A 1000 m3 lake is found to be contaminated with TCE (trichloroethane) that is potentially toxic to organisms. The concentration of TCE is 1.5 mg/L under steady-state conditions. Assume the lake behaves as a CSTR (completely stirred tank reactor). The decay of TCE is a first-order reaction with the rate constant of 2×10-6 s-1. If the source of TCE is closed off and the lake is to be flushed with clean water at a rate of 0.15 m3/s, how long will it take to lower the TCE concentration to 0.15 mg/L? Hint: You need to write the mass balance equation (VdC/dt=input rate-output rate-reaction rate) for this flushing (dilution) process and derive the concentration over time. The reaction rate for the first order kinetics is dC/dt= -kCV, where C is the pollutant concentration in the lake, t is the time, V is the lake water volume and k is the reaction rate constant.Group of answer choicesA. 3 hB. 4.2 hC. 5.3 hD. 6.4 h

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Answered: A 1000 m3 lake is found to be…

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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A 1000 m³ lake is found to be contaminated with TCE (trichloroethane) that is potentially toxic to organisms. The concentration of TCE is 1.5 mg/L under steady-state conditions. Assume the lake behaves as a CSTR (completely stirred tank reactor). The decay of TCE is a first-order reaction with the rate constant of 2×10^-6 s^-1. If the source of TCE is closed off and the lake is to be flushed with clean water at a rate of 0.15 m³/s, how long will it take to lower the TCE concentration to 0.15 mg/L? Hint: You need to write the mass balance equation (VdC/dt=input rate-output rate-reaction rate) for this flushing (dilution) process and derive the concentration over time. The reaction rate for the first order kinetics is dC/dt= -kCV, where C is the pollutant concentration in the lake, t is the time, V is the lake water volume and k is the reaction rate constant.

Group of answer choices

A. 3 h

B. 4.2 h

C. 5.3 h

D. 6.4 h

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