What is the maximum mass of ammonium sulfate that can be obtained from 2 kg of sulfuric acid and 1 kg of ammonia?

Question

Sulfuric acid (H₂SO₄) reacts with ammonia (NH₃) to produce the fertilizer ammonium sulfate ((NH₄)₂SO₄) according to the following equation:

H₂SO₄(aq)+2NH₃(g)→(NH₄)₂SO₄(aq)

What is the maximum mass of ammonium sulfate that can be obtained from 2 kg of sulfuric acid and 1 kg of ammonia?

Answer 1

\(H_2SO_4 (aq) + 2NH_3(g) \longrightarrow (NH_4)_2 SO_4 (aq)\)

Number of moles of \(H_2SO_4 = \frac{2000}{98} = 20.4 \,moles \)

Number of moles of \(NH_3 = \frac{1000}{17} = 58.8\, moles\)

\(\because\) 1 mole of H₂SO₄ react with 2 mole of NH₃ to form = 1 mole (NH₄)₂ SO₄

\(\therefore \) Number of moles of NH3 required to complete reaction with 20.4 mole of H₂SO₄ = 20.4 x 2 = 40.8 mole

but we have NH₃ = 58.8 mole

\(\therefore \) H₂SO₄ is a limiting reagent.

\(\therefore \) Number of moles of (NH₄)₂ SO₄ formed = 20.4 mol

\(\therefore \) Mass of (NH₄)₂ SO₄ formed = 20.4 x 132

= 2692.8 g

= 2.7 kg

Hence, maximum mass of (NH₄)₂ SO₄ can be formed = 2.7 kg.