Explanation The given isothermal reversible first order reaction is as follows. A ⇌ B The constant for the forward reaction is 0.4 h − 1 . The equilibrium constant, K e = 4.0 . The total amount of feed of A given to the plant is 100 kg/m 3 . The feed A enters at the rate of 12 m 3 /h The given volume of CSTR is 60 m 3 . The fraction that is unreacted effluent is f 1 which contains the concentration of A equals to 100 kg/m 3 . The value of product B is $ 2 per kg . The given operating costs are $ 50 per m 3 of the solution. The model for the given reaction taking place in CSTR is shown below. Figure 1 The rate law for the above mentioned reaction is given below. − r A = k [ C A − C B / K e ] (1) Where, k is the rate constant. C A is the concentration of A. C B is the concentration of B. K e is the equilibrium constant. The value of C A = C A0 ( 1 − X ) and C B = C A0 X . Where, X is the conversion. C A0 is the initial concentration of A. Substitute C A = C A0 ( 1 − X ) and C B = C A0 X in equation (1). − r A = k [ C A0 ( 1 − X ) − C A0 X / K e ] (2) The value of initial molar feed rate is calculated by the expression given below. F A0 = v 0 × C A0 Where, v 0 is the volumetric flow rate initially. Substitute C A0 = 100 kg/m 3 and v 0 = 12 m 3 /hr in equation (1). F A0 = 12 m 3 /hr × 100 kg/m 3 = 1200 kg/hr The general mole balance equation of CSTR is given below. V F Az0 = X − r A (3) Where, V is the volume of CSTR. F Az0 is the molar flow rate which equal to F A0 + C A0 f v 0 = F A0 ( 1 + f ) . X A is the conversion. − r A is the rate of disappearance of A. Substitute the values − r A = k [ C A0 ( 1 − X ) − C A0 X / K e ] and F Az0 as F A0 ( 1 + f ) . V F A0 ( 1 + f ) = X k [ C A0 ( 1 − X ) − C A0 X / K e ] Substitute the values, K e = 4.0 , k as 0.4 h − 1 , C A0 as 100 kg/m 3 , V as 60 m 3 and F A0 as 1200 kg/hr in the above equation

Elements of Chemical Reaction Engineering (5th Edition) (Prentice Hall International Series in the Physical and Chemical Engineering Sciences)

5th Edition

ISBN: 9780133887518

Author: H. Scott Fogler

Publisher: Prentice Hall

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Question

Chapter 6, Problem 6.13P

Interpretation Introduction

Interpretation:

The value of f that maximizes the operational profit of the plant is to be stated. The optimum conversion of A that is fed to the plant is to be stated.

Concept introduction:

The full form of CSTR is Continuous-Stirred Tank Reactor. This reactor has its application in the industrial processes. This reactor is actually used for liquid-phase reactions.

The conversion, X can be defined as the moles of any species A that are reacted per mole of A fed in the reactor.

Expert Solution & Answer

Chapter 6 Solutions

Elements of Chemical Reaction Engineering (5th Edition) (Prentice Hall International Series in the Physical and Chemical Engineering Sciences)

Ch. 6 - Prob. 6.3P Ch. 6 - Prob. 6.4P Ch. 6 - Prob. 6.13P

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