A forensic scientist uses thin-layer chromatography (TLC) to compare an ink sample found at a crime scene with inks from three suspect pens, labelled P, Q and R. The crime-scene ink produces two spots at distances of 3.2 cm and 5.6 cm from the baseline. The solvent front travels 8.0 cm from the baseline. Pen P produces one spot at 5.6 cm, pen Q produces spots at 3.2 cm and 5.6 cm, and pen R produces spots at 1.6 cm and 3.2 cm. Explain how the scientist can use these results to identify which pen was used at the crime scene, and justify that conclusion.

The Rf value is calculated as the distance moved by a spot divided by the distance moved by the solvent front.

For the crime‑scene ink the two spots are at 3.2 cm and 5.6 cm. The solvent front is at 8.0 cm, so

• Rf₁ = 3.2 cm ÷ 8.0 cm = 0.40
• Rf₂ = 5.6 cm ÷ 8.0 cm = 0.70

Pen Q gives spots at exactly the same distances (3.2 cm and 5.6 cm), giving the same Rf values (0.40 and 0.70). Matching Rf values under identical conditions mean the same chemical components are present.

Pen P only gives one spot at 5.6 cm (Rf = 0.70) – it lacks the component that moves 3.2 cm, so it cannot match the crime‑scene ink.

Pen R gives spots at 1.6 cm and 3.2 cm (Rf = 0.20 and 0.40). It lacks the component that moves 5.6 cm, so it also cannot match.

Therefore the crime‑scene ink matches pen Q, and the other pens can be ruled out because they do not show the same set of Rf values.