In some laboratory analyses, the preferred technique is to dissolve a sample in an excess of acid or base and then “back-titrate” the unreacted acid or base with a standard base or acid. To assess the purity of a sample of (NH₄)₂SO₄ you dissolve a 0.475-g sample of impure (NH₄)₂SO₄ in aqueous KOH.

The NH3 liberated in the reaction is distilled from the solution into a flask containing 50.0 mL of 0.100 M HCl. The ammonia reacts with the acid to produce NH₄Cl, but not all of the HCl is used in this reaction. The amount of excess acid is determined by titrating the solution with standardized NaOH. This titration consumes 11.1 mL of 0.121 M NaOH. What is the weight percent of (NH₄)₂SO₄ in the 0.475-g sample?

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(NH4)2SO4(aq) + 2 KOH(aq) → 2 NH3(aq) + K₂SO4(aq) + 2 H₂O(l)