A dilute aqueous solution of sulfuric acid is to be mixed with a concentrated su

Question

A dilute aqueous solution of sulfuric acid is to be mixed with a concentrated sulfuric acid aqueous solution containing 90 wt% acid. The goal is to produce a product solution with 75 wt% acid. Because the concentration and flowrate of the dilute acid input can fluctuate, the input pipeline is fitted with a flowmeter and a concentration analyzer. Based on the readings R1 (for flow) and R2 (for wt%), a valve on the pipeline for the concentrated acid can be adjusted by a technician until the reading on concentrated feed flowmeter (R3) reads a desired set point value so that the final product quality remains constant. Calibration data for the flowmeters and analyzer are shown below.

Dilute Acid Input Line Concentrated Acid Input Line Analyzer flowmeter flowmeter R v (GPM) x (wt%) R V (GPM) 1 7.81 2.45 5.26 15 86.3 8.92 79.1 173 19.3 152 35 2011 15 35.2 35 245 45 325 21 61.1 46 313 55 420 75.7 405 Using mass balances, develop a formula that relates Ra in terms of readings R1 and R2 and that a technician can use to control the valve. Assume a weighted average approximation approach for density ofmixtures

Explanation / Answer

Dilute R1 & corresponding Flow (V1) and for the same anlyser (R2) with weight % (x)

Conc flowmeter (R3) & Volume (V2) with conc. 90%

For achieving 75% dilution R3 required to be adjusted

Now for any given situation

V1.(x/100) +V2.0.9 = (V1+V2).0.75

On adjusting,

V2 (0.90 - 0.75) =V1.(0.75 - x/100)

or V2 = V1 (0.75 - x/100)(1/0.15)

or V2 = V1(5 - x/15)

Since R3 for V2, R1 for V1 and R2 for x

R3 = R1 (5 - R2/15)

So, we require to adjust R3 accordingly in order to achieve 75% conc. of the output.

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