Problem 4.9: You must neutralize 1000 gallons of acid

From Chapter 4 Problem Set. Level 3: System Integration.

Question

You must neutralize 1,000 gallons of acid cleaning solution from pH 1.0 to pH 7.0 using 100% KOH (56.1 g/mol). How many pounds of KOH are required? If the starting pH had been 2.0 instead, how many pounds would be needed? (Assume an ideal solution with no buffering).

Field Warning: Never calculate the neutralization requirement of a real acid-cleaning solution from pH alone. Determine demand through titration and add incrementally.

Answer

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At pH 1.0: [H⁺] = 0.1 mol/L. Volume: 1,000 gal × 3.785 L/gal = 3,785 L. Moles H⁺: 3,785 × 0.1 = 378.5 mol. KOH reacts 1:1, so 378.5 mol × 56.1 g/mol = 21,234 g ÷ 453.6 g/lb = 46.8 lb. At pH 2.0: [H⁺] = 0.01 mol/L. Moles: 3,785 × 0.01 = 37.85 mol. Mass: 37.85 × 56.1 = 2,123 g = 4.68 lb. One pH unit difference → 10× less chemical needed.