# A spent sulfuric acid solution is brought up to strength for a pickling process in a mixer. Spent solution at 3% sulfuric acid (by weight) is mixed with a 50% solution (by weight) to obtain the desired product concentration of 40% acid by weight. All are aqueous solutions. Determine all flowrates on the basis of 100 lbm/h of product. If the actual flow of the spent stream is 300 lbm/h, what must the flowrates of the streams be?

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A spent sulfuric acid solution is brought up to strength for a pickling process in a mixer. Spent solution at 3% sulfuric acid (by weight) is mixed with a 50% solution (by weight) to obtain the desired product concentration of 40% acid by weight. All are aqueous solutions. Determine all flowrates on the basis of 100 lbm/h of product. If the actual flow of the spent stream is 300 lbm/h, what must the flowrates of the streams be?

GIven:

concentration of spent solution is 3%

This is mixed with 50% Sulphuric acid

Product has 40% concentration of Sulfuric acid

Solution:

Basis:Take 100 lbm/hr of product as given in the question

Let flow rate of spent stream be ‘x’

and flow rate of second stream be ‘y’

Doing a total mass balance

Mass of spent stream + Mass of secon stream = Mass of product stream

x+y=100…………………..(1)

Doing a component mass balance for sulphuric acid

Mass of sulphuric acid in spent stream + Mass of Sulfuric acid in second stream = Mass of sulfuric acid in product stream

0.03x +0.5y = 0.4*100……………….(2)

From (1),y=100-x

Substituting in (2)

0.03x + 0.5(100-x) =40

50- 0.47x = 40

0.47x=10

x=21.28 lbm/hour

y=100-x = 78.72 lbm/hour

Flow rate of spent stream is 21.28 lbm/hour and of second stream is 78.72 lbm/hour

If flow rate of spent stream is 300 lbm/hr and if we let flow rate of product stream be ‘z’

Total mass balance becomes

300+y=z…………….(3)

Sulfuric acid mass balance becomes

0.03*100 +0.5y = 0.4z………..(4)

Substituting for z from (3)

3 + 0.5y =0.4(300+y)

3 + 0.5y =120 +0.4y

0.1y=117

y=1170 lbm/hour

z=300+y = 1470 lbm/hour

Flow rate of second stream is 1170 lbm/hour and of product stream is 1470 lbm/hour