will give the maximum yield of B. Hint: First derive the expressions for the concentration of A and B in the reactor outlet (CA and CB) as functions of reactor volume, then maximize CB/C4,0 with respect to reactor volume (C4,0 is the concentration of A at the reactor inlet).

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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It is proposed to react 1 t/h of a pure liquid A to a desired product B. Byproducts C and D are formed through series and parallel reactions as follows: A B k₁ → B D k₂ C k₁k₂k3= 0.1 min¹ Assuming an average density of 800 kg/m³, estimate the size of a mixed-flow reactor that will give the maximum yield of B. Hint: First derive the expressions for the concentration of A and B in the reactor outlet (CA and CB) as functions of reactor volume, then maximize CB/C4,0 with respect to reactor volume (C4,0 is the concentration of A at the reactor inlet).
Transcribed Image Text:It is proposed to react 1 t/h of a pure liquid A to a desired product B. Byproducts C and D are formed through series and parallel reactions as follows: A B k₁ → B D k₂ C k₁k₂k3= 0.1 min¹ Assuming an average density of 800 kg/m³, estimate the size of a mixed-flow reactor that will give the maximum yield of B. Hint: First derive the expressions for the concentration of A and B in the reactor outlet (CA and CB) as functions of reactor volume, then maximize CB/C4,0 with respect to reactor volume (C4,0 is the concentration of A at the reactor inlet).
Expert Solution
Step 1

Feed mass flow rate, MA0 = 1 t/h or 1000 kg/h

MA0 = 1000kgh×1 h60 min ⇒16.667 Kgmin

Density, ρ = 800 Kgm3

So, volumetric flow rate, v0 = MA0ρ ⇒16.667 kgmin800 kgm3⇒ 0.020834 m3min

Given reaction scheme;

A →k1 B →k2CB →k3 D

k1 = k2 = k3 = 0.1 min-1

 

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