Elementary Principles of Chemical Processes, Binder Ready Version
Elementary Principles of Chemical Processes, Binder Ready Version
4th Edition
ISBN: 9781118431221
Author: Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher: WILEY
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Chapter 10, Problem 10.1P

A solution containing hydrogen peroxide with a mass fraction . x p 0 ( k g H 2 O 2 / k g s o l u t i o n ) is added to a storage tank at a steady rate m ˙ 0 (kg/h). During this process, the liquid level reaches a corroded spot in the tank wall and a leak develops. As the filling continues, the leak rate m ˙ 0 (kg/h) becomes progressively worse. Moreover, once it is in the tank the peroxide begins to decompose at a rate

   r d ( k g / h ) = k M p

where M p (kg) is the mass of peroxide in the tank. The tank contents are well mixed, so that the peroxide concentration is the same at all positions. At a time t = 0 the liquid level reaches the corroded spot. Let M 0 and M P 0 be the total liquid mass and mass of peroxide, respectively, in the tank at t = 0, and let M(t) be the total mass of liquid in the tank at any time thereafter.

Show' that the leakage rate of hydrogen peroxide at any time is m ˙ 1 M P / M .

  1. Write differential balances on the total tank contents and on the peroxide in the tank, and provide initial conditions. Your solution should involve only the quantities m ˙ 0 , m ˙ 1 , x p 0 , k, M, M 0 , M P , M P 0 , and t.

Expert Solution
Check Mark
Interpretation Introduction

(a)

Interpretation:

Prove that leakage rate of hydrogen peroxide at any time is m1Mp/M.

Concept introduction:

The General Balance Equation is given as:

Accumulation = Input − Output + Generation − Consumption

Answer to Problem 10.1P

Leakagerate=m1Mp/M

Explanation of Solution

The peroxide mass fraction in the liquid equals that in the contents of the tank. We can write the following equation,

xp=MPM

Where M is the mass of all the contents in the tank.

The leakage rate of the hydrogen peroxide is given by the product of the peroxide mass fraction and the leak rate,

Leakagerate=m1Mp/M

Expert Solution
Check Mark
Interpretation Introduction

(b)

Interpretation:

Write differential balances on the total tank contents and on the peroxide in the tank, provide initial conditions.

Concept introduction:

The General Balance Equation is given as:

Accumulation = Input − Output + Generation − Consumption

Answer to Problem 10.1P

The derived equations are,

dMdt=m0-m1whent=0,M=M0(initialcondition)

And

dMpdt=m0xP0-m1(MPM)-kMpwhent=0,MP=MP0(initialcondition)

Explanation of Solution

The total accumulation in the tank is equal to the difference in the mass input and the mass output.

First perform mass balance as,

Accumulation=input-outputdMdt=m0-m1whent=0,M=M0(initialcondition)

Perform H2 O2 balance as,

Accumulation=input-output-consumptiondMpdt=m0xP0-m1(MPM)-kMpwhent=0,MP=MP0(initialcondition)

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