Solved: A solution containing hydrogen peroxide with a

Chapter 10, Problem 10.1

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A solution containing hydrogen peroxide with a mass fraction xp0 (kg H2O2/kg solution) is added to a storage tank at a steady rate m_ 0kg/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_ 1kg/h becomes progressively worse. Moreover, once it is in the tank the peroxide begins to decompose at a rate rdkg/h kMp where Mpkg 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 M0 and Mp0 be the total liquid mass and mass of peroxide, respectively, in the tank at t 0, and let Mt be the total mass of liquid in the tank at any time thereafter. (a) Show that the leakage rate of hydrogen peroxide at any time is m_ 1Mp=M. (b) 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, xp0, k, M, M0, Mp, Mp0, and t.