Question

Two aqueous sulfuric acid solutions containing 20.0 wt% H2SO4 (SG=1.139) and
60.0 wt% H2SO4 (SG=1.498) are mixed to form a 4.00 molar solution (SG=1.213).
The amount of 20.0% solution fed to the process is 100 kg/h.
(a) Calculate the mass fraction of sulfuric acid in the product solution.
(b) Draw and label a flow chart for the process. Determine the number of
unknowns and the number of independent balances that can be written. Show that
you have enough information to solve the problem.
(c) Calculate the mass flow rates of the 60.0% stream and the product stream.
(d) What feed rate (in L/h) of the 60% solution would be needed to produce 1250
kg/h of the product.

Answer 1

A)

Density of product = 1.213 x 1,000 kg/m3 = 1,213 kg/m3 H2SO4 in the product = (4 mol/L x 98 g/mol x 1,000 L/m3 x 10-3 kg/g)/1,213 kg/m3 = 0.323 kg H2SO4/kg

B)

V1 = 100 kg/(1,139 kg/m3 ) = 0.0878 m3 = 87.8 L Sulfuric acid balance: 100 (0.2) + m2 (0.6) = m3 (0.323) 20 + 0.6 m2 = 0.323 m3 m2 = 0.538 m3 - 33.33 Water balance: 100 (0.8) + m2 (0.4) = m3 (1‐0.323) 80 + 0.4 m2 = 0.677 m3 80 + 0.4 (0.538 m3 - 33.33) = 0.677 m3 80 + 0.2152 m3 - 13.33 = 0.677 m3 66.67 = 0.4618 m3 m3 = 144 kg V3 = 144 kg/(1,213) kg/m3 = 118.7 m3 m2 = 0.538 (144) - 33.33 = 44.14 kg V2 = 44 kg/(1,498 kg/m3 ) = 0.0294 m3 = 29.37 L Feed ratio = 87.8 L (20% solution)/29.37 L (60% solution) = 2.99 L of 20% solution/L of 60% solution

D)

V2 = 29.4 L required to produce 144 kg of product to produce 1,250 kg of product requires (1,250 x 29.4)/144 = 255 L of 60% solution 100 kg, V1 (L), SG = 1.139 0.2 kg H2SO4/kg 0.8 kg H2O/kg m3 kg, V3 (L), SG = 1.213 4M H2SO4 (x3) m (1‐x3) kg H2O/kg 2 kg, V2 (L), SG = 1.498 0.6 kg H2SO4/kg 0.4 kg H2O/kg

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