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Kjeldahl and Carius Numericals: Formulas Solved Step by Step

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Two classic quantitative methods estimate elements in organic compounds: Kjeldahl's method for nitrogen and Carius method for halogens (and sulphur). Kjeldahl converts the compound's nitrogen into ammonia, which is trapped and measured, while Carius converts halogens into silver halide precipitate, which is weighed — gravimetric analysis at its simplest.

The formulas are pure plug-and-chug once you understand where the 1.4 comes from — and nearly every board paper carries one such problem.

Key Concepts

  • Kjeldahl's method: organic compound + conc. H₂SO₄ → (NH₄)₂SO₄; then + NaOH → NH₃ distilled into a known volume of standard acid; excess acid back-titrated.
  • Carius method: organic compound + fuming HNO₃ + AgNO₃ in a sealed tube → AgX precipitate (X = Cl, Br, I); weighed to find % halogen.
  • Kjeldahl limitation: fails for nitro, azo, diazo compounds and nitrogen in rings (e.g. pyridine) — their nitrogen does not convert to ammonium sulphate.
  • Units: %N and %X are mass percentages; V = volume of acid consumed in mL; N = normality of the acid; W = sample mass in grams.

The distilled ammonia neutralises part of the standard acid (NH₃ + H⁺ → NH₄⁺); the acid consumed = total acid − back-titration volume. Key fact: 1 mL of 1 N acid ≡ 14 mg of nitrogen. In the Carius method, all halogen ends up as AgX: moles of AgX = moles of halogen in the sample.

Formulas

  • Kjeldahl: %N = (1.4 × N × V) ÷ W, where V = mL of standard acid consumed, N = normality of acid, W = sample mass in g.
  • Carius (halogen): %X = (atomic mass of X × mass of AgX × 100) ÷ (molar mass of AgX × W).
  • Carius (sulphur): %S = (32 × mass of BaSO₄ × 100) ÷ (233 × W), since sulphur is precipitated as BaSO₄.
  • Assumptions: complete conversion of N to NH₃ (Kjeldahl) and of X to AgX (Carius); no loss of volatile products.

Worked Example

Kjeldahl: 0.50 g of an organic compound gives NH₃ absorbed in 50 mL of 0.1 N H₂SO₄; the excess acid needs 20 mL of 0.1 N NaOH for back titration. Find %N. Step 1: acid consumed = 50 − 20 = 30 mL. Step 2: %N = (1.4 × 0.1 × 30) ÷ 0.50 = 4.2 ÷ 0.50 = 8.4%. Carius: 0.25 g of a compound gives 0.47 g of AgBr. Find %Br. Step 1: %Br = (80 × 0.47 × 100) ÷ (188 × 0.25). Step 2: numerator = 3760; denominator = 47. Step 3: %Br = 3760 ÷ 47 = 80.0%. So the compound is 8.4% nitrogen and the second sample is 80.0% bromine.

Common Misconceptions

  • "Kjeldahl works for every nitrogen compound." No — nitrobenzene, azo dyes and pyridine give wrong (low) results because their nitrogen resists conversion to (NH₄)₂SO₄.
  • "V in the formula is the total acid taken." Wrong — V is the acid actually consumed by ammonia, i.e. total acid minus the back-titration volume.
  • "Carius precipitate can be any silver salt." It must be the specific AgX (or BaSO₄ for sulphur) — weighing the wrong precipitate ruins the gravimetric factor.

Real-World Applications

  • Food industry: Kjeldahl nitrogen × 6.25 estimates protein content in milk, grains and animal feed.
  • Fertilizers: the nitrogen percentage of urea and ammonium salts is assayed by Kjeldahl for quality control.
  • Pharmaceuticals: Carius-type halogen estimation verifies the composition of organochlorine and organobromine drugs.

Kjeldahl turns nitrogen into measurable ammonia; Carius turns halogens into weighable silver halide. Memorise %N = 1.4NV/W, subtract the back titration, use the atomic-mass ratio for Carius.

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