Chromatography

How the model works

In paper or thin-layer chromatography, a dye partitions between the stationary phase (paper) and the mobile phase (solvent). If it spends a fraction f of its time dissolved in the moving solvent, it advances at about f times the solvent speed. Its retention factor is

R_f = distance moved by spot / distance moved by solvent front ≈ 1 / (1 + K)

where K is the partition (affinity) ratio for the paper. High affinity means a low R_f; the dye lags behind.

Spots also spread as they move, by diffusion and uneven flow paths. Their width grows roughly with the square root of distance travelled, so two dyes with close R_f values may overlap. The resolution readout compares separation with spot width: values above about 1.5 mean baseline-separated spots.

The solvent front slows as it climbs: distance ∝ √t, as with capillary rise in paper.

Idealised linear partitioning, constant K, uniform paper. Dye names are illustrative; real R_f values depend on the solvent and paper used.

Guided experiments

1. Three-dye ink. Run the default mixture. Prediction: three bands, with the lowest-affinity dye at the top. R_f values stay constant as the run continues. Run the ink
2. Two similar dyes. Affinities K = 1.0 and 1.2. Prediction: R_f values of 0.50 and 0.45, too close. The spots overlap early and only separate partially near the end (resolution below 1.5). Similar dyes
3. Change the solvent. A more polar solvent halves every K. Prediction: all dyes travel further, and the gaps between their R_f values change, so a solvent change can improve separation. Polar solvent

Challenge

After a run, the solvent front is at 8.0 cm. A dye spot is centred at 3.2 cm. What is its R_f, and what affinity ratio K does that imply?

References

• OpenStax, Chemistry: Atoms First 2e, §11.5 (separation by intermolecular forces).
• Royal Society of Chemistry, “Chromatography” (Learn Chemistry practical guides).