Question

A well mixed 10m³ closed mixing tank at 18C is used to dilute 100kg/min of a 2.0% by mass NaClO₃ solution to a 0.60% solution by adding water.

Part 1) What is the mass flowrate of water into the tank needed at steady-state to accomplish this dilution?

Part 2) You notice that some gas bubbles appear in the effluent, and after some additional literature reading, hypothesize that NaCl₃ is decomposing to NaCl and O₂ inside the tank because of impurities in its walls. You do not have an oxygen detector handy and so decide to build a 0.5m³ chamber above the tank to collect all the gas generated. Initially the pressure (absolute) in this collection chamber is 760mmHg. After five minutes you measure the pressure to be 1320mmHg.

a) if your hypothesis is correct, what is the mass rate of oxygen generation?

b) assuming that the NaCl₃ solution flowing in and the NaCl₃/NaCl solution flowing out each have a density of 1.0g/mL (which will be within 1% of truth), what is the concentration (g/L) of NaCl in the effluent?

c) if a portion of water from the effluent were evaporated without any additional decomposition occuring, what would be the purity of the NaClO₃?

d) after more literature reading, you believe that the rate of  NaClO₃ decomposition is directly proportional to the molar concentration of  NaClO₃ in the tank and the tank volume, Based on this hypothesis, determine the value of the proportionality constant, thereby obtaining a general expression for the rate of  NaClO₃ decomposition.

Part 3) The dilution water has been flowing and the  NaClO₃ decomposing at steady state rate. suddenly, the valve controlling the flow of dilution water malfunctions and closes, halting its flow. assuming the densities of all the solutions are approximately the same, how much time passes before the concentration of  NaClO₃ in the effluent exceeds 1%?

Answer 1

Part 1 )

100 kg/min of 2.0% by mass NaClO3 solution

                               ↓   add water

                     0.60% solution

Let mass of NaCl03 = x

Then x = 2/100 *100 kg   =   2 kg   ie. 2 kg NaClO3 + 98 lg water

     again x = O.60/100* 100   = 0.6 kg of water + 99.4 kg water

So mass flow of water = 99.4 - 98   = 1.4 kg of water / 5 minute = 1.4/5 = 0.28 kg of water/minute

Part 2 )

a)

2NaClO3    → 2 NaCl + 3O2 (inside tank)

   2                    2           3     mole ratio

2( 23+35.5+48)   2(23+35.5)     3*32    weight ratio

213                     117               96

P1 = 760 mm   P2 = 1320 mm , V1   = 0.5 m^3

mass flow = 100 kg/minute

so total flow in 5 minutes = 100*5 = 500 kg

    NaClO3        O2

    213            96     weight ratio

      500*0.60/100 =3    (96/213)*3 = 1.3521 kg = 1.3521*22.4*1000/32 = 946 .46 litres

b)

density = 1.0 g /ml

NaClO3       NaCl

213             117

    3           (117/213) * 3 = 152.60*1000g/L ±1%

c)

Purity of NaClO3 = (1.353 /3 ) *100 = 45.100%

d)   NaClO3  

r   = k (conc of NaClO3)   = 1.353/ (5*60)   =k*3

So k = 1.353 /(3*5*60) = 1.50