Checking a fertiliser label by ammonia distillation and back-titration
A fertiliser cooperative in Magway receives a 25.0 kg bag labelled 'ammonium sulphate, 21% N'. The quality officer takes a 1.20 g sample, dissolves it, and adds excess sodium hydroxide. The liberated ammonia is distilled into 50.0 cm³ of 0.500 M hydrochloric acid. The unreacted acid is then titrated with 0.250 M sodium hydroxide, requiring 28.40 cm³ to reach the methyl orange end-point. The officer must decide whether to accept the bag or reject it as adulterated. Reactions: (NH₄)₂SO₄ + 2NaOH → Na₂SO₄ + 2NH₃ + 2H₂O; NH₃ + HCl → NH₄Cl; HCl + NaOH → NaCl + H₂O. Molar masses: N = 14.0, H = 1.0, S = 32.0, O = 16.0 g mol⁻¹. The cooperative also sells urea (46% N) and ammonium nitrate (35% N), so a mislabelled bag would matter to farmers.
1. Calculate the percentage of nitrogen in the sample and compare it with the label claim.
Read the worked answer
Initial HCl: n = 0.0500 dm³ × 0.500 mol dm⁻³ = 0.02500 mol.
NaOH used: n = 0.02840 dm³ × 0.250 mol dm⁻³ = 0.00710 mol.
This NaOH neutralises the HCl left after ammonia absorption, so excess HCl = 0.00710 mol.
HCl reacted with NH₃ = 0.02500 − 0.00710 = 0.01790 mol.
From NH₃ + HCl → NH₄Cl, mol NH₃ = 0.01790 mol.
Each NH₃ contains one N: mass N = 0.01790 × 14.0 = 0.2506 g.
%N = (0.2506 / 1.20) × 100 = 20.9%.
This is very close to the 21% label, so the result supports the claim within normal experimental error.
2. Calculate the theoretical nitrogen percentage of pure ammonium sulphate and use it to estimate the purity of the sample.
Read the worked answer
Molar mass of (NH₄)₂SO₄ = 2(14.0 + 4.0) + 32.0 + 4(16.0) = 132.0 g mol⁻¹.
There are two N atoms per formula unit: mass N = 28.0 g.
Theoretical %N = (28.0 / 132.0) × 100 = 21.2%.
Estimated purity = (20.9 / 21.2) × 100 ≈ 98.6%.
So the sample is consistent with ammonium sulphate of about 98–99% purity, not a grossly adulterated material. A small negative error could come from incomplete distillation or titration error.
3. Explain why excess sodium hydroxide is used and why a back-titration is preferred to direct titration of the distilled ammonia.
Read the worked answer
Excess NaOH is needed to displace all ammonium ions as ammonia: NH₄⁺ + OH⁻ → NH₃ + H₂O. If NaOH were insufficient, some ammonium sulphate would remain in the distillation flask and the nitrogen result would be low.
A back-titration is preferred because ammonia is volatile and escapes easily; absorbing it in a known excess of standard acid traps it completely. The remaining acid is then titrated with standard alkali. Direct titration of ammonia would risk loss of NH₃ and would make the end-point less reliable.