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?
EXPERT ANSWER
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